Kaname Narukawa

An empirical study on similarity-based mating for evolutionary multiobjective combinatorial optimization

We have already proposed a similarity-based mating scheme to recombine extreme and similar parents for evolutionary multiobjective optimization. In this paper, we examine the effect of the similarity-based mating scheme on the performance of evolutionary multiobjective optimization (EMO) algorithms. First we examine which is better between recombining similar or dissimilar parents. Next we examine the effect of biasing selection probabilities toward extreme solutions that are dissimilar from other solutions in each population. Then we examine the effect of dynamically changing the strength of this bias during the execution of EMO algorithms. Computational experiments are performed on a wide variety of test problems for multiobjective combinatorial optimization. Experimental results show that the performance of EMO algorithms can be improved by the similarity-based mating scheme for many test problems.

Some Issues on the Implementation of Local Search in Evolutionary Multiobjective Optimization

This paper discusses the implementation of local search in evolutionary multiobjective optimization (EMO) algorithms for the design of a simple but powerful memetic EMO algorithm. First we propose a basic framework of our memetic EMO algorithm, which is a hybrid algorithm of the NSGA-II and local search. In the generation update procedure of our memetic EMO algorithm, the next population is constructed from three populations: the current population, its offspring population generated by genetic operations, and an improved population obtained from the offspring population by local search. We use Pareto ranking and the concept of crowding in the same manner as in the NSGA-II for choosing good solutions to construct the next population from these three populations. For implementing local search in our memetic EMO algorithm, we examine two approaches, which have been often used in the literature: One is based on Pareto ranking, and the other is based on a weighted scalar fitness function. The main difficulty of the Pareto ranking approach is that the movable area of the current solution by local search is very small. On the other hand, the main difficulty of the weighted scalar approach is that the offspring population can be degraded by local search. These difficulties are clearly demonstrated through computational experiments on multiobjective knapsack problems using our memetic EMO algorithm. Our experimental results show that better results are obtained from the weighted scalar approach than the Pareto ranking approach. For further improving the weighted scalar approach, we examine some tricks that can be used for overcoming its difficulty.

Comparison between lamarckian and baldwinian repair on multiobjective 0/1 knapsack problems

This paper examines two repair schemes (i.e., Lamarckian and Baldwinian) through computational experiments on multiobjective 0/1 knapsack problems. First we compare Lamarckian and Baldwinian with each other. Experimental results show that the Baldwinian repair outperforms the Lamarckian repair. It is also shown that these repair schemes outperform a penalty function approach. Then we examine partial Lamarckianism where the Lamarckian repair is applied to each individual with a prespecified probability. Experimental results show that a so-called 5% rule works well. Finally partial Lamarckianism is compared with an island model with two subpopulations where each island has a different repair scheme. Experimental results show that the island model slightly outperforms the standard single-population model with the 50% partial Lamarckian repair in terms of the diversity of solutions.

Modification of Evolutionary Multiobjective Optimization Algorithms for Multiobjective Design of Fuzzy Rule-Based Classification Systems

We examine three methods for improving the ability of evolutionary multiobjective optimization (EMO) algorithms to find a variety of fuzzy rule-based classification systems with different tradeoffs with respect to their accuracy and complexity. The accuracy of each fuzzy rule-based classification system is measured by the number of correctly classified training patterns while its complexity is measured by the number of fuzzy rules and the total number of antecedent conditions. One method for improving the search ability of EMO algorithms is to remove overlapping rule sets in the three-dimensional objective space. Another method is to choose similar rule sets as parents for crossover operations. The other method is to bias the selection probability of parents toward rule sets with high accuracy. The effectiveness of each method is examined through computational experiments on benchmark data sets

Recombination of similar parents in EMO algorithms

This paper examines the effect of crossover operations on the performance of EMO algorithms through computational experiments on knapsack problems and flowshop scheduling problems using the NSGA-II algorithm. We focus on the relation between the performance of the NSGA-II algorithm and the similarity of recombined parent solutions. First we show the necessity of crossover operations through computational experiments with various specifications of crossover and mutation probabilities. Next we examine the relation between the performance of the NSGA-II algorithm and the similarity of recombined parent solutions. It is shown that the quality of obtained solution sets is improved by recombining similar parents. Then we examine the effect of increasing the selection pressure (i.e., increasing the tournament size) on the similarity of recombined parent solutions. An interesting observation is that the increase in the tournament size leads to the recombination of dissimilar parents, improves the diversity of solutions, and degrades the convergence performance of the NSGA-II algorithm.

Incorporation of decision maker's preference into evolutionary multiobjective optimization algorithms

The main characteristic feature of evolutionary multiobjective optimization (EMO) is that no a priori information about the decision makers preference is utilized in the search phase. EMO algorithms try to find a set of well-distributed Pareto-optimal solutions with a wide range of objective values. It is, however, very difficult for EMO algorithms to find a good solution set of a multiobjective combinatorial optimization problem with many decision variables and/or many objectives. In this paper, we propose an idea of incorporating the decision makers preference into EMO algorithms to efficiently search for Pareto-optimal solutions of such a hard multiobjective optimization problem.

Effects of removing overlapping solutions on the performance of the NSGA-II algorithm

The focus of this paper is the handling of overlapping solutions in evolutionary multiobjective optimization (EMO) algorithms. In the application of EMO algorithms to some multiobjective combinatorial optimization problems, there exit a large number of overlapping solutions in each generation. We examine the effect of removing overlapping solutions on the performance of EMO algorithms. In this paper, overlapping solutions are removed from the current population except for a single solution. We implement two removal strategies of overlapping solutions. One is the removal of overlapping solutions in the objective space. In this strategy, one solution is randomly chosen among the overlapping solutions with the same objective vector and left in the current population. The other overlapping solutions with the same objective vector are removed from the current population. As a result, each solution in the current population has a different location in the objective space. It should be noted that the overlapping solutions in the objective space are not necessary the same solution in the decision space. Thus we also examine the other strategy where the overlapping solutions in the decision space are removed from the current population except for a single solution. As a result, each solution in the current population has a different location in the decision space. The effect of removing overlapping solutions is examined through computational experiments where each removal strategy is combined into the NSGA-II algorithm.

Comparison of evolutionary multiobjective optimization with rference solution-based single-objective approach

In this paper, we demonstrate advantages and disadvantages of an evolutionary multiobjective optimization (EMO) approach in comparison with a reference solution-based single-objective approach through computational experiments on multiobjective 0/1 knapsack problems. The main characteristic feature of the EMO approach is that no a priori information about the decision makers preference is assumed. The EMO approach tries to find well-distributed trade-off solutions with a wide range of objective values as many as possible. A final solution is supposed to be chosen from the obtained trade-off solutions by the decision maker. On the other hand, the reference solution-based approach utilizes the information about the decision makers preference in the form of a reference solution. We examine whether the EMO approach can find good trade-off solutions close to an arbitrarily given reference solution. Experimental results show that good solutions are not always obtained by the EMO approach. We also examine where the reference solution-based approach can find many trade-off solutions around the given reference solution. Experimental results show that many trade-off solutions can not be obtained even when an archive population of non-dominated solutions is stored in the reference solution-based approach. Based on these observations, we suggest a hybrid approach.

Spatial implementation of evolutionary multiobjective algorithms with partial Lamarckian repair for multiobjective knapsack problems

Multiobjective 0/1 knapsack problems have been frequently used as test problems for the performance evaluation of evolutionary multiobjective optimization algorithms. It has been shown that their performance on such test problems strongly depends on the choice of a repair method to transform infeasible solutions into feasible ones. We examine partial Lamarckianism where Lamarckian repair is probabilistically applied to infeasible solutions. When the Lamarckian repair is not applied to an infeasible solution, Baldwinian repair is used. We propose an island model to spatially implement the partial Lamarckianism where each island is based on either Lamarckian or Baldwinian.

An empirical study on the handling of overlapping solutions in evolutionary multiobjective optimization

We focus on the handling of overlapping solutions in evolutionary multiobjective optimization (EMO) algorithms. First we show that there exist a large number of overlapping solutions in each population when EMO algorithms are applied to multiobjective combinatorial optimization problems with only a few objectives. Next we implement three strategies to handle overlapping solutions. One strategy is the removal of overlapping solutions in the objective space. In this strategy, overlapping solutions in the objective space are removed during the generation update phase except for only a single solution among them. As a result, each solution in the current population has a different location in the objective space. Another strategy is to remove overlapping solutions so that each solution in the current population has a different location in the decision space. The other strategy is the modification of Pareto ranking where overlapping solutions in the objective space are allocated to different fronts. As a result, each solution in each front has a different location in the objective space. Effects of each strategy on the performance of the NSGA-II algorithm are examined through computational experiments on multiobjective 0/1 knapsack problems, multiobjective flowshop scheduling problems, and multiobjective fuzzy rule selection problems.