Jun-ichi Kushida

Island-based differential evolution with varying subpopulation size

Differential evolution (DE) is one of the evolutionally algorithms for solving optimization problems in a continuous space. DE has been widely applied to solve various optimization problems. Additionally, many modified DE algorithms have been developed in an attempt to improve search performance. In this paper, we propose island-based DE with varying subpopulation size. Island model is one of the effective parallel distributed model in evolutionary algorithms. In the proposed method, total population is divided into independent sub-populations called islands. The basic island model uses same control parameters for each subpopulation. In contrast, we allocate different control parameters to each island. Therefore, each island has a different convergence characteristic by using own control parameters. At fixed generation intervals, migration among islands is performed in order to preserve diversity of subpopulation. Additionally, by incorporating the operation of individual transfer, proposed method can vary subpopulation dynamically according to the function landscape. Numerical experiments are performed to illustrate the performance of the proposed method compared with basic DE. The results show that the proposed method outperforms basic DE on standard test functions including various landscape features.

Rank-based Semantic Control Crossover in Genetic Programming

Subtree exchange crossover which is usually used in Genetic Programming (GP) can not control the search properties such as global or local search, because crossover points in parental individuals are selected at random. To overcome the problem, crossover based on semantic distance of subtrees has been studied recent years. If similar subtrees in semantic space are exchanged, the local search can be performed. In contrast, dissimilar subtrees are exchanged, the global search can be performed. In Semantic Control Crossover (SCC), the global search can be performed in early generations, and the local search can be performed in later generations. In this paper, we propose a new SCC based on the ranking information of parents, Rank-based SCC. The method controls search properties according to not generations but ranking information of parents. In case of the crossover to a pair of parents with higher ranks, similar subtrees should be exchanged for local search around the parents. In contrast, in case of the crossover to a pair of parents with lower ranks, dissimilar subtrees should be exchanged for global search. We compared the search performance of three methods, standard crossover, conventional SCC and Rank-based SCC, and showed the effectiveness of our method.

Geometric Semantic Genetic Programming Using External Division of Parents

In this paper, we focus on symbolic regression problems, in which we find functions approximating the relationships between given input and output data. If we do not have the knowledge on the structure (e.g. Degree) of the true functions, Genetic Programming (GP) is often used for evolving tree structural numerical expressions. In GP, crossover operator has a great influence on the quality of the acquired solutions. Therefore, various crossover operators have been proposed. Recently, new crossover operators based on semantics of tree structures have attracted many attentions for efficient search. In the semantics-based crossover, offspring is created from its parental individuals so that the offspring can be similar to the parents not structurally but semantically. Geometric Semantic Genetic Programming (GSGP) is a method in which offspring is produced by a convex combination of two parental individuals. This operation corresponds to the internal division of two parents. This method can optimize solutions efficiently because the crossover operator always produces better solution than a worse parent. But, in GSGP, if the true function exists outside of two parents in semantic space, it is difficult to produce better solution than both of the parents. In this paper, we propose an improved GSGP which can also consider external divisions as well as internal ones. By comparing the search performance among several crossover operators in symbolic regression problems, we showed that our methods are superior to the standard GP and conventional GSGP.

Solving quadratic assignment problems by differential evolution

Differential evolution (DE) was introduced by Stone and Price in 1995 as a population-based stochastic search technique for solving optimization problems in a continuous space. DE has been successfully applied to various real world numerical optimization problems. In recent years not only continuous real-valued function, the applications of DE on combinatorial optimization problems with discrete decision variables are reported. However, genetic operator in the standard DE can not directly applied to discrete space. In this paper, we propose a method to solve quadratic assignment problems (QAP) by DE. The QAP is a well-known combinatorial optimization problem with a wide variety of practical applications. It is NP-hard and is considered to be one of the most difficult problems. In the QAP, a candidate solution can represented a permutation of integer. The proposed method employs permutation representation for individuals in DE. Therefore, a individual vector is encoded directly as a permutation. In discrete space, to realize effcient solution search like standard DE which have continuous nature, we modify differential operator to handle permutation encoding. Additionally, in order to maintain diversity of population, restart strategy and tabu list are introduced to proposed method instead of crossover operator. Finally, we show the experimental results using instances of QAPLIB and the efficacy of proposed method.

Deterministic Crossover Based on Target Semantics in Geometric Semantic Genetic Programming

In this paper, we focus on solving symbolic regression problems, in which we find functions approximating the relationships between given input and output data. Genetic Programming (GP) is often used for evolving tree structural numerical expressions. Recently, new crossover operators based on semantics of tree structures have attracted many attentions for efficient search. In the semantics-based crossover, offspring is created from its parental individuals so that the offspring can be similar to the parents not structurally but semantically. Geometric Semantic Genetic Programming (GSGP) is a method in which offspring is produced by a convex combination of two parental individuals. In order to improve the search performance of GSGP, we propose an improved Geometric Semantic Crossover utilizing the information of the target semantics. In conventional GSGP, ratios of convex combinations are determined at random. On the other hand, our proposed method can use optimal ratios for affine combinations of parental individuals. We confirmed that our method showed better performance than conventional GSGP in several symbolic regression problems.

Adaptive particle swarm optimization with multi-dimensional mutation

The paper presents adaptive particle swarm optimization with multi-dimensional mutation (MM-APSO), which can perform move efficient search than the conventional adaptive particle swarm optimization (APSO). In particular, it can solve non-separable fitness functions such as banana functions with high accuracy and rapid convergence. MM-APSO consists of APSO and additional two methods. One is multi-dimensional mutation, which uses movement vector of population. The other is reinitializing velocity to 0 when mutation occurs. Experiments were conducted on 10 unimodal and multimodal benchmark functions. The experimental results show that MM-APSO substantially enhances the performance of the APSO in terms of convergence speed and solution accuracy.

Rank-based differential evolution with multiple mutation strategies for large scale global optimization

Differential Evolution (DE) is one of the most powerful global numerical optimization algorithms in the field of evolutionary algorithm. However, the performance of DE is affected by control parameters and mutation strategies. In addition, the choice of the control parameters and mutation strategies is strongly dependent on the characteristics of optimization problems. As a result, studies focused on controlling the parameters and mutation strategies is currently an active area of research. One of them, DE with landscape modality detection (LMDEa) which detects the landscape modality using the current search points, showed excellent performance for large scale optimization problem. In our research, we improve LMDEa by introducing the concept of Rank-based Differential Evolution (RDE). The proposed method utilizes ranking information of search points in order to assign a suitable scaling factor (F) and a crossover rate (CR) for each individual. Furthermore multiple mutation strategies are employed; in addition, they are also assigned by the ranking information for realizing a well-balanced exploration and exploitation ability. Through experimentation, using the set of benchmark functions, we show the effectiveness of the proposed method.

Cartesian Ant Programming with adaptive node replacements

Ant Colony Optimization (ACO) is a swarm-based search method. Multiple ant agents search various solutions and their searches focus on around good solutions by positive feedback mechanism based on pheromone communication. ACO is effective for combinatorial optimization problems. The attempt of applying ACO to automatic programming has been studied in recent years. As one of the attempts, we have previously proposed Cartesian Ant Programming (CAP) as an ant-based automatic programming method. Cartesian Genetic Programming (CGP) is well-known as an evolutionary optimization method for graph-structural programs. CAP combines graph representations in CGP with pheromone communication in ACO. The connections of program primitives, terminal and functional symbols, can be optimized by ants. CAP showed better performance than CGP. However, quantities of respective symbols are limited due to the fixed assignments of functional symbols to nodes. Therefore, if the number of given nodes is not enough for representing program, the search performance becomes poor. In this paper, to solve the problem, we propose CAP with adaptive node replacements. This method finds unnecessary nodes which are not used for representing programs. Then, new functional symbols, which seems to be useful for constructing good programs, are assigned to the nodes. By this method, given nodes can be utilized efficiently. In order to examine the effectiveness of our method, we apply it to a symbolic regression problem. CAP with adaptive node replacements showed better results than conventional methods, CGP and CAP.

Deterministic Geometric Semantic Genetic Programming with Optimal Mate Selection

To solve symbolic regression problems, Genetic Programming (GP) is often used for evolving tree structural numerical expressions. Recently, new crossover operators based on semantics of tree structures have attracted many attentions. In the semantics-based crossover, offspring is created from its parental individuals so that the offspring can inherit the characteristics of the parents not structurally but semantically. Geometric Semantic GP (GSGP) is a method in which offspring is produced by a convex combination of two parental individuals. In order to improve the search performance of GSGP, deterministic Geometric Semantic Crossover utilizing the information of the target semantics has been proposed. In conventional GSGP, ratios of convex combinations are determined at random. On the other hand, the deterministic crossover can use optimal ratios for affine combinations of parental individuals so that created offspring can be closest to the target solution. In these methods, parents which crossover operators will be applied to are selected based only on their fitness. In this paper, we propose a new selection method of parents for generating offspring which can approach to a target solution more efficiently. In this method, we select a pair of parents so that a distance between a straight line connecting the parents and a target point can be smallest in semantic space. We confirmed that our method showed better performance than conventional GSGP in several symbolic regression problems.

Cartesian ant programming with transition rule considering internode distance

In recent years, Cartesian Ant Programming (CAP) has been proposed as a swarm-based automatic programming method, which combines graph representations in Cartesian Genetic Programming with search mechanism of Ant Colony Optimization. In CAP, once an ant jumps a number of nodes, the skipped nodes are not utilized and wasted in search. To make the use frequency of nodes uniform, we propose CAP with transition rule considering internode distance. We focus on the distance at the beginning of search to utilize a large number of nodes for exploration of search. As the search proceeds, the search comes to depend on the pheromone information for exploitation of search. In addition, to prevent the excessive use of the unnecessary nodes, we modify the method of dynamic symbol assignments to nodes so that not only functional symbols but also terminal symbols can be assigned to the respective nodes. We examined the effectiveness of our proposed method by applying it to symbolic regression problems. From the experimental results, we confirmed the improvement of performance and the relief of bias in use frequency of nodes by our proposed method.