Pedro M. Mateo

A new approach for solving linear bilevel problems using genetic algorithms

Bilevel programming involves two optimization problems where the constraint region of the first level problem is implicitly determined by another optimization problem. This paper develops a genetic algorithm for the linear bilevel problem in which both objective functions are linear and the common constraint region is a polyhedron. Taking into account the existence of an extreme point of the polyhedron which solves the problem, the algorithm aims to combine classical extreme point enumeration techniques with genetic search methods by associating chromosomes with extreme points of the polyhedron. The numerical results show the efficiency of the proposed algorithm. In addition, this genetic algorithm can also be used for solving quasiconcave bilevel problems provided that the second level objective function is linear.

Optimization with simulation and multiobjective analysis in industrial decision-making: A case study

Abstract In order to ensure that end of life vehicles (ELVs) are discarded without endangering the environment, appropriate collection systems should be set up. In accordance with the European Community Directive, the construction of an industrial plant for the decontamination and recycling processes of ELVs is currently being planned in Navarra (Spain). The aim of this study is to optimize the design and management of this industrial plant. We will provide a modelling framework that integrates different OR methodologies: queueing networks, optimization with simulation, evolutionary computation and multiobjective methods.

An approach for the network flow problem with multiple objectives

This paper deals with getting optimal solutions for the multiobjective network flow problem with preemptive priorities. The proposed approach enables one to maintain the network structure of the problem and hence to develop network-based algorithms which usually are proved to be more efficient than general ones. In addition, an application to the problem of evaluating the performance of an hydrological system is shown.

A genetic algorithm for solving linear fractional bilevel problems

Bilevel programming has been proposed for dealing with decision processes involving two decision makers with a hierarchical structure. They are characterized by the existence of two optimization problems in which the constraint region of the upper level problem is implicitly determined by the lower level optimization problem. In this paper a genetic algorithm is proposed for the class of bilevel problems in which both level objective functions are linear fractional and the common constraint region is a bounded polyhedron. The algorithm associates chromosomes with extreme points of the polyhedron and searches for a feasible solution close to the optimal solution by proposing efficient crossover and mutation procedures. The computational study shows a good performance of the algorithm, both in terms of solution quality and computational time.

A mutation operator based on a Pareto ranking for multi-objective evolutionary algorithms

Evolutionary Algorithms, EA’s, try to imitate, in some way, the principles of natural evolution and genetics. They evolve a population of potential solutions to the problem using operators such as mutation, crossover and selection. In general, the mutation operator is responsible for the diversity of the population and helps to avoid the problem of premature convergence to local optima (a premature stagnation of the search caused by the lack of population diversity).In this paper we present a new mutation operator in the context of Multi-Objective Evolutionary Algorithms, MOEA’s, which makes use of the definition of Pareto optimality and manages the maximal amplitude or maximal step size of the mutation according to the Pareto layer of the individual and also of the iteration number. The behaviour of our mutation operator reveals that the use of variation operators which take into consideration the quality of the solutions, in terms of Pareto dominance or Pareto layers, can help to improve them. The Pareto based mutation operator proposed is compared with four well established and extensively used mutation operators: random mutation, non-uniform mutation, polynomial mutation and Gaussian mutation. The accomplished experiments reveal that our mutation operator performs, in most of the test problems considered, better than the others.

A comparative study of variation operators used for evolutionary multi-objective optimization

Abstract In this paper, several variation operators based on Pareto efficiency, extracted from Differential Evolution, Estimation of Distribution Algorithms, Evolution Strategies and Evolutionary Programming, are compared in order to determine whether or not they increase the performance of the non-Pareto based versions. Firstly, we compare the selected variation operators in pairs, each operator with a modification of itself, in which we remove those elements related to the Pareto efficiency. Then, in a second experiment we compare among the selected operators, the variation operators used in the NSGA-II algorithm and the ones presented by the authors, PBCO and RBMO. In all the experiments the variation operators are incorporated in a well-known algorithm usually considered as a reference for making the comparisons, the NSGA-II algorithm. The experiments show that the Pareto based variation operators selected from the literature do not usually present a better behavior than their non-Pareto based versions; and none of them presents a better performance than the one reached by the variation operators defined by the authors, which were entirely built around the Pareto information of the individuals. These facts suggest that more effort should be placed in the design of variation operators devoted to multi-objective algorithms in order to achieve superior results to those obtained by means of general variation operators.

A multi-objective micro genetic ELM algorithm

The extreme learning machine (ELM) is a methodology for learning single-hidden layer feedforward neural networks (SLFN) which has been proved to be extremely fast and to provide very good generalization performance. ELM works by randomly choosing the weights and biases of the hidden nodes and then analytically obtaining the output weights and biases for a SLFN with the number of hidden nodes previously fixed. In this work, we develop a multi-objective micro genetic ELM (@mG-ELM) which provides the appropriate number of hidden nodes for the problem being solved as well as the weights and biases which minimize the MSE. The multi-objective algorithm is conducted by two criteria: the number of hidden nodes and the mean square error (MSE). Furthermore, as a novelty, @mG-ELM incorporates a regression device in order to decide whether the number of hidden nodes of the individuals of the population should be increased or decreased or unchanged. In general, the proposed algorithm reaches better errors by also implying a smaller number of hidden nodes for the data sets and competitors considered.

A bi-objective micro genetic Extreme Learning Machine

The Extreme Learning Machine (ELM) is a recent algorithm for training single-hidden layer feedforward neural networks (SLFN) which has shown promising results when compared with other usual tools. ELM randomly chooses weights and biases of hidden nodes and analytically obtains the output weights and biases. It constitutes a very fast algorithm with a good generalization performance in most cases. Since the original ELM was presented, several papers have been published using similar ideas, EI-ELM, OP-ELM, OS-ELM, EM-ELM, etc. In this paper, we present a bi-objective micro genetic ELM (μG-ELM). This algorithm, instead of considering random hidden weights and biases, generates them by means of a micro genetic algorithm. It is conducted considering two objectives, the number of hidden nodes and the mean square error (MSE). Furthermore, as a novelty, μG-ELM incorporates a regression model in order to decide whether the number of hidden nodes should be increased or decreased. The proposed algorithm reaches similar errors but involves, in general, a smaller number of hidden nodes, while maintaining competitive execution time.

Representation and management of MOEA populations based on graphs

Abstract Until now, in the literature, little attention has been paid to the storage and handling of populations of multiobjective evolutionary algorithms (MOEAs). In this work, we present a new tool for representing and managing populations of MOEAs by means of the use of graphs that keep the information on the relations among the individuals of the population. In the paper, we establish the theoretical basis of this sort of graph. In addition, we develop algorithms for its construction and updating (addition and removal of individuals in the population), analyzing their theoretical complexities. We also study several aspects of their practical behaviour including storage requirements, time needed for the construction and the management of these graphs. Finally, we present a selection process time comparison with and without the proposed methodology.

A Sequential Network-Based Approach for the Multiobjective Network Flow Problem with Preemptive Priorities

This paper presents a sequential approach for the problem of getting an optimal solution to the multiobjective network flow problem with preemptive priorities. This approach considers a priority every time, while maintaining through the sequence the network structure. This allows to use in each iteration of the process any efficient network-based algorithm for the single objective minimum cost flow problem.