Marc Pirlot

General local search methods

Abstract This paper is a tutorial introduction to three recent yet widely used general heuristics: Simulated Annealing, Tabu Search, and Genetic Algorithms. A relatively precise description and an example of application are provided for each of the methods, as well as a tentative evaluation and comparison from a pragmatic point of view.

Two-phases Method and Branch and Bound Procedures to Solve the Bi–objective Knapsack Problem

The classical 0–1 knapsack problem is considered with two objectives. Two methods of the “two–phases” type are developed to generate the set of efficient solutions. In the first phase, the set of supported efficient solutions is determined by optimizing a parameterized single-objective knapsack problem. Two versions are proposed for a second phase, determining the non-supported efficient solutions: both versions are Branch and Bound approaches, but one is “breadth first”, while the other is “depth first”. Extensive numerical experiments have been realized to compare the results of both methods.

Evaluation and Decision Models

1. Introduction. 2. Choosing on the basis of several opinions. 3. Building and aggregating evaluations. 4. Constructing measures. 5. Assessing competing projects. 6. Comparing on several attributes. 7. Deciding automatically. 8. Dealing with uncertainty. 9. Supporting decisions. Appendix A. Appendix B. 10. Conclusion. Bibliography. Index.

Bipolar and bivariate models in multicriteria decision analysis: Descriptive and constructive approaches

Multicriteria decision analysis studies decision problems in which the alternatives are evaluated on several dimensions or viewpoints. In the problems we consider in this article, the scales used for assessing the alternatives with respect to a viewpoint are bipolar and univariate or unipolar and bivariate. In the former case, the scale is divided in two zones by a neutral point; a positive feeling is associated to the zone above the neutral point and a negative feeling to the zone below this point. On unipolar bivariate scales, an alternative can receive both a positive evaluation and a negative evaluation, reflecting contradictory feelings or stimuli. The article discusses procedures and models that have been proposed to aggregate multicriteria evaluations when the scale of each criterion is of one of these two types. We present both a constructive view and a descriptive view on this question; the descriptive approach is concerned with characterizations of models of preference, whereas the constructive approach aims at building preferences by questioning the decision maker. We show that these views are complementary.

Evaluation and decision models with multiple criteria: Case studies

This book showcases a large variety of multiple criteria decision applications (MCDAs), presenting them in a coherent framework provided by the methodology chapters and the comments accompanying each case study. The chapters describing MCDAs invite the reader to experiment with MCDA methods and perhaps develop new variants using data from these case studies or other cases they encounter, equipping them with a broader perception of real-world problems and how to overcome them with the help of MCDAs.

ACUTA: A novel method for eliciting additive value functions on the basis of holistic preference statements

In multiple criteria decision aiding, it is common to use methods that are capable of automatically extracting a decision or evaluation model from partial information provided by the decision maker about a preference structure. In general, there is more than one possible model, leading to an indetermination which is dealt with sometimes arbitrarily in existing methods. This paper aims at filling this theoretical gap: we present a novel method, based on the computation of the analytic center of a polyhedron, for the selection of additive value functions that are compatible with holistic assessments of preferences. We demonstrate the most important characteristics of this technique with an experimental and comparative study of several existing methods belonging to the UTA family.

A characterization of concordance relations

Abstract The notion of concordance is central to many multiple criteria techniques relying on ordinal information, e.g. outranking methods. It leads to compare alternatives by pairs on the basis of a comparison of coalitions of attributes in terms of “importance”. This paper proposes a characterization of the binary relations that can be obtained using such comparisons within a general framework for conjoint measurement that allows for intransitive preferences. We show that such relations are mainly characterized by the very rough differentiation of preference differences that they induce on each attribute.

Embedding of linear programming in a simulated annealing algorithm for solving a mixed integer production planning problem

The present paper is concerned with the grouping of book covers on offset plates in order to minimize the total production cost. The mathematical formulation of the problem involves both binary and continuous variables. As exact methods are unable to provide solutions in reasonable time, a heuristic algorithm of the simulated annealing type is proposed. At each iteration, the values of the current solution binary variables are altered in order to yield a neighboring solution. To compute the corresponding values of the continuous variables and the value of the objective function, a linear programming routine is called at each iteration. This constitutes the main originality of the present approach and is in principle applicable in mixed integer programming problems. The procedure is tested on several examples.

Algorithmic Decision Theory

Judgment aggregation is a formal theory reasoning about how a group of agents can aggregate individual judgments on connected propositions into a collective judgment on the same propositions. Three procedures for successfully aggregating judgments sets are: premisebased procedure, conclusion-based procedure and distance-based merging. The conclusion-based procedure has been little investigated because it provides a way to aggregate the conclusions, but not the premises, thus it outputs an incomplete judgment set. The goal of this paper is to present a conclusion-based procedure outputting complete judgment sets.

Leximin optimality and fuzzy set-theoretic operations

Abstract The leximin ranking of vectors of values taken from a totally ordered set is sometimes encountered in fields like operational research, social choice or numerical analysis, but has seldom been studied in connexion with fuzzy optimization. In this paper we prove that a leximin-optimal solution to a vector ranking problem on the unit hypercube can be obtained as the limit of optimal solutions to a problem of fuzzy multiple criteria optimization where fuzzy sets are aggregated either using a triangular norm or a generalized mean or an ordered weighted average (OWA) operation.