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## Publications

Publications (113)

A great majority of methods designed for Multiple Criteria Decision Aiding (MCDA) assume that all assessment criteria are considered at the same level, however, decision problems encountered in practice often impose a hierarchical structure of criteria. The hierarchy helps to decompose complex decision problems into smaller and manageable subtasks,...

In this article, we consider bi-dimensional knapsack problems with a soft constraint, i.e., a constraint for which the right-hand side is not precisely fixed or uncertain. We reformulate these problems as bi-objective knapsack problems, where the soft constraint is relaxed and interpreted as an additional objective function. In this way, a sensitiv...

Multiobjective combinatorial optimization problems are known to be hard problems for two reasons: their decision versions are often NP-complete, and they are often intractable. Apart from this general observation, are there also variants or cases of multiobjective combinatorial optimization problems that are easy and, if so, what causes them to be...

Abstract In this paper we propose an improved version of a core based algorithm for the multi-objective extension of one of the most well-known combinatorial optimization problems, the multi-dimensional knapsack problem. The original algorithm was designed only for bi-objective problems combining an extension of the core concept and a branch-and-bo...

In this paper, we deal with the bi-objective non-convex combined heat and power (CHP) planning problem. A medium and long term planning problem decomposes into thousands of single period (hourly) subproblems and dynamic constraints can usually be ignored in this context. The hourly subproblem can be formulated as a mixed integer linear programming...

The hypervolume subset selection problem consists of finding a subset, with a given cardinality k, of a set of nondominated points that maximizes the hypervolume indicator. This problem arises in selection procedures of evolutionary algorithms for multiobjective optimization, for which practically efficient algorithms are required. In this article,...

Multi-Objective Combinatorial Optimization (MOCO) problems, apart from being notoriously difficult and complex to solve in reasonable computational time, they also exhibit high levels of instability in their results in case of uncertainty, which often deviate far from optimality. In this work we propose an integrated methodology to measure and anal...

Motivated by a proposal of the local authority for improving the existing healthcare system in the Parana State in Brazil, this article presents an optimization-based model for developing a better system for patients by aggregating various health services offered in the municipalities of Parana into some microregions. The problem is formulated as a...

Many water supply systems in Brazil have serious problems related to the high index of water losses, which provokes financial and environmental impacts. This is an immediate consequence of an inadequate maintenance plan, allied to natural and budgetary constraints. In addition, in these types of problems it is commonplace to consider the opinions o...

This paper presents two new dynamic programming (DP) algorithms to find the exact Pareto frontier for the bi-objective integer knapsack problem. First, a property of the traditional DP algorithm for the multi-objective integer knapsack problem is identified. The first algorithm is developed by directly using the property. The second algorithm is a...

Inverse multi-objective combinatorial optimization consists of finding a minimal adjustment of the objective functions coefficients such that a given set of feasible solutions becomes efficient. An algorithm is proposed for rendering a given feasible solution into an efficient one. This is a simplified version of the inverse problem when the cardin...

This paper presents several methodological and algorithmic improvements over a state-of-the-art dynamic programming algorithm for solving the bi-objective {0,1} knapsack problem. The variants proposed make use of new definitions of lower and upper bounds, which allow a large number of states to be discarded. The computation of these bounds are base...

This paper deals with stability analysis in multi-objective combinatorial optimization problems. The stability radius of an efficient solution is defined as the maximal adjustment of the problem parameters such that this solution remains efficient. An algorithm based on inverse optimization is proposed to compute it. The adjustment is limited to th...

Many real-world decision-making situations possess both a discrete and combinatorial structure and involve the simultaneous consideration of conflicting objectives. Problems of this kind are in general of large size and contains several objectives to be “optimized”. Although Multiple Objective Optimization is a well-established field of research, o...

The successful application of the real-coded differential evolution (DE) to a wide range of real-valued problems has motivated researchers to investigate its potentiality to integer and discrete valued problems. In most of such works, a real-valued solution is converted into a desired integer-valued solution by applying some posterior decoding mech...

This paper deals with the multicriteria 0-1 knapsack problem (KP) with kk-min objectives (MkMIN-KP) in which the first objective is of classical sum type and the remaining objectives are kk-min objective functions. The kk-min objectives are ordinal objectives, aiming at the maximization of the kk th smallest objective coefficient in any feasible kn...

The inverse {0,1}-knapsack problem consists of finding a minimal adjustment of the profit vector such that a given feasible set of items becomes an optimal solution. In this paper, two models are considered. In the first, the adjustment is measured by the Chebyshev norm. A pseudo-polynomial time algorithm is proposed to solve it. In the second, the...

We present main characteristics of ELECTRE (ELimination Et Choix Traduisant la REalité ‐ ELimination and Choice Expressing the REality) family methods, designed for multiple criteria decision aiding. These methods use as a preference model an outranking relation on the set of actions—it is constructed in result of concordance and nondiscordance tes...

This study addresses the issue of scheduling medical treatments for resident patients in a hospital. Schedules are made daily according to the restrictions on medical equipment and physicians who are being assigned at the same time. The problem is formulated as a multi-objective binary integer programming (BIP) model. Three types of metaheuristics...

There is still a big question to the community of multi-objective optimization: how to compare effectively the performances of multi-objective stochastic optimizers? The existing metrics suffer from different drawbacks to address this question. In this article, three convergence-based M-ary cardinal metrics are proposed, based on different forms of...

This paper studies a group of basic state reduction based dynamic programming (DP) algorithms for the multi-objective 0–1 knapsack problem (MKP), which are related to the backward reduced-state DP space (BRDS) and forward reduced-state DP space (FRDS). The BRDS is widely ignored in the literature because it imposes disadvantage for the single objec...

This paper presents Electre Tri-nC, a new sorting method which takes into account several reference actions for characterizing each category. This new method gives a particular freedom to the decision maker in the co-construction decision aiding process with the analyst to characterize the set of categories, while there is no constraint for introdu...

The paper focuses on a case study of delineating census tracts (CTs) in the Census Metropolitan area of London, Ontario, Canada. The procedure for defining the actual pattern of CTs by a local committee and Statistics Canada has involved such consideration as the compactness of CTs and their population-based and area-based uniformity as well as som...

In this paper, a permutation-based genetic algorithm (GA) is applied to the NP-hard problem of arranging a number of facilities on a line with minimum cost, known as the single row facility layout problem (SRFLP). The GA individuals are obtained by using some rule-based as well as random permutations of the facilities, which are then improved towar...

The graph partitioning is usually tackled as a single-objective optimization problem. Moreover, various problem-specific versions of different algorithms are proposed for solving this integer-valued problem, thus confusing practitioners in selecting an effective algorithm for their instances. On the other hand, although various metaheuristics are c...

The successful application of particle swarm optimization (PSO) to various real-valued problems motivates to develop some integer-coded versions of PSO for working directly with integer and discrete variables of a problem. However, in most of such works, actually a real-valued solution is just converted into a desired integer-valued solution by app...

The aim of this paper is to apply an informatics tool for dealing with a medical decision aiding problem to help infertile couples to become parents, when using assisted reproduction.
A multiple criteria decision aiding method for sorting or ordinal classification problems, called Electre Tri-C, was chosen in order to assign each couple to an embry...

Within disaggregation–aggregation approach, ordinal regressionaims at inducing parameters of a preference model, for example, parameters of a value function, which represent some holistic preference comparisons of alternatives given by the Decision Maker (DM). Usually, from among many sets of parameters of a preference model representing the prefer...

In this paper, a new sorting method, following a decision aiding constructive approach, is proposed. This method is called Electre Tri-C. As a sorting method, a set of categories must be defined to represent the way in which the actions that are going to be assigned to each of them should further be processed. This method is appropriate to deal wit...

http://dx.doi.org/10.1007/978-3-540-92828-7_3 We present main characteristics of ELECTRE family methods, designed for multiple criteria decision aiding. These methods use as a preference model an outranking relation in the set of actions – it is constructed in result of concordance and non-discordance tests involving a specific input preference inf...

The successful application of differential evolution(DE) algorithms to various real-valued problems encourages to develop
some integer-coded versions of DE for working directly with integer and discrete variables of a problem. However, in most
of those works, actually a real-valued solution is just converted into a desired integer-valued solution b...

Dynamic MCDM, Habitual Domains and Competence Set Analysis for Effective Decision Making in Changeable Spaces.- The Need for and Possible Methods of Objective Ranking.- Preference Function Modelling: The Mathematical Foundations of Decision Theory.- Robustness in Multi-criteria Decision Aiding.- Preference Modelling, a Matter of Degree.- Fuzzy Sets...

This paper presents an extension of the comprehensive (overall) concordance index of ELECTRE methods, which takes the interaction between criteria into account. In real-world decision-aiding situations, it is reasonable to consider only the interaction between a small number of criterion pairs. Three types of interaction have been considered: mutua...

In this paper we present a primal-dual interior-point algorithm to solve a class of multi-objective network flow problems. More precisely, our algorithm is an extension of the single-objective primal-dual infeasible and inexact interior point method for multi-objective linear network flow problems. A comparison with standard interior point methods...

We present a method called Generalized Regression with Intensities of Preference (GRIP) for ranking a finite set of actions evaluated on multiple criteria. GRIP builds a set of additive value functions compatible with preference information composed of a partial preorder and required intensities of preference on a subset of actions, called referenc...

The paper by Wang and Triantaphyllou [Ranking irregularities when evaluating alternatives by using some ELECTRE methods. Omega, 2008; 36(1): 45-63] (W & T) pinpoints in an interesting way some limitations of ELECTRE II and III methods. The objective of this note is to draw the attention of the reader to a different philosophy of interpreting the re...

ELECTRE TRI is a multiple criteria decision aiding sorting method with a history of successful real-life applications. In ELECTRE TRI, values for certain parameters have to be provided. We propose a new method, SMAA-TRI, that is based on stochastic multicriteria acceptability analysis (SMAA), for analyzing the stability of such parameters. The stab...

In this chapter, we present a new interactive procedure for multiobjective optimization, which is based on the use of a set
of value functions as a preference model built by an ordinal regression method. The procedure is composed of two alternating
stages. In the first stage, a representative sample of solutions from the Pareto optimal set (or from...

On propose dans cet article une nouvelle méthode qui s’insère dans la famille Electre. Elle permet de traiter les problèmes de tri ordinaux lorsque les catégories sont définies par des actions de référence centrales et non pas des profils limites. Nous avons appelé cette nouvelle méthode Electre Tri-C. La méthode appelée jusqu’à présent Electre Tri...

Various stakeholders are increasingly interested in the potential toxicity and other risks associated with nanomaterials throughout
the different stages of a product’s life cycle (e.g., development, production, use, disposal). Risk assessment methods and
tools developed and applied to chemical and biological materials may not be readily adaptable f...

Stochastic multicriteria acceptability analysis (SMAA) comprises a family of multiple criteria decision-aiding (MCDA) methods for problems including incomplete, imprecise, and uncertain information. Methods of the family allow solving MCDA problems of various types. Even though the methods have been applied in the past in various real-life decision...

The graph partitioning problem has numerous applications in various scientific fields. It usually involves the effective partitioning of a graph into a number of disjoint sub-graphs/zones, and hence becomes a combinatorial optimization problem whose worst case complexity is NP-complete. The inadequacies of exact methods, like linear and integer pro...

In this chapter we present a new interactive procedure for multiobjective optimization, which is based on the use of a set of value functions as a preference model built by an ordinal regression method. The procedure is composed of two alternating stages. In the first stage, a representative sample of solutions from the Pareto optimal set (or from...

Districting problems are of high importance in many different fields. Multiple criteria models seem a more adequate representation of districting problems in real-world situations. Real-life decision situations are by their very nature multidimensional. This paper deals with the problem of partitioning a territory into “homogeneous” zones. Each zon...

This paper deals with the problem of inaccuracy of the solutions generated by metaheuristic approaches for combinatorial optimization bi-criteria {0, 1}-knapsack problems. A hybrid approach which combines systematic and heuristic searches is proposed to reduce that inaccuracy in the context of a scatter search method. The components of this method...

ELECTRE TRI is a multiple criteria decision aiding sorting method with a history of successful real-life applications. ELECTRE TRI requires as input several parameters, such as criteria weights, thresholds, category profiles, and lambda cutting level. We propose the SMAA-TRI method for analyzing the stability of ELECTRE TRI analysis and for derivin...

Sorting models consist in assigning alternatives evaluated on several criteria to ordered categories. To implement such models it is necessary to set the values of the preference parameters used in the model. Rather than fixing the values of these parameters directly, a usual approach is to infer these values from assignment examples provided by th...

In this paper, we present an aggregate production planning (APP) model applied to a Portuguese firm that produces construction materials. A multiple criteria mixed integer linear programming (MCMILP) model is developed with the following performance criteria: (1) maximize profit, (2) minimize late orders, and (3) minimize work force level changes....

This paper presents a scatter search (SS) based method for finding a good approximation of the non-dominated frontier for large size bi-criteria {0,1}-knapsack instances. The method follows the usual structure of SS: (1) diversification, (2) improvement, (3) reference set update, (4) subset generation, and (5) solution combination. For each compone...

Annals of Operations Research, Volume 147, Number 1 / octobre 2006. ISSN 0254-5330

The most efficient algorithms for solving the single-criterion {0,1}-knapsack problem are based on the concept of core, i.e., a small number of relevant variables. But this concept goes unnoticed when more than one criterion is taken into account. The main purpose of the paper is to check whether or not such a set of variables is present in bi-crit...

Purpose – To propose a multi-criteria approach for ranking the performance of the economic sectors of the Portuguese economy and to identify the most attractive sectors. Design/methodology/approach – A multi-criteria approach using ELECTRE III and SRF software for eliciting the weights of criteria is used to solve the ranking problem statement. Fin...

We present an overview of the current state of multiple criteria decision-making (MCDM) decision support software. Many approaches
have been proposed in the literature to solve multiple criteria decision-making problems, and there is an abundance of software
that implements these approaches. Much of the software is still quasi-experimental, develop...

This paper offers a brief and nontechnical introduction to the use of conjoint measurement in multiple criteria decision making.
The emphasis is on the, central, additive value function model. We outline its axiomatic foundations and present various possible
assessment techniques to implement it. Some extensions of this model, e.g. nonadditive mode...

We provide an introduction to the use of interactive methods in multiple objective programming. We focus on discussing the
principles to implement those methods. Our purpose is not to review existing procedures, but some examples are picked to illustrate
the main ideas behind those procedures. Furthermore, we discuss two available software systems...

Over the last three decades a large body of research in the field of ELECTRE family methods appeared. This research has been conducted by several researchers mainly in Europe. The purpose of this chapter
is to present a survey of the ELECTRE methods since their first appearance in mid-sixties, when ELECTRE I was proposed by Bernard Roy and his coll...

We present the methodology of Multiple-Criteria Decision Aiding (MCDA) based on preference modelling in terms of “if. ⋯, then ⋯” decision rules. The basic assumption of the decision rule approach is that the decision maker (DM) accepts to give preferential
information in terms of examples of decisions and looks for simple rules justifying her decis...

This chapter aims at a unified presentation of various methods of MCDA based on fuzzy measures (capacity) and fuzzy integrals,
essentially the Choquet and Sugeno integral. A first section sets the position of the problem of multicriteria decision making,
and describes the various possible scales of measurement (cardinal unipolar and bipolar, and or...

UTA methods refer to the philosophy of assessing a set of value or utility functions, assuming the axiomatic basis of MAUT
and adopting the preference disaggregation principle. UTA methodology uses linear programming techniques in order to optimally
infer additive value/utility functions, so that these functions are as consistent as possible with t...

We present our view of the state of the art in multiobjective programming. After an introduction we formulate the multiobjective
program (MOP) and define the most important solution concepts. We then summarize the properties of efficient and nondominated
sets. In Section 4 optimality conditions are reviewed. The main part of the chapter consists of...

The interaction between a complex socio-economic environment and the extremely fast pace of development of new telecommunication
technologies and services justifies the interest in using multicriteria evaluation in decision making processes associated
with several phases of network planning and design. Based on an overview of current and foreseen e...

Many MCDA models are based on essentially deterministic evaluations of the consequences of each action in terms of each criterion,
possibly subjecting final results and recommendations to a degree of sensitivity analysis. In many situations, such an approach
may be justified when the primary source of complexity in decision making relates to the mu...

MACBETH (Measuring Attractiveness by a Categorical Based Evaluation Technique) is a multicriteria decision analysis approach
that requires only qualitative judgements about differences of value to help an individual or a group quantify the relative
attractiveness of options. This chapter presents an up-to-date survey of the mathematical foundations...

In this chapter we survey several approaches to derive a recommendation from some preference models for multiple criteria
decision aid. Depending on the specificities of the decision problem, the recommendation can be a selection of the best alternatives,
a ranking of these alternatives or a sorting. We detail a sorting procedure for the assignment...