Shigeyoshi Tsutsui

Genetic algorithms with a robust solution searching scheme

A large fraction of studies on genetic algorithms (GAs) emphasize finding a globally optimal solution. Some other investigations have also been made for detecting multiple solutions. If a global optimal solution is very sensitive to noise or perturbations in the environment then there may be cases where it is not good to use this solution. In this paper, we propose a new scheme which extends the application of GAs to domains that require the discovery of robust solutions. Perturbations are given to the phenotypic features while evaluating the functional value of individuals, thereby reducing the chance of selecting sharp peaks (i.e., brittle solutions). A mathematical model for this scheme is also developed. Guidelines to determine the amount of perturbation to be added is given. We also suggest a scheme for detecting multiple robust solutions. The effectiveness of the scheme is demonstrated by solving different one- and two-dimensional functions having broad and sharp peaks.

Forking genetic algorithms: Gas with search space division schemes

In this article, we propose a new type of genetic algorithm (GA), the forking GA (fGA), which divides the whole search space into subspaces, depending on the convergence status of the population and the solutions obtained so far. The fGA is intended to deal with multimodal problems that are difficult to solve using conventional GAs. We use a multi-population scheme that includes one parent population that explores one subspace and one or more child populations exploiting the other subspace. We consider two types of fGAs, depending on the method used to divide the search space. One is the genoqtypic fGA (g-fGA), which defines the search subspace for each subpopulation, depending on the salient schema within the genotypic search space. The other is the phenotypic fGA (p-fGA), which defines a search subspace by a neighborhood hypercube around the current best individual in the phenotypic feature space. Empirical results on complex function optimization problems show that both the g-fGA and the p-GA perform well compared to conventional GAs. Two additional utilities of the p-fGA are also studied briefly.

Search space boundary extension method in real-coded genetic algorithms

Abstract In real-coded genetic algorithms (GAs), some crossover operators do not work well on functions which have their optimum at the corner of the search space. To cope with this problem, we have proposed a boundary extension method which allows individuals to be located within a limited space beyond the boundary of the search space. In this paper, we give an analysis of the boundary extension methods from the viewpoint of sampling bias and perform a comparative study on the effect of applying two boundary extension methods, namely the boundary extension by mirroring (BEM) and the boundary extension with extended selection (BES). We were able to confirm that to use sampling methods which have smaller sampling bias had good performance on both functions which have their optimum at or near the boundaries of the search space, and functions which have their optimum at the center of the search space. The BES/SD/A (BES by shortest distance selection with aging) had good performance on functions which have their optimum at or near the boundaries of the search space. We also confirmed that applying the BES/SD/A did not cause any performance degradation on functions which have their optimum at the center of the search space.

Solving quadratic assignment problems by genetic algorithms with GPU computation: a case study

This paper describes designing a parallel GA with GPU computation to solve the quadratic assignment problem (QAP) which is one of the hardest optimization problems in permutation domains. For the parallel method, a multiple-population, coarse-grained GA model was used. Each subpopulation is evolved by a multiprocessor in a GPU (NVIDIA GeForce GTX285). At predetermined intervals of generations all individuals in subpopulations are shuffled via the VRAM of the GPU. The instances on which this algorithm was tested were taken from the QAPLIB benchmark library. Results were promising, showing a speedup ration from 3 to 12 times, compared to the Intel i7 965 processor.

Theoretical Analysis of Simplex Crossover for Real-Coded Genetic Algorithms

In this paper, we perform theoretical analysis and experiments on the Simplex Crossover (SPX), which we have proposed. Real-coded GAs are expected to be a powerful function optimization technique for real-world applications where it is often hard to formulate the objective function. However, we believe there axe two problems which will make such applications difficult; 1) performance of real-coded GAs depends on the coordinate system used to express the objective function, and 2) it costs much labor to adjust parameters so that the GAs always find an optimum point efficiently. The result of our theoretical analysis and experiments shows that a performance of SPX is independent of linear coordinate transformation and that SPX always optimizes various test function efficiently when theoretical value for expansion rate, which is a parameter of SPX, is applied.

Probabilistic Model-Building Genetic Algorithms in Permutation Representation Domain Using Edge Histogram

Recently, there has been a growing interest in developing evolutionary algorithms based on probabilistic modeling. In this scheme, the offspring population is generated according to the estimated probability density model of the parent instead of using recombination and mutation operators. In this paper, we have proposed probabilistic model-building genetic algorithms (PMBGAs) in permutation representation domain using edge histogram based sampling algorithms (EHBSAs). Two types of sampling algorithms, without template (EHBSA/WO) and with template (EHBSA/WT), are presented. The results were tested in the TSP and showed EHBSA/WT worked fairly well with a small population size in the test problems used. It also worked better than well-known traditional two-parent recombination operators.

Function optimization in nonstationary environment using steady state genetic algorithms with aging of individuals

The authors explore the utility of the concept of aging of individuals in the context of steady state GAs for nonstationary function optimization. Age of an individual is used as an additional factor in addition to the objective functional value in order to determine its effective fitness value. Age of a newly generated individual is taken as zero, and in every iteration it is increased by one. Individuals undergoing genetic operations are selected based on the effective fitness value, which changes dynamically. This helps to maintain diversity in the population and is useful to trace changes in environment. Simulation results show some promise for the utility of the present technique for nonstationary function optimization.

Multi-parent Recombination in Genetic Algorithms with Search Space Boundary Extension by Mirroring

In previous work, we have investigated real coded genetic algorithms with several types of multi-parent recombination operators and found evidence that multi-parent recombination with center of mass crossover (CMX) seems a good choice for real coded GAs. But CMX does not work well on functions which have their optimum on the corner of the search space. In this paper, we propose a method named boundary extension by mirroring (BEM) to cope with this problem. Applying BEM to CMX, the performance of CMX on the test functions which have their optimum on the corner of the search space was much improved. Further, by applying BEM, we observed clear improvement in performance of two-parent recombination on the functions which have their optimum on the corner of the search space. Thus, we suggest that BEM is a good general technique to improve the efficiency of crossover operators in real-coded GAs for a wide range of functions.

A study on the effect of multi-parent recombination in real coded genetic algorithms

We investigate real coded genetic algorithms in which more than two parents are involved in recombination operation. We propose three types of multi-parent recombination operators; the center of mass crossover (CMX), multi-parent feature-wise crossover (MFX), and seed crossover (SX). Each of these operators is a natural generalization of 2-parent recombination operator. These operators are evaluated on several test functions. The results showed clearly that multi-parent recombinations lead to better performance, although the performance improvement for different techniques were found to be dependent on problems.

A Robust Solution Searching Scheme in Genetic Search

Many of the studies on GAs give emphasis on finding the global optimal solution. In this paper, we propose a new method which extend the application of GAs to domains that require detection of robust solutions. If a global optimal solution found is on a sharp-pointed location, there may be cases where it is not good to use this solution. In nature, the phenotypic feature of an organism is determined from the genotypic code of genes in the chromosome. During this process, there may be some perturbations. Let X be the phenotypic parameter vector, f(X) a fitness function and δ a noise vector. As can be easily understood from the analogy of nature, actual fitness function should be of the form f(X+δ). We use this analogy for the present work. Simulation results confirm the utility of this approach in finding robust solutions.