Marc Aymes

A Tale of Mediterranean Coinage

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Ever since, the term reform has functioned like a time capsule for Ottomanists dealing with the history of this period, as it seems to encompass the whole set of its key ingredients: "administrative rationalization, scientific and technological progress, market economy and monetarization, bureaucratization, centralization and individualization." What is more (and of particular importance here), the term presents yet another advantage to its users, that of "not predetermining the question of agency. Reforms may be launched by a government or by foreign powers, and different social groups may also instigate them." [START_REF] Neumann | Ottoman Provincial Towns from the Eighteenth to the Nineteenth Century: A Re-Assessement of Their Place in the Transformation of the Empire[END_REF] In other words, "reform" may be embodied in many simultaneous ways.

Profiling key protagonists often helped historians to better understand how Ottoman reform looked like. Group portraits aimed at a sociology of the "Men of the Tanzimat," as Stanford Shaw once called them. [START_REF] Shaw | Some Aspects of the Aims and Achievements of the Nineteenth-Century Ottoman Reformers[END_REF] Biographies of leading statesmen or high-profile intellectuals imparted a more personalized hue to the topic. In what follows I will be focusing on a much dimmer protagonist of reform: a man named Vaĥdetî Efendi, who served as a designer of stamps, bonds, and deeds issued at the Sublime Porte in Istanbul in the mid-nineteenth century. In 1864 he was dispatched to Paris (then to London) for a few months, with a commission to help prepare the issuance of certification stamps and bonds for the Ottoman Treasury. Three years later he stood trial in Istanbul, charged with having fraudulently kept and circulated some of the paper money he had been testing out. For this, he was sentenced to one year in prison. What is important about Vaĥdetî Efendi's coinage story is that it helps shift the emphasis from the roaring voices of key protagonists to the nondescript "little tools of knowledge" that shaped the practice of everyday reform. [START_REF] For Instance | Belgelerle Tanzimat: Osmanlı Sadrıazamlarından Âli ve Fuad Paşalarının Siyasî Vasiyyetnâmeleri[END_REF] In so doing it provides us with a blueprint for thinking of Mediterranean history as a synchronic set of technical and symbolic currencies.

[p. 170]

The Mediterranean Enfrenchised: Set Theory All things Mediterranean did not turn French-of this there is no denying. Yet Mediterranean history is never quite far from turning, to coin a word, into a Frenchise. Let us begin by pondering this rather incongruous dictum.

The phrase "French Mediterraneans" calls to mind a complex set of mare nostrum reminiscences, making it sound eerily familiar. It was not that long ago (indeed, still today, in too many cases) that students would have been taught, in Julia Clancy-Smith's terms, "that older historical narrative still structured around binaries, 'the French' or 'Muslims' and so forth," anchored in "the nation-state framework and nationalist narrative undergirding research on the modern Maghrib." [START_REF]Little Tools of Knowledge: Historical Essays on Academic and Bureaucratic Practices[END_REF] "Heading eastwards" [START_REF] Clancy-Smith | Mediterraneans: North Africa and Europe in an Age of Migration, ca. 1800-1900[END_REF] -toward countries that were once part of the Ottoman realms-does little to change this general framework, as similar binary chains of thought also applied there. In André Raymond's words, "the long French presence on the southern and eastern Mediterranean shores" helped produce a "classic concept of the Muslim city" that lumped together Aleppo, Algiers, Damascus and Fes, all subsumed into a category defined by "a morose enumeration of all those elements [they] obviously lacked." [START_REF] Bozarslan | Pourquoi Daniel Rivet est-il parti à l'Est?[END_REF] Approaches that rest on a distinction between a "center" and one or more "peripheries" have been imbued with a similar sense of dichotomy. Inasmuch as "Eurocentrism is constitutive of the geoculture of the modern world," [START_REF] Raymond | Islamic City, Arab City: Orientalist Myths and Recent Views[END_REF] the Ottoman realms have been enshrouded in a dialectic that relies on "peripheralization." [START_REF] Wallerstein | Eurocentrism and Its Avatars: The Dilemmas of Social Science[END_REF] This helps explain why textbook histories of the modern Mediterranean have given center stage to "the piecemeal incorporation or integration of the Ottoman Empire into the European economic and political orbits." [START_REF] Immanuel Wallerstein | The Incorporation of the Ottoman Empire into the World-Economy[END_REF] In the longer time frame of the nineteenth and twentieth centuries, this geometry also played out in scholarly accounts of "Middle Eastern ideas": "here were nationalisms modularly imagined; the common good, a shaky transcript of some Lockean commonweal or Benthamite utility; Pan-movements, belated emulations of the Continental counterparts." [START_REF] Doumani | Rediscovering Palestine: Merchants and Peasants in Jabal Nablus, 1700-1900[END_REF] Key to such "modular" thinking is the metaphor of "technology transfer," meaning "an 'interaction' between cultures," with the Ottoman Middle [p. 171] East standing at the receiving end of this unequal trade. [START_REF] Hamzah | The Making of the Arab Intellectual (1880-1960): Empire, Public Sphere, and the Colonial Coordinates of Selfhood[END_REF] Even today, critical reappraisals of the issue of modernity in the region often need sheathing in painstaking examinations of how not to consider (post-)Ottoman "modernization" either "incomplete" or "failed." [START_REF] Virginia | Breaking the Spell of the Baron de Tott: Reframing the Question of Military Reform in the Ottoman Empire, 1760-1830[END_REF] It can seem as if anyone seeking to understand the Mediterranean as a whole must rehearse a preliminary set theory that distinguishes between haves and have-nots.

One may certainly object that no contemporary scholar in the field would argue for the analytical purchase of such a polarized rendering, which has been thoroughly unraveled by advocates of "multiple modernities," "global" or "connected" history, and "postcolonial studies" over the past few decades. No one would argue for it, yet does this imply that none of such thinking remains at work? To quote but one example: a recent study of radical ideas and networks in the Middle East aims at "deprovincializing the Eastern Mediterranean" by "using a synchronic lens . . . to conjure up a polyvalent, polyglot, and global leftist radical movement," thus "circumventing the whole project of genealogy and decentering it from northwestern Europe." In view of its promising argument, this undertaking would appear to yield perplexing results, as the author concludes: "The appropriation of socialism and anarchism by networks of intellectuals, dramatists, and workers and their recasting, reinvention, and ultimate subversion of these two European ideologies in ways that made them appealing to local audiences sheds light on the very active participation of peripheral locals in the making of a global world." From this statement one understands that "radical" ideas were first and foremost "European," while their Cairene or Beiruti protagonists remained "peripheral" once and for all. Rather than "deprovincializing" the Eastern Mediterranean, the set theory implicitly endorsed here only helps to reprovincialize it. Furthermore, the author concedes in the following sentence that "appropriation is perhaps not the only way to think of these processes by which socialism and anarchism were indigenized." [START_REF] Iordachi | The Making of Citizenship in the Post-Ottoman Balkans: State Building, Foreign Models, and Legal-Political Transfers[END_REF] One is left wondering which other ways could be envisioned. In a similar fashion, the expectations raised by Juan Cole's criticism of the "binary opposition of Western hegemony and Middle Eastern resistance" may seem only partially fulfilled by the [p. 172] suggestion that "in order to understand colonialism we must appreciate the mutual appropriation of cultural forms by colonized and colonizer." [START_REF] Khuri-Makdisi | The Eastern Mediterranean and the Making of Global Radicalism, 1860-1914[END_REF] Even though one conceives of "appropriation" as "mutual," this notion leaves the aforementioned binary set theory undisturbed.

As it turns out, then, terminological moves do by no means entail logical shifts. Nomenclatures are easier to replace than heuristic rules. [START_REF] Cole | Napoleon's Egypt: Invading the Middle East[END_REF] Such an observation cuts across issues of periodization. Formerly, when historians narrated the "impact of the West" on the Middle East, Bonaparte's campaign to Egypt in 1798-1801 marked the symbolic terminus a quo of the story. Significantly enough, later critiques of "Eurocentric" approaches did little to alter this chronology. Consequently, Edward Said's critical theory of "Orientalism as a Western style for dominating, restructuring, and having authority over the Orient" maintained the date of 1798 as a defining moment for the nineteenth-century Mediterranean. [START_REF]The Changing Face of the Fertile Crescent in the XVIIIth Century[END_REF] However pervasive the shift in nomenclature that the Saidian critique introduced, it reasserted the watershed value of a supposedly initial French impetus. Bleu blanc rouge remained the primary colors of its historiographical heuristics. [START_REF] Said | See also Dror Ze'evi's insightful discussion in "Back to Napoleon? Thoughts on the Beginning of the Modern Era in the Middle East[END_REF] Similar patterns of long-lasting (if intermittent) recurrence apply to the idea that the nineteenth-century Ottoman experience patterned itself on "the French model." [START_REF] Edhem | Pride and Privilege: A History of Ottoman Orders, Medals, and Decorations[END_REF] To be sure, the protagonists of such a conception warn that this "model" was never without competitors, starting with its German archrival, [START_REF] In | Le Tanzimat et le modèle français: Mimétisme ou adaptation?[END_REF] and hence that it often involved an eclectic mode of "appropriation." But these caveats ultimately serve to highlight how very Frenchified the Ottomans became over the course of the nineteenth century. Recent pieces of scholarship still consider French to have been the only non-native language that, in the Ottoman Empire (and later post-Ottoman countries like the Turkish Republic), provided the means to self-representation, cultural extroversion, and social distinction. [START_REF] Ortaylı | German leverage in the Ottoman Empire[END_REF] Pushed to the extreme, this line of reasoning is self-vindicated by arguing that the French (language and people) played a determining role in "inventing" the Mediterranean. [START_REF] Römer | Herrschaft und Staat: Politische Terminologie des Osmanischen Reiches der Tanzimatzeit[END_REF] All in all, modern Mediterranean history comes down to a process of ineluctable enfranchisement, in both senses of the term. On the one hand it means that civil rights could be secured and came hand in hand (or so [p. 173] it is often assumed) with cultural extroversion; on the other it denotes a license to trade in privilege, obtained via social distinction. Since this enfranchisement of the Mediterranean has been systematically equated to a Frenchification, it ought really to be termed an enfrenchisement. In this way we get back to the idea of a "Frenchise" first suggested above. Schematic though it is, this outline points to the long-established mappings that replicate the scholarly geopolitics of "area studies" and split up the Mediterranean according to their topoi. [START_REF]L'invention scientifique de la Méditerranée: Égypte[END_REF] Recent developments in the history of circulations, transfers, or diasporas may certainly be credited with unsettling area-coded notions of agency. [START_REF] Cabanel | offers a more "archipelagic" approach to "the immaterial empire of French language" in the Mediterranean: see his "Introduction-Trois France en Méditerranée orientale: L'empire immatériel de la langue[END_REF] Yet such approaches evince a translational metaphor that tends to reintroduce the idea of incommensurable regions under a different guise: more often than not, "connection" and "encounter" are viewed as a stage subsequent to localized production. [START_REF]Les musulmans dans l'histoire de l'Europe[END_REF] In the last resort compartmentalization prevails, and with it a certain idea of the enfrenchised Mediterranean endures.

Little Currencies of Reform: The Miniaturization of Authentication

By contrast, what follows aims to put forward an approach to currencies, that is, devices produced and reproduced by the experience of circulation itself. Here, then, the Mediterranean is being approached with a focus on the "little tools" of knowledge and authority that circulate throughout. What the notion of currency aims to stress is that we are dealing with concrete abstractions endowed with a technical efficacy, a semiotic relevance, and a symbolic energy. [START_REF] Kaiser | Negotiating Transcultural Relations in the Early Modern Mediterranean: Ottoman-Venitian Encounters[END_REF] Convertible paper money is a case in point, [START_REF] Bromberger | Technologie et analyse sémantique des objets: Pour une sémiotechnologie[END_REF] yet other kinds of officially sanctioned made-forcirculation documents may be considered as well.

"Reform" indeed affected both the technical and symbolic features of administration, as its implementation often went hand in hand with a change in their material form-to begin with, on paper. Starting in the second half of the nineteenth century, administrative proceedings developed into an ever-growing paper economy of their own, where large-scale fabrication and circulation of pre-printed documents of many kinds became common. [START_REF] Davison | The First Ottoman Experiment with Paper Money[END_REF] Among these were the evrâḳ-ı ṣaḥîḥe [p. 174] (authenticated documents, lit., valid documents), a kind of stamped paper that the Istanbul authorities started implementing from the mid-1840s onward as a technique of certification and revenue raising. Except for matters involving canon law, any legal proceeding or commercial transaction was to be sanctioned (upon payment of a fixed or proportional issuance fee) by an official certificate, the "validity" of which manifested itself by the use of a specific pre-printed and embossed paper. [START_REF] Aymes | Histoire provinciale des réformes ottomanes à Chypre au XIXe siècle[END_REF] This mechanical reproducibility of the government's paper currencies, which was supplementary to the mostly calligraphic mode of sultanic rule to date, allowed bureaucrats keen on a renewed notion of state control to multiply and disembody the signs testifying to their authority. But while the authentication tool kit of government multiplied, its circulation put public finances under strain: Authenticated paper that is currently in use has been causing much complication and waste when dispatched to the provinces, which makes it impossible to keep these kinds of pieces available in all places; besides, it has been found that most of the revenues [derived from issuance fees] are being absorbed by shipping expenses, and that even when available authenticated paper is not being used when putting together bills of exchange and contracts with foreign subjects. [START_REF] Zeki | Finance ministers of the Tanzimat[END_REF] "Authenticated documents," as a means to reforming the Ottoman paper economy, thus turned out to be a costly and cumbersome tool of administration. Such difficulties forced new symbolization techniques for government's hallmarks. Rather than entrusting authentication to the document's sheet of paper itself, the Ottomans made it incumbent on stamps to perform this task:

Arrangements are being made to produce printed stamps that it would be quite feasible to deliver to all places at low cost, so that public interest ensues, and whose conception would allow to substitute them for the current documents, in accordance with the rule drafted as per the Council of Ministers' decision.

[p. 175] As with embossed and pre-printed headings, stamps could certify that the document came from a trusted official source and that issuance fees had been properly paid. They also testified to the authenticity of the document's production and to that of its "consumption." What made them more handy than previous headings is that they remained distinct from the document's sheet of paper until the final stage of issuance. Any paper near at hand could be used and become, once stamped, an authenticated document in its own right. What is more, small stamps could be circulated throughout the empire much more easily than whole paper wads. These glimpses of the micro-diplomatics of Ottoman governmental practice help make visible the kinds of "currencies" that are the focus of the present study. There is, however, more to it than can meet the eye. As it turns out, this miniaturization story closely dovetails with the set theory of the enfrenchised Mediterranean outlined earlier. To determine how this occurred, let us examine the people who originally designed these little currencies of reform.

Men of Movable Types

Starting in the 1860s, the Ottoman government commissioned draftsmen to design miniaturized means of authentication. Records indicate that among those who took charge of producing the examples above, an odd couple of travelers stands out:

Arrangements are being made to produce printed stamps that it would be quite feasible to deliver to all places at a low cost. . . . To that end it has been resolved that Mösyö Çörçîl would set off for Paris, and that Vaĥdetî Efendi, who counts among the attendants to the Office of Imperial Protocol, would accompany the [p. 176] aforementioned and provide him with assistance in the duty of engraving the molds as required, for which he would be paid twenty thousand piastres to cover his travel expenditures. The Ministry of Finance memorandum pertaining thereto has been read during a special conference meeting [of the Council of Ministers], and when inspecting and examining the drafts of the aforesaid stamps [see fig. 6.2] it appeared that nice arrangements for their use in lieu of authenticated documents would result in admirable features; meanwhile the engraving of the molds in the desired way was deemed contingent on the aforementioned efendi's travel. Assignment has therefore been sent to the aforesaid Ministry so that the aforementioned be sent to the place in question in Mösyö Çörçîl's company, and receive the above-said amount to cover for his travel expenditures. [START_REF] Osmanlı | Prime Ministership Ottoman Archives[END_REF] The currency of reform here materializes in a sequence that is familiar to scholars studying modern Mediterranean history-one [p. 177] that may be dubbed "An Ottoman in Paris." It foregrounds men of many skills, many of them still "students," whom the Sublime Porte commissioned to travel abroad (most notably to France, but also to Great Britain and Austria) to bring back technical devices that might foster the Ottoman government's "modernizing" project. [START_REF] Boa | MMS. 27/1193[END_REF] At the core of this story lies a craftsmen's tradition akin to "the practice of a grand tour-travels aimed at acquiring knowledge and experience through observation, formal studies and contact with other men of science." The question then arises as to whether "the interpretation of such practice in terms of technical and scientific dependence becomes highly relevant" with regard to the nineteenth-century Mediterranean. [START_REF] Kreiser | Étudiants ottomans en France et en Suisse (1909-1912[END_REF] Insofar as enfrenchisement remains the rule, it is quite difficult to even think about any answer that looks elsewhere. Clearly then, the "Ottoman in Paris" story line ties in with the reform-cumenfrenchisement overall set theory. [START_REF] Martykánová | [END_REF] [p. 178] Let us now take a closer look at the present episode's two protagonists. Not much is known about either of them, but a few supplementary documents may allow for some basic information about who they were, what they did, and even what they experienced. Vaĥdetî Efendi, we learn, was a ḫaṭṭâṭ (calligrapher). [START_REF]Rifa'âh Râfi' al-Ŧahŧawî's account of his travels to Paris in 1826-31, Taḫlîṣ-i ibrîz fî talḫîṣ-i Bârîz[END_REF] In 1856, while serving as a "secretary to the Office of Imperial Insignia," he (along with two others) received praise and promotions for "having deployed lustiness in the service of drafting and designing the sublime badges and imperial peace certificates to be delivered and granted to classes of officialdom, servants of the exalted sultanate and more especially officials, officers and private soldiers from the helper states." [START_REF] Boa | [END_REF] Vaĥdetî Efendi therefore reached the rütbe-i sâlise (third rank) in the hierarchy of principal Ottoman civil servants-which, as per its reorganization in 1832-33, included five different levels. Eight years on, he now "count[ed] among the attendants to the Office of Imperial Protocol," which situated him at the core of the Ottoman Palace. 37 This testifies to his ascending career as a court official. Meanwhile, his cursus honorum highlights that he was trained in the use of various writing techniques, ranging from calligraphed to printed and engraved letters-a training very similar to the one that some "intellectuals," publishers, and newspapermen could receive at about the same time, though at varying levels and in more strictly bureaucratic services. [START_REF] Zeki Pakalın | Dictionary of Ottoman historical terms and phrases[END_REF] This is how Vaĥdetî Efendi came to meet Mösyö Çörçîl, also known as Alfred Churchill. [START_REF] See | the case of Ebüzżiyâ Meĥmed Tevfîķ Beg as studied by Özgür Türesay[END_REF] The latter's father, William Churchill, was an English merchant long established in the Ottoman Empire. He first settled in Smyrna in 1815, before he moved to Istanbul in 1831 for a two-year stint as a secretary to the United States embassy. [START_REF] Boa | Lettre d'introduction de Djemil Pacha pour Mr Churchill & Vahdetti Eff.-1864[END_REF] In 1836 he was briefly involved in what became known as the "Churchill affair," when after a few days in prison for hurting a child in a hunting accident he was released under British diplomatic pressure. [START_REF]Cerîde-i Havâdis[END_REF] In compensation for such avanies (humiliations) he obtained, along with a decoration set with diamonds and a sultanic ferman (decree) granting him the right to export olive oil from the Ottoman realms, [START_REF] Koloğlu | Miyop Çörçil Olayı: Ceride-i Havadis'in Öyküsü [The myopic Churchill affair: The story of the "Minute book of news[END_REF] [p. 179] the right to publish a newspaper: this became the Cerîde-i Ḥavâdis (Minute book of news)-which his son took over upon his death in 1846. [START_REF] Boa | [END_REF] The reason for Alfred Churchill's Paris assignment was undoubtedly his expertise in letterpress printing and movable types and his prolonged experience of collaboration with the Ottoman authorities. His father had founded the Cerîde-i Ḥavâdis at a time when the Ottoman government was busy ensuring the regular publication of the official gazette Taḳvîm-i Veḳâyi' (Almanac of events). Though privately owned, his paper enjoyed the Sublime Porte's financial and technical support: types and proofreaders were employed for the design of both publications. [START_REF] Boa | MVL. 83/1666, recommendation to award the "cerîdecilik ḫiẕmeti[END_REF] It therefore is hardly surprising that the younger Churchill would contribute his expertise to the design of other printed currencies, by appointment to His Majesty the Sultan.

In many respects Alfred Churchill's features may seem to match the generic profile of the "foreign experts [who] were invited to carry out particular projects" on an occasional basis, namely, "to supply ideas on the innovation and reorganization of existing institutions, to design new ones and even to carry out the reforms." [START_REF]Cerîde-i Havâdis[END_REF] In all likelihood Churchill remained categorized an ecnebî (foreigner) in the Ottoman administrators' parlance, not least because he enjoyed legal protection from British consular authorities. 46 Still, the enduring character of his "minutekeeping" for the Ottoman state sets his business apart from occasional, freelance consultancy. As a matter of fact, this collaboration ran so deep as to be called a ḫiẕmet (service). Moreover, not only did Churchill serve the Ottoman state, but he must also have been versed in Ottoman Turkish, which gave him an insider's acquaintance of the "Ottoman way." Under such circumstances his profile could be likened to that of a generic "Ottoman," as per the tentative definition once provided by Norman Itzkowitz and Max Mote:

The term Ottoman here is used to signify those who qualified for first-class status in that society by serving the religion (being Muslim), serving the state (holding the position that gave them a state income [p. 180] and a privileged tax status), and knowing the Ottoman Way (using the Ottoman Turkish language and conforming to the manners and customs of the society that used Ottoman Turkish). 47 Clearly there is much to distinguish this ideal type from what we know of Alfred Churchill's standing. In contrast to Vaĥdetî Efendi, he was no official member of the Ottoman chancery, and to the best of our knowledge, he never "turned Turk," that is, became a Muslim. And yet, to judge by the above-quoted definition, there remains something Ottoman about him. To this extent one may conclude that the two Paris companions had several traits of "Ottomanness" in common. [START_REF]Mubadele: An Ottoman-Russian Exchange of Ambassadors[END_REF] A Portrait of the "Attendant" as a "Unique Master"

What is gained by reflecting at length on Alfred Churchill's and Vaĥdetî Efendi's profiles and roles? The payoff is the possibility of significantly altering our understanding of the "Ottoman in Paris" story line. Portraying Churchill as a "foreign expert" would almost automatically define Vaĥdetî Efendi as a typical enfrenchised Ottoman-an eternal "student" sent to Paris in the hope of coming back learned and "modern" at last. Conversely, the Ottomanization of Churchill's foreignness makes it problematic to abide by the set theory of Mediterranean enfrenchisement.

To be sure, at the time Vaĥdetî Efendi traveled to Paris he was still called a ḫalîfe (attendant)-a word that testifies to his junior status within the patronage-cum-bureaucracy Ottoman chancery system. [START_REF]Routledge, 2014), 40-52 and 114-26. With regard to debates about "Ottoman identity[END_REF] Should we then conclude that he was sent abroad to complete his education under the tutelage of "Professor" Churchill? This does not stand up to a close reading of the document excerpted above. Vaĥdetî Efendi was mandated not to learn from Churchill's towering experience but to "accompany the aforementioned and provide him with assistance" (mûmaileyhe terfîḳen). [START_REF] Pakalın | [END_REF] Since the adverb terfîḳen refers to somebody being sent "as companion, attendant, guide," the Ottoman wording makes it difficult here to decide whether Vaĥdetî Efendi joined Churchill as a mere auxiliary or actually as a guide-or maybe both, depending on how their mission was to unfold. [START_REF] Boa | MMS. 27/1193[END_REF] This is why my rendering of the previous Ottoman quotation into English had to remain deliberately [p. 181] ambiguous. Hence "we shall be careful not to interpret the presence of foreign experts, significant as it might be, automatically in terms of backwardness or dependence." 52 Similarly, there is no necessity to conclude that Churchill and Vaĥdetî Efendi simply lived out behaviors presumed by the enfrenchisement set theory. Rather, the two travelers may well have teamed up as equals.

Existing listings and biographies make clear that Vaĥdetî Efendi was no ordinary "attendant"; he was one of the finest calligraphers active at the Ottoman court in this period, better known under his full name, Meĥmed Şevķet Vaĥdetî Efendi. Born in 1833, "he became a unique master in all eighteen handwriting patterns used by Muslims," according to the earlytwentieth-century compiler Clément Huart, whose biographical sketch provides us with the most complete information to date. "The task of drawing imperial diplomas, Huart continues, was granted exclusively to him." He also penned "gilded calligraphic panels in celi style that are to be found in most mosques throughout Constantinople," including Hagia Sophia. Upon Sultan 'Abdül'azîz's accession to the throne in 1861 it was Vaĥdetî Efendi who designed his ṭuġrâ (sultanic monogram). In accordance with an imperial decree, this henceforth set the standard for the design of ṭuġrâs. Huart also mentions Vaĥdetî Efendi's travels to London and Paris. While in France, he relates, the calligrapher took due care to earn the sovereign's favor: he designed cufflinks for Emperor Napoleon III and Empress Eugénie, with their names enciphered on them, of which both were very fond. Yet his mission's key purpose, Huart stresses, was "to direct the etching and printing of postal stamps, Ottoman Bank notes and debenture bonds." [START_REF] Martykánová | [END_REF] Judging the banknotes to be "particularly remarkable," the biographer then attempts to describe them in minute detail:

At the top, under the European numbering placed on both sides, are the words "five Turkish pounds" repeated twenty times, in so fine a writing that it takes a magnifying glass to read them; on the right side these same words are written twice in oval divânî celi style, and repeated twenty times on a blue background. No calligrapher in our time has been capable of such a tour de force. [START_REF] Huart | Les calligraphes et les miniaturistes de l'Orient musulman[END_REF] [p. 182] Judging from this ex post facto record of Vaĥdetî Efendi's achievements, it is clear that he by no means played second fiddle. In particular, Huart's account shows (and other documents concur) that Paris was the prime destination of his travels, and that this "Ottoman in Paris" mission was much wider-ranging than mere stamp design. [START_REF] Huart | [END_REF] Still, this panegyric needs to be read with precaution for several reasons. What it provides is nothing but a inverted mirror image of the enfrenchisement set theory: whereas mastery was previously identified with the Westerner's expertise, and therefore presumed to rest in Alfred Churchill's hands, it now becomes the exclusive privilege of Vaĥdetî Efendi, the gifted Ottoman.

If one is to eschew the old dichotomous pattern of analysis, a different scheme of things is in order.

Now on Trial, the Enfrenchised Speaks

While meticulously compiling the list of Vaĥdetî Efendi's illustrious achievements Huart said nothing of the shameful affair the master calligrapher found himself embroiled in following his European travels. Unbeknownst to readers of eulogistic biographies, the draftsman's mission to Paris brought about a serious setback in his prestigious career. Only a couple of years after he came back to Istanbul, he was accused of misusing some documents he had designed and printed during his mission to Paris. Early in 1868 he was indicted for "daring to sell coupons of public bonds that were out of order" and was given a one-year jail sentence. 56 We learn this thanks to a few reports from within the Ottoman bureaucracy, which interestingly enough include minutes of Vaĥdetî Efendi's interrogation at the Sublime Porte. These reports provide us with precious (though ex post facto) insights into what the draftsman did, thought he did, or said he thought he did while in Paris. The enfrenchised speaks. However cautious and at times indecisive our reading remains, Vaĥdetî Efendi's trial file helps to put the enfrenchisement set theory to the test.

Let us start by quoting a few lengthy excerpts of the report summing up Vaĥdetî Efendi's case:

Certain coupons of public bonds turned out to be redundant and erroneous in numbering, so that investigations had to be carried out [p. 183] as a result. It was thus ascertained that these pieces had been circulated by Vaĥdetî Efendi, himself a mold engraver for public bonds. Once placed under arrest and trialed . . . the above-mentioned efendi admitted that being in Paris at the time when the molds were completed he took with him as a souvenir thirteen 100-pound bonds and some bits of damaged coupons among those which had been printed first for the sake of experiment, since he considered them a work of art, and that subsequent needs forced him to sell them. He pointed out that all in all fifty-four coupons were in his possession, out of which twenty-six had been detached from the thirteen mentioned bonds, whereas the other twenty-eight consisted of fragments and blank coupons.

. . . According to the summary proceedings [of the case] the above-mentioned efendi took great care over the printing of the public bonds, which he drew and had printed by official appointment to the state: each was processed five or six times through the machine tool, some two or three thousand ended up torn or mashed to pieces, others that lacked inking were torn and thrown away, so the mentioned thirteen documents and twenty-eight coupons were the most valid, and since the coupons were split into three parts he cut the surplus to a four-part format. This being done he withheld them for more than a year, as he would keep a talisman, until he changed them for money after his salary shrank. He declared that all of them remained as they came out of the machine, except for two which had Frankish and Turkish numbering that conflicted, so he rectified the French figure on the first piece and the Turkish figure on the second to make them tally. 57 The meaning and implications of this quote are analyzed in the following sections. All the same, the reference to "coupons" leads us to presume that what Vaĥdetî Efendi produced looked more like the one in figure 6.6. At the bond's bottom right corner, one may notice tiny mention which allows us to ascertain that it was issued in "Paris-Imprimerie Poitevin, Rue Damiette 2 et 4." A letter from the Ottoman embassy in Paris pertaining to Vaĥdetî Efendi's work on "mobile stamps" identifies "Monsieur Poitevin" as "the provider of the aforesaid stamps." [START_REF] Boa | 400/25, #3, round robin of the Meclis-i vâlâ-yı aḥkâm[END_REF] It therefore stands to reason, given the match of date and place, that Vaĥdetî Efendi himself contributed to designing the document above. Moreover, the facsimile is particularly helpful in making sense of the difference between "bonds" and "coupons" affirmed in the above-quoted report. The bond proper consists of the sheet's largest section, laid out in a triptych composed (from left to right) in English, Ottoman, and French. Below are the coupons themselves-the coupons of interest, that is, which could be detached one by one from the document's main body whenever the bondholder claimed repayment for his initial loan (in the present case this was to happen in biannual installments, at a 5 percent annual rate).

What Small Print, Numbers, and Slips Have to Tell

Printed on the same sheet of paper, bond and coupons are further bound together by a common numbering system. The same number appears in both Arabic and Indic numerals (for the English/French and Ottoman Turkish sections of the document, respectively). It shows up again at the bottom left corner of each and every coupon. Finally, the use of gray-tinted boxes makes clear that these numbered zones were deemed crucial to the document's validity, while signaling a concern for possible tampering. In short, this sprouting of numbers throughout each and every segment of the document testifies to the same miniaturization of authentication that was studied above. These numbers were responsible for Vaĥdetî Efendi's misfortune. It [p. 186] was because "certain coupons of public bonds turned out to be redundant and erroneous in numbering" that the draftsman ended up being indicted and put on trial. Later on, in the confession quoted above, Vaĥdetî Efendi admits that among the bonds he produced there were "two which had Frankish and Turkish numbering that conflicted, so he rectified the French figure on the first piece and the Turkish figure on the second to make them tally." [START_REF] Boa | [END_REF] This slight "rectification" is what allowed the Ottoman authorities to sniff out the draftsman's inside job and catch him red-handed.

Vaĥdetî Efendi could thus be declared guilty of "altering numbers" on official documents that were considered "the Sublime State's exclusive insignia." By tampering with paper money in such a way he clearly [p. 187] usurped the sovereign's fiduciary privileges. Judging from the correspondence, the Ottoman authorities did not feel the need to label this misdeed a "forgery."

Still, one may argue that, while in Paris, Vaĥdetî Efendi did indeed forge a bond of a different kind, and a quite distinctive one at that.

Public Bonds, Intimate Ties

There is more to Vaĥdetî Efendi's confession than a tarnished reputation. His story has a considerable bearing on our understanding of the "Ottoman in Paris" experience-hence, of the patterns of transaction that are involved in Mediterranean history.

On the face of it, the draftsman's story dovetails nicely with the concept of enfrenchisement, that is, the idea that through servile reproduction of a presumed "French model" a framework of cultural extroversion and social distinction arose that brought about the "invention" of the modern Mediterranean. To proponents of the set theory that such a concept entails, Vaĥdetî Efendi's misfortune appears to be a case in point. It appears to show how an Ottoman strove to learn from abroad yet failed to articulate imported expertise into a full-fledged technical adoption, that is, a technology. [START_REF] Boa | /25, #3[END_REF] Indeed, the draftsman fully embraced the commitment to mechanical reproduction that was involved in his Paris mission. Feverishly he attempted to reproduce the printing process until satisfied with the outcome. His exertions may thus appear symbolically to materialize the Ottomans' attempt to align their history with that of other Mediterranean empires, under the spell of belated transfer and appropriation.

Emerging from such views is the idea that all such attempts ended up failing, due to an irreducible incongruence of "cultures" between European technologies of power and their "Ottoman-in-Paris" counterparts. Vaĥdetî Efendi's treatment of debenture bonds "as [one] would keep a talisman" could well lend itself to such an interpretation, since it seems to signal a confusion of values and an unbridgeable cultural chasm. [START_REF] Cf | Innovation and Empire in Turkey: Sultan Selim III and the Modernisation of the Ottoman Navy[END_REF] By the same token, it is revelatory that a few torn slips of paper money could become "a work of art" in the draftsman's eyes. For all his mastery of the fine arts of calligraphy, and perhaps precisely because [p. 188] he was such a master, Vaĥdetî Efendi seems to have misconstrued his mission as having to do with "art," whereas its primary purpose was to provide the Ottoman administration with reliable tools of miniaturized authentication. To be sure, the draftsman also fully grasped the importance of bureaucratic technicalities, such as keeping an eye on numbers: hence his readiness to "rectify" them whenever inconsistency arose. To name this "rectification" Vaĥdetî Efendi used the word taṣḥîḥ-literally, restoring to health or authenticating-by which he meant to convey that he acted in good faith. [START_REF]For background on talismans involving a certain "science of letters[END_REF] But the Sublime Porte bureaucrats understood this move quite differently.

To them it amounted to a taġyîr (alteration) that would inevitably deprive the document of its preordained registration value, and thus showed Vaĥdetî Efendi's lack of reverence for authentication procedures.

As a matter of fact, the draftsman was less concerned about the correction of small numbers than about their consistency: in an era of technical reproducibility he looked for authenticity not in bureaucratic cross-checkability but in the aesthetic coherence of a "work of art." Trust in numbers was trivial to him; what really mattered was whether the design of the larger picture turned out successfully, the same thing that mattered most when drafting calligraphic panels for the Hagia Sophia mosque, or etching the Sultan's name on an emerald jewel. This is what one may call putting two and two together to make five. Vaĥdetî Efendi's understanding of his mission to Paris was thus more that of an artist-inresidence than of a "foreign expert." Does this mean he missed the point? And should we conclude that he remained the enfrenchised Ottoman whom many would claim he was? The ambiguities that linger on in the draftsman's account suggest something else. Vaĥdetî Efendi did choose to turn the technical specimen he had been designing into a non-reproducible unicumby calling it a "work of art," considering it a "talisman" and bringing it back to Istanbul as a "souvenir." But while withholding his precious and secret talisman, he never lost sight of its fiduciary value. If the bond could be converted into such an object of affection, so could the talisman be converted back again into the impersonal technology of paper money-which it eventually was, when "he changed [it] for money after his salary shrank." Rather [p. 189] than a sign of cultural incongruence, Vaĥdetî Efendi's play on values testifies to his sense of ambiguity and convertibility.

Last but not least, the bond the draftsman forged while in Paris differed from one of enfrenchisement inasmuch as it pledged no aping allegiance to its presumed "model." Vaĥdetî Efendi's attitude was not one of sheer technical reproduction: his confession offhandedly insists that he relished the "experimental" thrill of the production process. [START_REF]Son Altesse Fuad Pacha, Grand Vizir de l'Empire Ottoman[END_REF] This comes as a clear reminder that there is simply no such thing as ingenuous mimicry. Vaĥdetî Efendi's [p. 190] performance encapsulates both the quest for a technology of reproduction and a personal eagerness to experiment driven by singular fantasies. The "public bonds" he drafted were intimate ones indeed: made both out of duty and out of curiosity. open to circulation by no means implies that guards and patrols went off-duty. In such accounts, any understanding of historical trajectories requires that they be premised on preordained compartmentalizations, whether cultural, religious, jurisdictional, or otherwise. Thus, emphasis is laid "on connections between 'cultures' rather than the cultural conditions of connection." [START_REF] For Example | Mediterranean Borderlands: Early English Merchants in the Levant," in The Ottoman Empire: Myths, Realities, and "Black Holes[END_REF] One is therefore led to endorse the same old "production-then-circulation" sequential pattern, whereby all that circulates throughout the Mediterranean is primarily defined by its origins in one "area" or another. In sum, brokerage analysis is still invested in the kind of set theory that has been buttressing the historiography of Mediterranean enfrenchisement all along.

Forgers may be considered to resemble "brokers" at first sight, yet they critically differ.

While the latter always appear to live "in between" multiple orders or modernities without being indentured to any, the former faithfully abide by all that is legal tender. The forger's tale is one of perpetually reforming-that is, simultaneously reproducing and renewing-the authority of reigning legitimate currencies. So Vaĥdetî Efendi strove to work out a reliable system of madefor-circulation fiduciary tools. He was no loose cannon sprung from some unspecified inbetween, but a craftsman dedicated to exploring new means of aesthetic achievement while pursuing his commitment to calligraphy, and also a chancery man keen to keep pace with changing tools of certification while upholding the authenticity of his master's rule. On these two accounts he had a say in the technology of authority and could testify to the intricacy of its currencies. What he did was experiment with this intricacy: surely this implied allowing for possible conflicts between [p. 191] aesthetic and bureaucratic requirements to emerge in the process. More importantly still, given the fact that these currencies were designed to circulate as both symbols and techniques, their making could by no means be premised on an idea of compartmentalized, bounded worlds: it required devising specific cultural conditions of connection to start with, irrespective of whether this would imply connecting "cultures" in any way. That meant approaching culture as a matter of coinage, that is, of production that could only take place at the same time that circulation itself occurred.

Maybe, then, one should adopt, when thinking of Mediterranean history, a forger's scheme of things. [START_REF] Ben-Yehoyada | Transnational Political Cosmology: A Central Mediterranean Example[END_REF] In it, concomitances and interdependencies take center stage, unlike enfrenchised studies, which narrate Mediterranean history in terms of belated appropriation and mimetic transfer. In so doing one may also hope to draw up a revised chronology of the modalities of governance and change throughout the Mediterranean world, detached from the great rifts that have marked narratives of its history. Rather than in the mediating, let us approach the Mediterranean in the forging.

Fig. 6 . 1 .

 61 Fig. 6.1. Three drafts of stamps to be used for "authenticated documents." Each drawing measures about one inch in height. Courtesy of Başbakanlık Osmanlı Arşivi [Prime Ministership Ottoman Archives], Istanbul, İ.MMS. 27/1193, #2 (reverse), late B. 1280 [January 1-8, 1864].

Fig. 6 . 2 .

 62 Fig. 6.2. Detail of stamp used for "authenticated documents." Courtesy of Başbakanlık Osmanlı Arşivi, Istanbul, İ.MMS. 27/1193, #2 (reverse), late B. 1280 [January 1-8, 1864].

Fig. 6 . 4 .

 64 Fig. 6.4. Detail of Anastassiades's letter to the consul general of Russia in Istanbul. Courtesy of Başbakanlık Osmanlı Arşivi, Istanbul, ŞD. 2584/12, April 16/28, 1884.

  Understanding what "went wrong" with Vaĥdetî Efendi requires us to pursue a bit further the micro-diplomatics of Ottoman governmental practice initiated above. We need a better sense of what the "public [p. 184] bonds" the draftsman drafted and printed looked like in order to understand what prompted his indictment. While the files kept at the Ottoman archives do not provide us with a sample, other such bonds (eshâm-ı 'umûmiyye-i devlet-i 'aliyye) issued in the Ottoman realms at that time help illustrate what Vaĥdetî Efendi's work looked like. Molds mentioned in the report could have looked like the one in figure 6.5.

Fig. 6 . 5 .

 65 Fig. 6.5. Mold for an Ottoman debenture bond, undated. Courtesy of Ali Akyıldız, Osmanlı Finans Sisteminde Dönüm Noktası: Kağıt Para ve Sosyo-ekonomik Etkileri (Istanbul: Eren, 1996), xlviii.

Fig. 6 . 6 .

 66 Fig. 6.6. Ottoman debenture bond, March 18-30, 1865. Courtesy of Ali Akyıldız, Osmanlı Dönemi Tahvil ve Hisse Senetleri, "Ottoman Securities" (Istanbul: Tarih Vakfı Yurt yayınları, 2001), 309.

Conclusion: A Forger's Scheme of Things

To think about Mediterranean history, the present study weaves together two different lines of reasoning: an Ottoman paper money story on the one hand, and the historian's involvement in the Mediterranean "Frenchise" on the other. This approach highlights how the Ottoman draftsman's experiment with paper money may help unsettle the tenets of the enfrenchisement set theory.

There have been, of course, many similar or equivalent undertakings at work of late in studies of Mediterranean worlds. With the specter of "globalization" starting to haunt studies premised on regionalized topoi, the use-value of "areas" has been shaken to its foundations. As opposed to the topical and chronic regularity that an area is supposed to symbolize, accounting for the global has meant working to transcend the fixity of time and place framings. Works that question how to "mov[e] away not only from theories of territorial sovereignty but also from theories of spatialized sovereignty" have flourished. [START_REF] Boa | /25, #3[END_REF] One means to that end, in studies dealing with the Mediterranean world at large, has been an increased focus on "troublemakers"whether named translators, converts, or more generically, even, brokers-whose "intercultural prowess" overrode the area's "culture." [START_REF] Miller | Save Our State: A Decade of Writing on Jurisdiction and Sovereignty in East and West Asia[END_REF] While in many regards Vaĥdetî Efendi the draftsman may be counted among this motley crew, there also is specific historiographical relevance in further characterizing his performance. And although his misdeed never was labeled a "forgery" by the Ottoman authorities, to us this wording may become critically helpful when trying to think of the kind of disenfrenchised Mediterranean that his coinage story brings to light.

The idea of forgery conveys a sense of Janus-faced agency that brings it close to, yet sets it apart from, frameworks of "brokerage." Those historians who propose the latter approaches, mindful though they may be of the possibility of crossing or straddling boundaries, actually presuppose and perpetuate the overarching category of "boundary." [START_REF] Dakhlia | Trickster Travels' o la prodezza interculturale[END_REF] With regard to Ottoman Turkish language, I have here adhered to the transliteration system of the International Journal of Middle East Studies. Translations from all non-English sources are mine unless otherwise noted.


Marta Castilla-Gavilán

Bruno Cognie

Emilie Ragueneau

Vincent Turpin

Priscilla Decottignies

Evaluation of dried macrophytes as an alternative diet for the rearing of the sea urchin Paracentrotus lividus (Lamarck, 1816)

Keywords: Sea urchin, nutrition, Palmaria palmata, Saccharina latissima, Laminaria digitata, Grateloupia turuturu

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

The results suggest that P. lividus adults can be reared on dried macroalgae thalli without detriment to its somatic growth, especially over short periods. The low cost of feeding sea urchins with this diet could allow small shellfish farmers to diversify their production.

Key words

Sea urchin, nutrition, Palmaria palmata, Saccharina latissima, Laminaria digitata,

Grateloupia turuturu 1 Introduction

Sea urchin roe is highly regarded as a premium food: 100,000 metric tons of sea urchins are annually fished worldwide with a value of over 0.5 billion euros (FAO, 2016). In Europe, Paracentrotus lividus (Lamarck, 1816) is the most commonly consumed sea urchin [START_REF] Kelly | Sea urchin aquaculture: a review and outlook[END_REF] and its fishing has a long tradition [START_REF] Gall | La pêche de l'oursin en Bretagne[END_REF]. France is the second largest consumer of sea urchins in the world with around 1,000 metric tons per year [START_REF] Andrew | Status and management of world sea urchin fisheries[END_REF] and the third major importer of sea urchins with around 200 metric tons in 2015 (FAO, 2016). In fact, since the collapse of the French P. lividus fisheries, demand has been satisfied by increased Irish and Spanish imports [START_REF] Fernandez | Effect of different formulated diets and rearing conditions on growth parameters in the sea urchin Paracentrotus lividus[END_REF]. As a result of its high demand and market value [START_REF] Kelly | Sea urchin aquaculture: a review and outlook[END_REF], sea urchin aquaculture has been successfully developed worldwide [START_REF] Chow | Utilization of Gracilaria chilensis (Rhodophyta: Gracilariaceae) as a biofilter in the depuration of effluents from tank cultures of fish, oysters, and sea urchins[END_REF][START_REF] Cook | Co-culture of the sea urchin Paracentrotus lividus and the edible mussel Mytilus edulis L. on the west coast of Scotland, United Kingdom[END_REF][START_REF] Liu | The effect of diet type on growth and fatty-acid composition of sea urchin larvae, I. Paracentrotus lividus (Lamarck, 1816) (Echinodermata)[END_REF]. However, in

France, this activity remains anecdotal probably because farming methods are not economically sustainable for shellfish producers. P. lividus is described as a macroalgivore [START_REF] Lawrence | Sea Urchins: Biology and Ecology[END_REF] preferring different species of macrophytes depending

F o r R e v i e w O n l y
3 on its habitat, from Ireland to southern Morocco and throughout the Mediterranean sea [START_REF] Bayed | The Paracentrotus lividus populations from the northern Moroccan Atlantic coast: growth, reproduction and health condition[END_REF][START_REF] Byrne | Annual reproductive cycles of the commercial sea urchin Paracentrotus lividus from an exposed intertidal and a sheltered subtidal habitat on the west coast of Ireland[END_REF][START_REF] Sánchez-España | Gonadal growth and reproduction in the commercial sea urchin Paracentrotus lividus (Lamarck, 1816) (Echinodermata: Echinoidea) from southern Spain[END_REF]. The rearing of this species necessitates regular harvesting of fresh macroalgae and their conservation in facilities, which have a relatively high cost.

Moreover, fresh macrophytes currently used in echinoculture are not always available to farmers due to their seasonality [START_REF] Fleurence | Seaweed proteins: biochemical, nutritional aspects and potential uses[END_REF][START_REF] Lüning | Environmental and internal control of seasonal growth in seaweeds[END_REF][START_REF] Schiener | The seasonal variation in the chemical composition of the kelp species Laminaria digitata, Laminaria hyperborea, Saccharina latissima and Alaria esculenta[END_REF] and their conservation is difficult in summer due to their rapid degradation. Although P. lividus can adapt to artificial diets [START_REF] Fernandez | Effect of different formulated diets and rearing conditions on growth parameters in the sea urchin Paracentrotus lividus[END_REF], small sized shellfish producers cannot afford the high production costs of formulated feeds.

In order to promote shellfish aquaculture diversification on the northwest French coast with echinoculture, finding alternative sources of food is needed. Dried macroalgae are usually used as attractants in artificial diets [START_REF] Dworjanyn | The effect of the addition of algae feeding stimulants to artificial diets for the sea urchin Tripneustes gratilla[END_REF][START_REF] Naidoo | A comparison of various seaweed-based diets and formulated feed on growth rate of abalone in a landbased aquaculture system[END_REF], considering the dietary preference of the reared species for fresh algae (Vadas, Beal, Dowling, & Fegley, 2000;[START_REF] Vadas | Preferential feeding: An optimization strategy in sea urchins[END_REF]. With the aim of reducing costs (economically viable for small enterprises), we carried out sea urchin feeding with dried macroalgae thalli. The objective was to compare growth parameters in Paracentrotus lividus when this species is fed with the following local fresh or dry macroalgae species: Palmaria palmata, Saccharina latissima, Laminaria digitata and Grateloupia turuturu.

Materials and methods

Sea urchins

The sea urchins were reared in the Benth'Ostrea Prod aquaculture farm (Bouin, Vendée, France). Brittany, France). The individuals selected were 11 ± 0.25 mm (mean ± SD) in diameter (excluding spines) and one and a half years old at the beginning of the experiment.

Individuals were starved for 2 weeks prior the experiment to standardize their nutritional condition.

Macrophyte diets

Sea urchins were fed with four species of macroalgae in two different conditions (fresh and dry). Six different feeding treatments were studied: (1) fresh Palmaria palmata 2) fresh Saccharina latissima (diet FS), (3) dry P. palmata (diet DP), (4) dry S. latissima (diet DS), (5) dry Laminaria digitata (diet DL) and ( 6) dry Grateloupia turuturu (diet DG). These species are some of the dominant macrophytes in the intertidal zone of the study area. Macroalgae were collected every two weeks at low tide from the intertidal zone in Le Croisic (47°16'57.5''N 2°31'25.1''W, Pays de la Loire, France). They were rinsed, cleaned of epibionts and debris and stored in the dark at 8-10 °C in a filtered, oxygenated sea water until their use. Drying was carried out in a greenhouse over 24-48 h at a temperature from 25 to 30 °C.

(diet FP), (

Experimental design

The experiment was conducted in the dark, in a recirculating aquaculture system (Fig. 1) composed of two identical 150 L tanks equipped with a biofilter, over a period of 8 weeks. Seawater was aerated and maintained at 20°C, pH 8 and 37 mg/L. A 50% water exchange was carried out weekly.

In order to test the six feeding treatments in triplicate, sea urchins were placed in 18 PVC sieves of 30 cm depth, 20 cm diameter and 2 mm nylon-mesh pore. Twenty sea urchins were randomly distributed in each sieve. Three sieves were then assigned to

F o r R e v i e w
O n l y 5 each feeding treatment. For each diet type, a control sieve, devoid of sea urchins was placed in the tanks to correct for any variation of the macroalgal biomass. All sieves were randomly distributed in the tanks and their position rotated every day to avoid possible biases due to their location in the water mass.

Feeding, removal of remaining macroalgae and biometrics of sea urchins (i.e. diameter and wet weight; WW) were performed weekly. The sea urchins were fed ad libitum with the same amounts of macroalgae (WW). Fresh macroalgae were drained of excess water, wet weighed and supplied to the corresponding batches. Dried macroalgae were first rehydrated in seawater for 1h, drained, wet weighed and distributed. A sample of the same WW as the feeding ration was collected for each treatment. In order to avoid biases associated to macroalgal water content variation, macroalgal biomasses (given, remaining and control) were all estimated by their dry weight (DW) after storage at -20°C and freeze-drying.

Ingestion and absorption rates

Daily food consumption rates (DFC) and food conversion efficiencies (FCE) were calculated as follows:

DFC (g macroalgae g -1 sea urchin day -1 ) = (Fg -Fr -Fd) / (W x t)

Where Fg was the DW (g) of a given macroalgae, Fr was the DW (g) of the remaining macroalgae and Fd was the DW of the macroalgae lost by degradation. W was the WW (g) of the sea urchin and t was the time in days.

FCE (g macroalgae g -1 sea urchin weight gain) = (Fg -Fr -Fd) / (Wt -Wi)

Where Wt was the whole sea urchin WW (g) at time t and Wi was the initial whole sea urchin WW (g).

During the experiment, a high degradation of G. turuturu was observed, so its DFC and FCE could not be evaluated.

F o r R e v i e w O n l y 6 2.

Biometric parameters

Sea urchin diameter of each batch was determined every week by image analysis using ImageJ software [START_REF] Schindelin | Fiji: an open-source platform for biological-image analysis[END_REF]. The widest axis of the test (no spines) were measured. Animal batch wet weight was carried out following 5 min drying on absorbent paper.

Linear growth rate (LGR) and specific growth rate (SGR) were calculated according to the formulas (Cook & Kelly, 2007;[START_REF] Demetropoulos | Effects of nutrient enrichment and biochemical composition of diets of Palmaria mollis on growth and condition of Japanese abalone, Haliotis discus hannai and red abalone, Haliotis rufescens[END_REF][START_REF] García-Bueno | Can the European abalone Haliotis tuberculata survive on an invasive algae? A comparison of the nutritional value of the introduced 14 Grateloupia turuturu and the native Palmaria palmata, for the commercial European abalone industry[END_REF]:

LGR (mm day -1 ) = (Lt -Li) / t

where LGR was the sea urchin growth in test diameter, t was the time in days, Li was the initial test diameter (mm) and Lt the test diameter (mm) at time t.

SGR (% day -1 ) = 100 (ln Wt -ln Wi) / t where t was the time in days, Wi was the initial whole sea urchin WW (g) and Wt was the whole sea urchin WW (g) at time t.

Biochemical analyses

To characterize diet composition, samples of each fresh and rehydrated macroalgae were frozen at -20°C, freeze-dried, pooled by treatment and ground to a fine powder under liquid nitrogen. Aqueous crude extracts (CE) were obtained by homogenization of 1 g of powder in 20 ml of a phosphate buffer solution (20 mM; pH 7) and centrifugation (25 000 g, 20 min, 4 °C). Total water-soluble proteins in CE were analyzed following the bicinchoninic acid (BCA) assay [START_REF] Smith | Measurement of protein using bicinchoninic acid[END_REF] and quantified as bovine serum albumin (BSA). Total water-soluble carbohydrates in CE were analyzed according to the method of [START_REF] Dubois | Colorimetric method for determination of sugars and related substances[END_REF].

F o r R e v i e w O n l y 7
For total lipid analysis, 1 g of powder was rehydrated in 4 ml of ultrapure water. Lipids were then extracted with a mixture of dichloromethane/methanol (1:1 v/v) in a proportion sample/solvent of 1:5 (v/v) and measured gravimetrically as described by [START_REF] Bligh | A rapid method of total lipid extraction and purification[END_REF].

Statistics

Statistical analyses were performed using the SigmaPlot ® 9.0 software. Biometrics and growth parameters were compared using one-way ANOVA analysis. When normality or equal variance tests failed, a Kruskal-Wallis one way analysis of variance on ranks was performed. A posteriori multiple comparison tests were conducted between diets when significant differences (P < 0.05) were found.

For each diet, linear regressions were established between sea urchins weight and diameter. Slope and intercept comparisons were carried out between diets.

Results

Sea urchin growth

No mortality was observed in any of the diet treatments. Individual diameters and total biomass were similar at day 0 in all batches (Fig. 2 and Fig. 3). The same pattern was observed for both parameters. Significant differences between treatments were only observed from the 35 th day. Only the FP diet showed a significantly higher (P < 0.001) response compared to the other diets. There was no significant difference between the response with FS diet and the dry diets. However, biomass obtained with dry diets showed a tendency to separate from those obtained with FS diet (Fig. 3).

Somatic growth observed in all treatments showed a highly significant relationship (P < 0.001) between biomass and diameter (Fig. 4;Table 1). No difference for mean LGR was found between the studied treatments (Fig. 5a).

Significant differences were observed in mean SGR (P < 0.05): FP diet showed a significantly higher value than DP, DL and DG diets, while FS diet showed differences only in comparison to DG diet (Fig. 5b).

Daily food consumption and food conversion efficiency

Daily food consumption showed a high variability throughout the experiment within and between treatments (Fig. 6). Although not statistically supported, values tended to be higher in the first three weeks.

No significant difference was found between sea urchins mean DFC in all treatments (Fig. 5c). For mean FCE, a significant difference was observed only between FP and DL diets (Fig. 5d; P < 0.05).

Biochemical composition of diets

The same pattern was observed for water-soluble protein and carbohydrate contents: very low contents in dry diets and values for FS diet were higher compared to FP (Table 2). Regarding dried diets, DP and DG had double protein content compared to DS and DL. Carbohydrate content was twice as high in DG and three times less in DL compared to DP and DS diets.

FP and DP diets presented similar lipid contents and were half that of FS, DL and DG diets.

F o r R e v i e w O n l y 9 4 Discussion
This study is the first to test dried macroalgae thalli in sea urchin nutrition. Few studies on the use of dried macroalgae to feed abalones [START_REF] Naidoo | A comparison of various seaweed-based diets and formulated feed on growth rate of abalone in a landbased aquaculture system[END_REF] or to constitute formulated diets for fishes (Valente et al., 2006) and sea urchins [START_REF] Dworjanyn | The effect of the addition of algae feeding stimulants to artificial diets for the sea urchin Tripneustes gratilla[END_REF][START_REF] Jong-Westman | The effect of different nutrient formulations in artificial diets on gonad growth in the sea urchin Strongylocentrotus droebachiensis[END_REF] have been performed.

In our experiment, sea urchins consumed the same amounts of dried and fresh macroalgae. The weekly consumption assessment showed a high temporal variability with higher values in the first three weeks. This may be attributed to the two week starvation period prior to the experiment, indicating the ability to consume more food when it became available [START_REF] Bandolon | Evaluation of dietary feeding stimulants for the sea urchin Lytechinus variegatus[END_REF]Cook & Kelly, 2007). Along the duration of the experiment, consumption was, on average, similar in all treatments despite clear differences in the protein and carbohydrate contents between fresh and dried thalli due to rehydration of the latter. This is contradictory with previous works which found that consumption was negatively correlated to the protein content (Cook & Kelly, 2007;[START_REF] Fernandez | Nutrition of the sea urchin Paracentrotus lividus (Echinodermata: Echinoidea) fed different artificial food[END_REF][START_REF] Frantzis | Ingestion, absorption, and growth rates of Paracentrotus lividus (Echinodermata: Echinoidea) fed different macrophytes[END_REF]. As the lipid content was similar for all the diets, we hypothesize that this is also a factor regulating consumption.

Moreover, despite the loss of water-soluble compounds in dried diets, higher growth were observed for all the experimental diets compared to previous studies (Cook & Kelly, 2007;[START_REF] Fernandez | Effect of different formulated diets and rearing conditions on growth parameters in the sea urchin Paracentrotus lividus[END_REF][START_REF] Frantzis | Ingestion, absorption, and growth rates of Paracentrotus lividus (Echinodermata: Echinoidea) fed different macrophytes[END_REF][START_REF] Mccarron | Growth assessment on three size classes of the purple sea urchin Paracentrotus lividus using continuous and intermittent feeding regimes[END_REF]. In Cook & Kelly (2007), the difference could be explained by their use of older and larger animals, according to allometry relationships.

In the other studies, using animals of comparable size to ours, the use of lower nutritional value diets could be responsible of their lower growth rates. This indicates the great potential of natural diets composed of P. palmata, S. latissima, L. digitata and

F o r R e v i e w O n l y 10
G. turuturu compared to artificial food [START_REF] Fernandez | Effect of different formulated diets and rearing conditions on growth parameters in the sea urchin Paracentrotus lividus[END_REF] and other macrophytes [START_REF] Frantzis | Ingestion, absorption, and growth rates of Paracentrotus lividus (Echinodermata: Echinoidea) fed different macrophytes[END_REF][START_REF] Mccarron | Growth assessment on three size classes of the purple sea urchin Paracentrotus lividus using continuous and intermittent feeding regimes[END_REF].

Fresh macrophytes, specifically P. palmata, allowed the best growth performance, as illustrated by the biometric and SGR assessment. Their biochemical composition was in accordance with that previously published [START_REF] García-Bueno | Valorisation de la macroalgue proliférante Grateloupia turuturu dans l'élevage de l'ormeau européen Haliotis tuberculata[END_REF][START_REF] Harnedy | Extraction of protein from the macroalga Palmaria palmata[END_REF][START_REF] Jard | French Brittany macroalgae screening: Composition and methane potential for potential alternative sources of energy and products[END_REF][START_REF] Schiener | The seasonal variation in the chemical composition of the kelp species Laminaria digitata, Laminaria hyperborea, Saccharina latissima and Alaria esculenta[END_REF] and are known to best fit P. lividus nutritional requirements [START_REF] Lawrence | Sea Urchins: Biology and Ecology[END_REF]Vadas et al., 2000).

Sea urchins fed with dried diets presented similar diameters and biomass to those fed with fresh S. latissima. They also showed a mean LGR similar to sea urchins fed with fresh P. palmata. Conversion efficiencies were the same in both dried (except for L. digitata) and fresh diets. These results suggest that all the experimental diets could be used without detriment to somatic growth. They also indicate that their lipid content remained high enough after rehydration to promote growth.

Concerning G. turuturu, [START_REF] García-Bueno | Can the European abalone Haliotis tuberculata survive on an invasive algae? A comparison of the nutritional value of the introduced 14 Grateloupia turuturu and the native Palmaria palmata, for the commercial European abalone industry[END_REF] highlighted the difficulties in using fresh G. turuturu thalli in abalone aquaculture and concluded that it might be more appropriate to use in dry or powder form. In the present study, we could not evaluate the use of dried G. turuturu due to its high degradation, making its sampling and analysis impossible. However, it would be interesting, given its availability, to valorize this invasive algae [START_REF] Gavio | Grateloupia turuturu (Halymeniaceae, Rhodophyta) is the correct name of the non-native species in the Atlantic known as Grateloupia doryphora[END_REF] in the aquaculture industry. Its use as an ingredient for artificial foods has not yet been investigated.

Conclusion

We confirmed the suitability of P. palmata and fresh diets for P. lividus nutrition, but without denying the great growth performances of sea urchins when these diets are replaced with dried macroalgae. These feeds could therefore be used by farmers without Further investigations could be done on the effect of these diets on the sea urchin gonad enhancement and quality. However, for a fattening phase of the production cycle, the lower cost of feeding with natural dried algae compared to the cost of formulated diets could allow small producers to diversify their activities.

F o r R e v i

  L. digitata. Dried G. turuturu is not a suitable diet due to its rapid degradation after rehydration.

  , especially during short periods when, for example, the algal biomass is less abundant.

Fig. 1 Fig. 2

 12 Fig. 1 Experimental design. Dotted lines represent control sieves devoid of sea urchins.

Fig. 3

 3 Fig. 3 Mean biomass of sea urchins P. lividus batches fed with six different fresh or dry

Fig. 4

 4 Fig. 4 Sea urchins P. lividus biomass/diameter relationship depending on the type of

Fig. 5

 5 Fig. 5 Mean (a) linear growth rate, (b) specific growth rate, (c) daily food consumption

Fig. 6

 6 Fig. 6 Daily food consumption of sea urchins P. lividus fed with six different

  = dry P. palmata; DS = dry S. latissima; DL = dry L. digitata. Error bars represent confidence intervals (95%).

  Fig. 1

  Fig. 2

  They were obtained following fertilization carried out in April 2015 from a

	broodstock harvested in April 2013 in Port Manec'h (47°48'04.0"N 3°44'44.5"W,
	F o
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Table 1

 1 Beal, B., Dowling, T., & Fegley, J. C. (2000). Experimental field tests of natural algal diets on gonad index and quality in the green sea urchin, Equations describing relationships between weight and diameter of sea urchins P. lividus fed different experimental diets. FP = fresh P. palmata; FS = fresh S. latissima; DP = dry P. palmata; DS = dry S. latissima; DL = dry L. digitata; DG = dry G. turuturu.

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Table 2

 2 Biochemical composition (% DW) of the six experimental diets for sea urchins.

	turuturu.
		FP	FS	DP	DS	DL	DG
	Proteins	4.12	7.82	0.65	0.27	0.31	0.73
	Carbohydrates	6.80	10.29	0.78	0.71	0.25	1.35
	Lipids	1.77	3.36	1.69	2.22	3.53	3.19

FP = fresh P. palmata; FS = fresh S. latissima; DP = dry P. palmata; DS = dry S. latissima; DL = dry L. digitata; DG = dry G.

Acknowledgments

This research was supported by the TAPAS project "Tools for Assessment and Planning of Aquaculture Sustainability" funded by the EU H2020 research and innovation program under Grant Agreement No 678396. The authors wish to thank Benth'Ostrea Prod for providing the living resources. They are also grateful to J. Dumay and M.

Morançais for their assistance during biochemical analysis. Many thanks to Maygrett Maher for correcting the English of this paper.


David S Johnson

Challenge: Vehicle Routing Problems In Memory of

Why we care so much about CVRP?

 and the most basic VRP variant.

Common strategy in scientific research

Study the simplest (bust still representative!) case of a phenomenon Generalize the discoveries for more complex cases Drosophila Melanogaster

Hundreds of VRP variants

Vehicle capacities, time windows, heterogeneous fleet, multiple depots, split delivery, pickup and delivery, backhauling, optional customer service, arc routing, alternative delivery options, service levels, etc, etc

Some history [START_REF] Balinski | On an integer program for a delivery problem[END_REF] set-partitioning formulation for CVRP [Laporte and Nobert, 1983] MIP formulation with edge variables, rounded capacity cuts, and branch-and-bound [Desrochers et al., 1992] first branch-and-price [Lysgaard et al., 2004] best branch-and-cut algorithm [START_REF] Fukasawa | Robust branch-and-cut-and-price for the capacitated vehicle routing problem[END_REF] robust branch-cut-and-price [START_REF] Baldacci | An exact algorithm for the vehicle routing problem based on the set partitioning formulation with additional cuts[END_REF] enumeration technique [Jepsen et al., 2008] (non-robust) subset-row cuts [START_REF] Ii Baldacci | New route relaxation and pricing strategies for the vehicle routing problem[END_REF] ng-route relaxation [Pecin et al., 2017b] limited-memory technique, best branch-cut-and-price [START_REF] Poggi | An exact method with variable fixing for solving the generalized assignment problem[END_REF] [START_REF] Costa | Exact branch-price-and-cut algorithms for vehicle routing[END_REF]

directed graph G = (V 0 , A), V 0 = {0} ∪ V . Capacity resource Resource consumption of arc a = (i, j) ∈ A is d j , d 0 = 0. Accumulated resource consumption interval for v ∈ V 0 is [0, Q].
A set of feasible routes is modelled by set P of paths in G from node 0 to node 0 such that for each path p ∈ P each node v ∈ V is visited at most once. accumulated resource consumption for every node v visited by p is within given intervals [0, Q].

Set-partitioning formulation

Variable x a -arc a ∈ A is used in the solution or not Variable λ p -path p ∈ P is used in the solution or not h p a = 1 if and only if path p contains arc a, otherwise 0

δ -(v ) -set of arcs in A incoming to v ∈ V Min a∈A c a x a S.t. a∈δ -(v ) x a = 1, v ∈ V , Bx ≤ b, x a = p∈P h p a λ p , a ∈ A, p∈P k λ p ≤ K , x a ∈ {0, 1}, a ∈ A, λ p ∈ {0, 1}, p ∈ P.
Set-partitioning formulation

-(v ) -set of arcs in A incoming to v ∈ V Min a∈A c a x a S.t. a∈δ -(v ) x a = 1, v ∈ V , Bx ≤ b, x a = p∈P h p a λ p , a ∈ A, (π a ) p∈P k λ p ≤ K , (µ) 0 ≤ x a ≤ 1, a ∈ A, 0 ≤ λ p ≤ 1, p ∈ P.
Column and cut generation

Labeling algorithm

Every label represents a partial path starting from node 0.

Label L contains v L -last visited vertex πL -current arc reduced cost d L -current accumulated resource consumption V L -set of visited vertices Dominance Label L dominates L if v L = v L , πL ≤ πL , d L ≤ d L , V L ⊆ V L .
(any feasible completion of L is feasible for L and has larger or the same reduced cost)

Basic labeling algorithm

L = v ∈V L v -set of non-extended labels E = v ∈V E v -set of extended labels E ← ∅, L → {0, 0, 0, {0}} while L = ∅ do take a label L in L, v L = 0 or V L = ∅ L ← L \ {L}, E ← E ∪ {L} foreach v ∈ V \ V L do extend L to L along arc (v L , v ) if L is feasible and not dominated by a label in L v ∪ E v then L ← L ∪ {L } remove from L v ∪ E v all labels dominated by L return labels L in L 0 with πL < μ
Label-setting if labels are taken in a total order ≤ lex such that

L extends to L ⇒ L ≤ lex L , L dominates L ⇒ L ≤ lex L
Otherwise, it is label-correcting

Robust cutting planes and branching

Constraints of form Bx ≤ b are robust [START_REF] Pessoa | Enhanced branch-cut-and-price algorithm for heterogeneous fleet vehicle routing problems[END_REF],

i.e. their addition to the master does not change the structure of the pricing problem.

The most important robust cutting planes are Rounded Capacity Cuts (RCC) [Laporte and Nobert, 1983]:

a∈δ -(C) x a ≥ i∈C d i Q , ∀C ⊆ V .

Contents

Generic

Otherwise, it takes too much time to reimplement for every other problem variant.

Labeling algorithm enhancements

A subset of works tested on vehicle routing instances Keep track of vertices which cannot be visited instead of visited vertices in a label [START_REF] Feillet | An exact algorithm for the elementary shortest path problem with resource constraints: Application to some vehicle routing problems[END_REF] Resource discretization [START_REF] Fukasawa | Robust branch-and-cut-and-price for the capacitated vehicle routing problem[END_REF] Bi-directional search [START_REF] Righini | Symmetry helps: Bounded bi-directional dynamic programming for the elementary shortest path problem with resource constraints[END_REF] [ [START_REF] Tilk | Asymmetry matters: Dynamic half-way points in bidirectional labeling for solving shortest path problems with resource constraints faster[END_REF] "Pulse" algorithm: depth-first search and completion bounds [Lozano et al., 2016] "Bucketization" to limit the number of dominance checks [S. et al., 2017] Weakens the column generation lower bound, but keeps the BCP correct q-routes [START_REF] Christofides | Exact algorithms for the vehicle routing problem, based on spanning tree and shortest path relaxations[END_REF] k -cycle elimination [Irnich and Villeneuve, 2006] (too expensive for k ≥ 5)

ng-routes [START_REF] Ii Baldacci | New route relaxation and pricing strategies for the vehicle routing problem[END_REF] Non-elementary relaxations of the pricing problem

Weakens the column generation lower bound, but keeps the BCP correct q-routes [START_REF] Christofides | Exact algorithms for the vehicle routing problem, based on spanning tree and shortest path relaxations[END_REF] k -cycle elimination [Irnich and Villeneuve, 2006] (too expensive for k ≥ 5)

ng-routes [START_REF] Ii Baldacci | New route relaxation and pricing strategies for the vehicle routing problem[END_REF] For each vertex v ∈ V , define a memory M v of vertices which "remember" v .

If v L ∈ M v , v is removed from V L . Sets V L are smaller ⇒ stronger domination v L v Mv
Small memories (of size ≈8-10) produce a tight relaxation of elementarity constraints for most instances.

Dynamic ng-route relaxation [START_REF] Roberti | Dynamic ng-path relaxation for the delivery man problem[END_REF] Even tighter relaxation can be obtained by dynamically increasing ng-memories. Z RM -optimum value of (MP) which gives the lower bound Z inc -value of the incumbent integer solution Z pricing (a) -optimum solution value of the pricing problem solution, arc a being fixed to 1 Arc a can be removed from the graph (it cannot take part of any improving solution) if

Z RM + Z pricing (a) ≥ Z inc
Z RM -optimum value of (MP) which gives the lower bound Z inc -value of the incumbent integer solution Z pricing (a) -optimum solution value of the pricing problem solution, arc a being fixed to 1 Arc a can be removed from the graph (it cannot take part of any improving solution) if

Z RM + Z pricing (a) ≥ Z inc
A good heuristic is very important!

How we can find values Z pricing (a)?

We perform forward and backward labeling algorithms. Then for each a = (i, j), Let L i be set of forward labels at node i (v L = i) Let L j be set of backward labels at node j (v L = j)

We find a pair of compatible labels L ∈ L i and L ∈ L j :

d L + d L ≤ Q, V L ∩ V L = ∅, minimizing π L + π L Then Z pricing (a) = π L + π L + πa -µ
Subset-row cuts [Jepsen et al., 2008] Replacing variables x in set-partitioning constraints and relaxing to inequality:

a∈δ -(v ) p∈P h p a λ p ≤ 1, v ∈ V . (2) Aggregating (2) for a set C ⊂ V , |C| = 3, with multiplier 1 2 : p∈P 1 2 v ∈C a∈δ -(v ) h p a λ p ≤ 3 2 , ( 3
)
Performing Chvátal-Gomory rounding of (3):

p∈P     1 2 v ∈C a∈δ -(v ) h p a     λ p ≤ 1, 24 / 43
Subset-row cuts: example of violation

    1 2 v ∈Cη a∈δ -(v ) h p a     .
Path p passes 0 or 1 times by a vertex in C η → coefficient is 0. Path p passes 2 or 3 times by a vertex in C η → coefficient is 1, etc...

For each active cut η ∈ N we should keep binary state S L η in each label L.

Weaker dominance

Given dual values

ν η > 0, η ∈ N , L dominates L only if πL ≤ πL - η∈N : S L η >S L η ν η instead of πL ≤ πL .
Limited memory technique [Pecin et al., 2017b] For each active subset-row cut η ∈ N , define a memory M η of vertices which "remember" state S η .

If v L ∈ M η , S L η ← 0. States S L contain more zeros ⇒ stronger dominance ∈ Cη Mη v L
Limited-memory cuts are weaker than full-memory ones However, the pricing problem difficulty is much smaller Arbitrary cuts of Chvátal-Gomory rank 1 Chvátal-Gomory rounding using a vector p of multipliers:

p∈P     v ∈C a∈δ -(v ) p v h p a     λ p ≤ v ∈C p v
All best possible multiplier vectors p for Chvátal-Gomory rounding of up to 5 constraints were found by [START_REF] Pecin | Limited memory rank-1 cuts for vehicle routing problems[END_REF].

Arbitrary cuts of Chvátal-Gomory rank 1

Chvátal-Gomory rounding using a vector p of multipliers:

p∈P     v ∈C a∈δ -(v ) p v h p a     λ p ≤ v ∈C p v
All best possible multiplier vectors p for Chvátal-Gomory rounding of up to 5 constraints were found by [START_REF] Pecin | Limited memory rank-1 cuts for vehicle routing problems[END_REF].

Enumeration of elementary routes [START_REF] Baldacci | An exact algorithm for the vehicle routing problem based on the set partitioning formulation with additional cuts[END_REF] Z RM -optimum value of (MP) Z inc -value of the best known integer solution Reduced cost of λ p > Z inc -Z RM ⇒ it cannot participate in an improving solution.

We enumerate all elementary routes with reduced cost < Z inc -Z RM using a special labeling algorithm.

If enumeration is successful, add all such variables λ p to (RMP) and solve it using a MIP solver.

If number of enumerated routes is large, we create a pool of routes, and solve the pricing problem by inspection [START_REF] Contardo | A new exact algorithm for the multi-depot vehicle routing problem under capacity and route length constraints[END_REF].

Strong branching [START_REF] Røpke | Branching decisions in branch-and-cut-and-price algorithms for vehicle routing problems[END_REF]] [Pecin et al., 2017b] In branch-cut-and-price, strong branching should be multi-phase Phase 0 -choose branching candidates (both from history and "fresh" ones) Implementing such an algorithm takes months for an expert team, even if it is just an adaptation for another variant.

One would like to have a generic algorithm that could be easily customised to many variants.

Some attempts in the literature: [START_REF] Desaulniers | A Unified Framework for Deterministic Time Constrained Vehicle Routing and Crew Scheduling Problems[END_REF] [ Baldacci andMingozzi, 2009] [S. et al., 2017] Generic model used by VRPSolver

  Basic Branch-Cut-and-Price Improvement Techniques Generic BCP solver Some Results and Perspectives Modern Branch-Cut-and-Price for Vehicle Routing Non-robust Column and cut generation are interconnected Complex: not only Branch-Cut-and-Price, butStrongBranch-and-Price-and-Fix-and-Stabilize-and- Restrict-and-Cut-and-Enumerate-and-Heuristic-and-...

  Variable x a -arc a ∈ A is used in the solution or not Variable λ p -path p ∈ P is used in the solution or not h p a = 1 if and only if path p contains arc a, otherwise 0 δ

  Subset-row cuts: impact on the pricing problem Coefficient of variable λ p in cut η associated with subset C η is

		4%
			24%
	# of paths serving		30%
	at least two of these	28%
	three clients ≤ 1		16%
			40%
			48%
		16%
		2%
		4%	48%	8%
			38%	48%	18%

Table :

 : Generic solver vs. best specific algorithms on 13 problems.

Other important components

Generic BCP solver

Generic Branch-Cut-and-Price (BCP) state-of-the-art solver for Vehicle Routing Problems (VRPs) [START_REF] Pessoa | A generic exact solver for vehicle routing and related problems[END_REF].