THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

Differential Evolution: A review of more than two decades of research

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Orthogonal Arrays Theory And Applications

Review of swarm intelligence-based feature selection methods

The first cooperative co-evolutionary algorithm (CCEA) was proposed by Potter and De Jong in 1994 and since then many CCEAs have been proposed and successfully applied to solving various complex optimization problems. In applying CCEAs, the complex optimization problem is decomposed into multiple subproblems, and each subproblem is solved with a separate subpopulation, evolved by an individual evolutionary algorithm (EA). Through cooperative co-evolution of multiple EA subpopulations, a complete problem solution is acquired by assembling the representative members from each subpopulation. The underlying divide-and-conquer and collaboration mechanisms enable CCEAs to tackle complex optimization problems efficiently, and hence CCEAs have been attracting wide attention in the EA community. This paper presents a comprehensive survey of these CCEAs, covering problem decomposition, collaborator selection, individual fitness evaluation, subproblem resource allocation, implementations, benchmark test problems, control parameters, theoretical analyses, and applications. The unsolved challenges and potential directions for their solutions are discussed.

A Survey on Cooperative Co-Evolutionary Algorithms

Dynamic interval multiobjective optimization problems (DI-MOPs) are very common in real-world applications. However, there are few evolutionary algorithms (EAs) that are suitable for tackling DI-MOPs up to date. A framework of dynamic interval multiobjective cooperative co-evolutionary optimization based on the interval similarity is presented in this paper to handle DI-MOPs. In the framework, a strategy for decomposing decision variables is first proposed, through which all the decision variables are divided into two groups according to the interval similarity between each decision variable and interval parameters. Following that, two subpopulations are utilized to cooperatively optimize decision variables in the two groups. Furthermore, two response strategies, i.e., a strategy based on the change intensity and a random mutation strategy, are employed to rapidly track the changing Pareto front of the optimization problem. The proposed algorithm is applied to eight benchmark optimization instances as well as a multiperiod portfolio selection problem and compared with five state-of-the-art EAs. The experimental results reveal that the proposed algorithm is very competitive on most optimization instances.

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A Similarity-Based Cooperative Co-Evolutionary Algorithm for Dynamic Interval Multiobjective Optimization Problems

Dynamic multi-objective optimization problems (DMOPs) not only involve multiple conflicting objectives, but these objectives may also vary with time, raising a challenge for researchers to solve them. This paper presents a cooperative co-evolutionary strategy based on environment sensitivities for solving DMOPs. In this strategy, a new method that groups decision variables is first proposed, in which all the decision variables are partitioned into two subcomponents according to their interrelation with environment. Adopting two populations to cooperatively optimize the two subcomponents, two prediction methods, i.e., differential prediction and Cauchy mutation, are then employed respectively to speed up their responses on the change of the environment. Furthermore, two improved dynamic multi-objective optimization algorithms, i.e., DNSGAII-CO and DMOPSO-CO, are proposed by incorporating the above strategy into NSGA-II and multi-objective particle swarm optimization, respectively. The proposed algorithms are compared with three state-of-the-art algorithms by applying to seven benchmark DMOPs. Experimental results reveal that the proposed algorithms significantly outperform the compared algorithms in terms of convergence and distribution on most DMOPs.

Environment Sensitivity-Based Cooperative Co-Evolutionary Algorithms for Dynamic Multi-Objective Optimization

In many real-world engineering applications, a uniform design needs to be conducted in a constrained experimental domain that includes linear/nonlinear and inequality/equality constraints. In general, these constraints make the constrained experimental domain small and irregular in the decision space. Therefore, it is difficult for current methods to produce a predefined number of samples and make the samples distribute uniformly in the constrained experimental domain. This paper presents a two-phase differential evolution for uniform designs in constrained experimental domains. In the first phase, considering the constraint violation as the fitness function, a clustering DE is proposed to guide the population toward the constrained experimental domain from different directions promptly. As a result, a predefined number of samples can be obtained in the constrained experimental domain. In the second phase, maximizing the minimum Euclidean distance among samples is treated as another fitness function. By optimizing this fitness function, the samples produced in the first phase can be scattered uniformly in the constrained experimental domain. The performance of the proposed method has been tested and compared with another state-of-the-art method. Experimental results suggest that our method is significantly better than the compared method in the uniform designs of a new type of automotive crash box and five benchmark test problems. Moreover, the proposed method could be considered as a general and promising framework for other uniform designs in constrained experimental domains.

A Two-Phase Differential Evolution for Uniform Designs in Constrained Experimental Domains

Multi-objective optimization problems with changing variables are very common in real-world applications. This kind of problems often has a changing Pareto-optimal set and a complex relation among decision variables. In order to rapidly track the time-dependent Pareto-optimal front, we propose a framework of parallel cooperative co-evolution based on dynamically grouping decision variables. Decision variables are first divided into a number of groups using the Spearman rank correlation analysis, with different groups having a weak correlation. Then, a sub-population is employed to optimize decision variables in each group using a traditional multi-objective evolutionary algorithm. The evaluation of a complete solution is fulfilled through the cooperation among sub-populations. We compare the proposed algorithm with three state-of-the-art algorithms by applying them to two modified benchmark optimization problems. Empirical results show that the proposed algorithm is superior to the compared ones.

A parallel multi-objective cooperative co-evolutionary algorithm with changing variables

This paper presents a cooperative co-evolutionary dynamic multi-objective optimization algorithm, i.e., DNSGAII-CO for solving DMOPs based on environmental variable grouping. In this algorithm, a new method of grouping decision variables is first presented, in which all the decision variables are divided into two subcomponents according to whether they are interrelated with or without environment parameters. Then, when cooperatively optimizing the two subcomponents by using two populations, two prediction methods, i.e., differential prediction and Cauchy mutation, are employed to initialize them, respectively. The proposed algorithm is applied to a benchmark DMOPs, and compared with two state-of-the-art algorithms. The experimental results demonstrate that the proposed algorithm outperforms the compared algorithms in terms of convergence and distribution.

Biao Xu

Papers

A Similarity-Based Cooperative Co-Evolutionary Algorithm for Dynamic Interval Multiobjective Optimization Problems

Environment Sensitivity-Based Cooperative Co-Evolutionary Algorithms for Dynamic Multi-Objective Optimization

A Two-Phase Differential Evolution for Uniform Designs in Constrained Experimental Domains

A parallel multi-objective cooperative co-evolutionary algorithm with changing variables

Cooperative Co-evolutionary Algorithm for Dynamic Multi-objective Optimization Based on Environmental Variable Grouping.