On the representation of the search region in multi-objective optimization

Given a finite set $N$ of feasible points of a multi-objective optimization (MOO) problem, the search region corresponds to the part of the objective space containing all the points that are not dominated by any point of $N$, i.e. the part of the objective space which may contain further nondominated points. In this paper, we consider a representation of the search region by a set of tight local upper bounds (in the minimization case) that can be derived from the points of $N$. Local upper bounds play an important role in methods for generating or approximating the nondominated set of an MOO problem, yet few works in the field of MOO address their efficient incremental determination. We relate this issue to the state of the art in computational geometry and provide several equivalent definitions of local upper bounds that are meaningful in MOO. We discuss the complexity of this representation in arbitrary dimension, which yields an improved upper bound on the number of solver calls in epsilon-constraint-like methods to generate the nondominated set of a discrete MOO problem. We analyze and enhance a first incremental approach which operates by eliminating redundancies among local upper bounds. We also study some properties of local upper bounds, especially concerning the issue of redundant local upper bounds, that give rise to a new incremental approach which avoids such redundancies. Finally, the complexities of the incremental approaches are compared from the theoretical and empirical points of view.Comment: 27 pages, to appear in European Journal of Operational Researc

Optimizing over the Efficient Set of a Multi-Objective Discrete Optimization Problem

Optimizing over the efficient set of a discrete multi-objective problem is a challenging issue. The main reason is that, unlike when optimizing over the feasible set, the efficient set is implicitly characterized. Therefore, methods designed for this purpose iteratively generate efficient solutions by solving appropriate single-objective problems. However, the number of efficient solutions can be quite large and the problems to be solved can be difficult practically. Thus, the challenge is both to minimize the number of iterations and to reduce the difficulty of the problems to be solved at each iteration. In this paper, a new enumeration scheme is proposed. By introducing some constraints and optimizing over projections of the search region, potentially large parts of the search space can be discarded, drastically reducing the number of iterations. Moreover, the single-objective programs to be solved can be guaranteed to be feasible, and a starting solution can be provided allowing warm start resolutions. This results in a fast algorithm that is simple to implement. Experimental computations on two standard multi-objective instance families show that our approach seems to perform significantly faster than the state of the art algorithm

Éléments techniques d'une révolution agricole au début de l'époque contemporaine

L'existence d'une révolution agricole aux XVIIIe et XIXe siècles est objet de controverses depuis un demi-siècle. Tandis que les aspects économiques, juridiques, sociaux, ont été abondamment étudiés, les contraintes agronomiques et pratiques n'ont fait l'objet que d'études rares et ponctuelles. Par l'analyse des textes agronomiques européens ­ de l'Antiquité au XIXe siècle inclus ­, des livres de raison, des récits de voyageurs, des mémoires statistiques, des documents d'archives local..

Éléments techniques d'une révolution agricole au début de l'époque contemporaine. Thèse de doctorat en histoire

L'existence d'une révolution agricole aux XVIIIe et XIXe siècles est objet de controverses depuis un demi-siècle. Tandis que les aspects économiques, juridiques, sociaux, ont été abondamment étudiés, les contraintes agronomiques et pratiques n'ont fait l'objet que d'études rares et ponctuelles. Par l'analyse des textes agronomiques européens --de l'Antiquité au XIXe siècle inclus--, des livres de raison, des récits de voyageurs, des mémoires statistiques, des documents d'archives loca..

Éléments techniques d'une révolution agricole au début de l'époque contemporaine

L'existence d'une révolution agricole aux XVIIIe et XIXe siècles est objet de controverses depuis un demi-siècle. Tandis que les aspects économiques, juridiques, sociaux, ont été abondamment étudiés, les contraintes agronomiques et pratiques n'ont fait l'objet que d'études rares et ponctuelles. Par l'analyse des textes agronomiques européens ­ de l'Antiquité au XIXe siècle inclus ­, des livres de raison, des récits de voyageurs, des mémoires statistiques, des documents d'archives local..

One-Exact Approximate Pareto Sets

Papadimitriou and Yannakakis show that the polynomial-time solvability of a certain singleobjective problem determines the class of multiobjective optimization problems that admit a polynomial-time computable $(1+\varepsilon, \dots , 1+\varepsilon)$-approximate Pareto set (also called an $\varepsilon$-Pareto set). Similarly, in this article, we characterize the class of problems having a polynomial-time computable approximate $\varepsilon$-Pareto set that is exact in one objective by the efficient solvability of an appropriate singleobjective problem. This class includes important problems such as multiobjective shortest path and spanning tree, and the approximation guarantee we provide is, in general, best possible. Furthermore, for biobjective problems from this class, we provide an algorithm that computes a one-exact $\varepsilon$-Pareto set of cardinality at most twice the cardinality of a smallest such set and show that this factor of 2 is best possible. For three or more objective functions, however, we prove that no constant-factor approximation on the size of the set can be obtained efficiently

Approximating Multiobjective Optimization Problems: How exact can you be?

It is well known that, under very weak assumptions, multiobjective optimization problems admit $(1+\varepsilon,\dots,1+\varepsilon)$-approximation sets (also called $\varepsilon$-Pareto sets) of polynomial cardinality (in the size of the instance and in $\frac{1}{\varepsilon}$). While an approximation guarantee of $1+\varepsilon$ for any $\varepsilon>0$ is the best one can expect for singleobjective problems (apart from solving the problem to optimality), even better approximation guarantees than $(1+\varepsilon,\dots,1+\varepsilon)$ can be considered in the multiobjective case since the approximation might be exact in some of the objectives. Hence, in this paper, we consider partially exact approximation sets that require to approximate each feasible solution exactly, i.e., with an approximation guarantee of $1$, in some of the objectives while still obtaining a guarantee of $1+\varepsilon$ in all others. We characterize the types of polynomial-cardinality, partially exact approximation sets that are guaranteed to exist for general multiobjective optimization problems. Moreover, we study minimum-cardinality partially exact approximation sets concerning (weak) efficiency of the contained solutions and relate their cardinalities to the minimum cardinality of a $(1+\varepsilon,\dots,1+\varepsilon)$-approximation set

Comparison of immune responses in parenteral FaeG DNA primed pigs boosted orally with F4 protein or reimmunized with the DNA vaccine

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L’hygiène des vers à soie d’Olivier de Serres à Louis Pasteur

L’historien familier de la littérature dite « agronomique » se trouve fort dépourvu face à la problématique des épizooties ; la notion de contagion – vaches, moutons, chevaux – n’a pas stimulé l’intellect de nos grands auteurs modernes – Estienne et Liébault, Olivier de Serres, Liger, Rozier, etc. Les descriptions cliniques peuvent constituer des bases nosographiques, mais on ne trouve guère de mise en relation systématique des affections des animaux entre eux. C’est alors qu’en feuilletant u..