José Rui Figueira

Single row facility layout problem using a permutation-based genetic algorithm

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 towards the optimum by means of specially designed crossover and mutation operators. Such schemes led the GA to handle the SRFLP as an unconstrained optimization problem. In the computational experiments carried out with large-size instances of sizes from 60 to 80, available in the literature, the proposed GA improved several previously known best solutions.

A multiple criteria sorting method where each category is characterized by several reference actions: The Electre Tri-nC method

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 introducing only one reference action as typical of each category like in Electre Tri-C (Almeida-Dias et al., 2010). As in such a sorting method, this new sorting method is composed of two joint rules. Electre Tri-nC also fulfills a certain number of natural requirements. Additional results on the behavior of the new method are also provided in this paper, namely the ones with respect to the addition or removal of the reference actions used for characterizing a certain category. A numerical example illustrates the manner in which Electre Tri-nC can be used by a decision maker. A comparison with some related sorting procedures is presented and it allows to conclude that the new method is appropriate to deal with sorting problems.

The SMAA-PROMETHEE method

PROMETHEE methods are widely used in Multiple Criteria Decision Aiding (MCDA) to deal with real world decision making problems. In this paper, we propose to apply the Stochastic Multicriteria Acceptability Analysis (SMAA) to the family of PROMETHEE methods in order to explore the whole set of parameters compatible with some preference information provided by the Decision Maker (DM). The application of the presented methodology is described in a didactic example.

A real-integer-discrete-coded particle swarm optimization for design problems

Abstract: 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 applying some posterior decoding mechanisms, while some problem-specific integer-coded versions of PSO are proposed in others. In this article, a novel version of PSO of general form is proposed, which can work directly with real, integer and discrete variables of a problem without any conversion. Quite satisfactory performance is obtained by applying the proposed PSO to some classical mechanical design problems of different nature.

Dealing with a multiple criteria environmental problem with interaction effects between criteria through an extension of the Electre III method

In this article we compare five alternative projects for the requalification of an abandoned quarry. The starting point for this paper was a request made by a decision maker. It was not for help in making a decision as such, but rather for a comparison of different projects. In particular, we are interested in ranking the considered projects on the basis of six different criteria. An extension of the Electre III method with interactions between pairs of criteria was applied in the research. A focus group of experts (in economic evaluation, environmental engineering, and landscape ecology) was formed to be in charge of the process leading to the assignment of numerical values to the weights and interaction coefficients. We report on the way the process evolved and on the difficulties we encountered in obtaining consensual sets of values. Taking into account these difficulties, we considered other sets of weights and interaction coefficients. Our aim was also to study the impact on the final ranking of the fact that these numerical values, assigned to the parameters, were not perfectly defined. This allowed us to formulate robust conclusions which were presented to the members of the focus group.

Core problems in bi-criteria {0,1}-knapsack problems

The most efficient algorithms for solving the single-criterion {0,1}-knapsack problem are based on the core concept (i.e., based on a small number of relevant variables). But this concept is not used in problems with more than one criterion. The main purpose of this paper is to validate the existence of such a set of variables in bi-criteria {0-1}-knapsack instances. Numerical experiments were performed on five types of {0,1}-knapsack instances. The results are presented for the supported and non-supported solutions as well as for the entire set of efficient solutions. A description of an approximate and an exact method is also presented.

A real-integer-discrete-coded differential evolution

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 mechanisms. Only a limited number of works are found, in which attempts are made for developing an actual integer-coded DE. In this article, such a DE is presented which can work directly with real, integer and discrete variables of a problem without any conversion. In the computational experiments carried out with a set of test problems taken from literature, the DE improved several previously known best solutions, as well as outperformed some similar proposals in most of the cases.

Dynamic programming based algorithms for the discounted {0–1} knapsack problem

Abstract The discounted {0–1} knapsack problem (DKP) is an extension of the classical {0–1} knapsack problem (KP) that consists of selecting a set of item groups where each group includes three items and at most one of the three items can be selected. The DKP is more challenging than the KP because four choices of items in an item group diversify the selection of the items. Consequently, it is not possible to solve the DKP based on a classical definition of a core consisting of a small number of relevant variables. This paper partitions the DKP into several easier sub-problems to achieve problem reductions by imitating the core concept of the KP to derive an alternative core for the DKP. Numerical experiments with DP-based algorithms are conducted to evaluate the effectiveness of the problem partition by solving the partitioned problem and the original problem based on different types of DKP instances.

Graph partitioning by multi-objective real-valued metaheuristics: A comparative study

Abstract: 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 currently in great consideration towards different problem-domains, these are yet to be investigated widely to this problem. In this article, a novel attempt is made to investigate whether some common and established metaheuristics can directly be applied to different search spaces, instead of going through various problem-specific algorithms. For this, some mechanisms are proposed for handling the graph partitioning problem by general multi-objective real-valued genetic algorithm, differential evolution, and particle swarm optimization. Some algorithmic modifications are also proposed for improving the performances of the metaheuristics. Finally, the performances of the metaheuristics are compared in terms of their computer memory requirements, as well as their computational runtime and solution qualities based on some test cases with up to five objectives.

Benchmarking in a multiple criteria performance context: An application and a conceptual framework

Abstract This article presents a conceptual benchmarking framework which applies a multiple criteria approach to assess performance. In the process, a multiple criteria procedure is used to assess the performance of three hundred and ninety two (392) Portuguese firms. Based on the results of this procedure, a conceptual framework is devised to facilitate addressing relevant benchmarking implications. The framework is designed to provide a conceptual linkage between the performance measurement methodology and the organizational benchmarking system.