A variable reduction strategy for evolutionary algorithms handling equality constraints

Efficient constraint handling techniques are of great significance when Evolutionary Algorithms (EAs) are applied to constrained optimization problems (COPs). Generally, when use EAs to deal with COPs, equality constraints are much harder to satisfy, compared with inequality constraints. In this study, we propose a strategy named equality constraint and variable reduction strategy (ECVRS) to reduce equality constraints as well as variables of COPs. Since equality constraints are always expressed by equations, ECVRS makes use of the variable relationships implied in such equality constraint equations. The essence of ECVRS is it makes some variables of a COP considered be represented and calculated by some other variables, thereby shrinking the search space and leading to efficiency improvement for EAs. Meanwhile, ECVRS eliminates the involved equality constraints that providing variable relationships, thus improves the feasibility of obtained solutions. ECVRS is tested on many benchmark problems. Computational results and comparative studies verify the effectiveness of the proposed ECVRS.     

提高多目标进化算法分布性的动态调整机制

为提高多目标进化算法的分布性,提出一种基于极坐标的动态调整机制。在极坐标下,根据解集的拥挤程度,计算个体解的缩放系数。在进化过程中利用该缩放系数动态调整解集支配关系,适当提高分布性好的解在支配关系中的地位以改善解的分布。对测试函数的仿真试验结果表明,将该机制应用于经典算法能显著提高算法的分布性,同时保持良好的收敛性。     

A mixed strategy of combining evolutionary algorithms with multigrid methods

Multigrid methods have been proven to be an efficient approach in accelerating the convergence rate of numerical algorithms for solving partial differential equations. This paper investigates whether multigrid methods are helpful to accelerate the convergence rate of evolutionary algorithms for solving global optimization problems. A novel multigrid evolutionary algorithm is proposed and its convergence is proven. The algorithm is tested on a set of 13 well-known benchmark functions. Experiment results demonstrate that multigrid methods can accelerate the convergence rate of evolutionary algorithms and improve their performance.     

A tool for multiobjective evolutionary algorithms

This paper introduces a software tool based on illustrative applications for the development, analysis and application of multiobjective evolutionary algorithms. The multiobjective evolutionary algorithms tool (MOEAT) written in C# using a variety of multiobjective evolutionary algorithms (MOEAs) offers a powerful environment for various kinds of optimization tasks. It has many useful features such as visualizing of the progress and the results of optimization in a dynamic or static mode, and decision variable settings. The performance measurements of well-known multiobjective evolutionary algorithms in MOEAT are done using benchmark problems. In addition, two case studies from engineering domain are presented.     

Auto-tuning strategy for evolutionary algorithms: balancing between exploration and exploitation

Genetic Algorithms (GAs) and other Evolutionary Algorithms (EAs), as powerful and broadly applicable stochastic search and optimization techniques have been successfully applied in the area of management science, operations research and industrial engineering. In the past few years, researchers gave lots of great idea for improvement of evolutionary algorithms, which include population initialization, individual selection, evolution, parameter setting, hybrid approach with conventional heuristics etc. However, though lots of different versions of evolutionary computations have been created, all of them have turned most of its attention to the development of search abilities of approaches. In this paper, for improving the search ability, we focus on how to take a balance between exploration and exploitation of the search space. It is also very difficult to solve problem, because the balance between exploration and exploitation is depending on the characteristic of different problems. The balance also should be changed dynamically depend on the status of evolution process. Purpose of this paper is the design of an effective approach which it can correspond to most optimization problems. In this paper, we propose an auto-tuning strategy by using fuzzy logic control. The main idea is adaptively regulation for taking the balance among the stochastic search and local search probabilities based on the change of the average fitness of parents and offspring which is occurred at each generation. In addition, numerical analyses of different type optimization problems show that the proposed approach has higher search capability that improve quality of solution and enhanced rate of convergence.     

Global migration strategy with moving colony for hierarchical distributed evolutionary algorithms

In the established hierarchical distributed evolutionary algorithms (HDEAs), object of global migration is individual. To obtain better solutions of concrete problems, global migration strategy with moving colony is proposed in this paper. In global migration based on the proposed strategy, migration object is subpopulation which moves between groups. Such global migration can increase the efficiency of thereafter local migration. Moreover, realizing it even needs no communication because it can be executed by regrouping subpopulations. In our experiments, the basement of parallelism is an EA for the Traveling Salesman Problem. Outcomes of HDEAs based on proposed scheme which have different global migration topology are compared with those of traditional ones on nine benchmark instances. The results show that a HDEA based on the proposed strategy having the ring global topology performs better than traditional HDEAs for high difficulty instances. However, the advantage of that having the random global topology is not so significant because of conflicting migrations arisen from this topology.     

Data reduction and fast routing: A strategy for efficient algorithms for message-passing parallel computers

This paper presents several algorithms for solving problems using massively parallel SIMD hypercube and shuffle-exchange computers. The algorithms solve a wide variety of problems, but they are related because they all use a common strategy. Specifically, all of the algorithms use a divide-and-conquer approach to solve a problem withN inputs using a parallel computer withP processors. The structural properties of the problem are exploited to assure that fewer thanN data items are communicated during the division and combination steps of the divide-and-conquer algorithm. This reduction in the amount of data that must be communicated is central to the efficiency of the algorithm.This paper addresses four problems, namely the multiple-prefix, data-dependent parallel-prefix, image-component-labeling, and closest-pair problems. The algorithms presented for the data-dependent parallel-prefix and closest-pair problems are the fastest known whenN P and the algorithms for the multiple-prefix and image-component-labeling problems are the fastest known whenN is sufficiently large with respect toP.This work was supported in part by our NSF Graduate Fellowship.     

Data reduction and fast routing: A strategy for efficient algorithms for message-passing parallel computers

This paper presents several algorithms for solving problems using massively parallel SIMD hypercube and shuffle-exchange computers. The algorithms solve a wide variety of problems, but they are related because they all use a common strategy. Specifically, all of the algorithms use a divide-and-conquer approach to solve a problem withN inputs using a parallel computer withP processors. The structural properties of the problem are exploited to assure that fewer thanN data items are communicated during the division and combination steps of the divide-and-conquer algorithm. This reduction in the amount of data that must be communicated is central to the efficiency of the algorithm. This paper addresses four problems, namely the multiple-prefix, data-dependent parallel-prefix, image-component-labeling, and closest-pair problems. The algorithms presented for the data-dependent parallel-prefix and closest-pair problems are the fastest known whenN ≥P and the algorithms for the multiple-prefix and image-component-labeling problems are the fastest known whenN is sufficiently large with respect toP.     

A novel population initialization method for accelerating evolutionary algorithms

Population initialization is a crucial task in evolutionary algorithms because it can affect the convergence speed and also the quality of the final solution. If no information about the solution is available, then random initialization is the most commonly used method to generate candidate solutions (initial population). This paper proposes a novel initialization approach which employs opposition-based learning to generate initial population. The conducted experiments over a comprehensive set of benchmark functions demonstrate that replacing the random initialization with the opposition-based population initialization can accelerate convergence speed.     

A constraint-guided method with evolutionary algorithms for economic problems

This paper presents an evolutionary algorithms based constrain-guided method (CGM) that is capable of handling both hard and soft constraints in optimization problems. While searching for constraint-satisfied solutions, the method differentiates candidate solutions by assigning them with different fitness values, enabling favorite solutions to be distinguished more likely and more effectively from unfavored ones.We illustrate the use of CGM in solving two economic problems with optimization involved: (1) searching equilibriums for bargaining problems; (2) reducing the rate of failure in financial prediction problems. The efficacy of the proposed CGM is analyzed and compared with some other computational techniques, including a repair method and a penalty method for the problem (1), a linear classifier and three neural networks for the problem (2), respectively. Our studies here suggest that the evolutionary algorithms based CGM compares favorably against those computational approaches.     

A survey: hybrid evolutionary algorithms for cluster analysis

Clustering is a popular data analysis and data mining technique. It is the unsupervised classification of patterns into groups. Many algorithms for large data sets have been proposed in the literature using different techniques. However, conventional algorithms have some shortcomings such as slowness of the convergence, sensitive to initial value and preset classed in large scale data set etc. and they still require much investigation to improve performance and efficiency. Over the last decade, clustering with ant-based and swarm-based algorithms are emerging as an alternative to more traditional clustering techniques. Many complex optimization problems still exist, and it is often very difficult to obtain the desired result with one of these algorithms alone. Thus, robust and flexible techniques of optimization are needed to generate good results for clustering data. Some algorithms that imitate certain natural principles, known as evolutionary algorithms have been used in a wide variety of real-world applications. Recently, much research has been proposed using hybrid evolutionary algorithms to solve the clustering problem. This paper provides a survey of hybrid evolutionary algorithms for cluster analysis.     

一种并行免疫进化策略算法研究

基于克隆选择原理,提出一种自适应并行免疫进化策略．在算法中根据抗体抗原亲和度将初始抗体种群分为两个子群,相应地提出了精英克隆算子和超变异算子．通过精英克隆算子提高算法局部搜索能力,同时利用超变异算子维持种群多样性,通过这两个功能互补算子的并行操作实现种群进化．仿真表明,自适应并行免疫进化策略搜索效率高,能有效抑制早熟收敛现象,可用于解决复杂机器学习问题．     

Backward-chaining evolutionary algorithms

Starting from some simple observations on a popular selection method in Evolutionary Algorithms (EAs)—tournament selection—we highlight a previously-unknown source of inefficiency. This leads us to rethink the order in which operations are performed within EAs, and to suggest an algorithm—the EA with efficient macro-selection—that avoids the inefficiencies associated with tournament selection. This algorithm has the same expected behaviour as the standard EA but yields considerable savings in terms of fitness evaluations. Since fitness evaluation typically dominates the resources needed to solve any non-trivial problem, these savings translate into a reduction in computer time. Noting the connection between the algorithm and rule-based systems, we then further modify the order of operations in the EA, effectively turning the evolutionary search into an inference process operating in backward-chaining mode. The resulting backward-chaining EA creates and evaluates individuals recursively, backward from the last generation to the first, using depth-first search and backtracking. It is even more powerful than the EA with efficient macro-selection in that it shares all its benefits, but it also provably finds fitter solutions sooner, i.e., it is a faster algorithm. These algorithms can be applied to any form of population based search, any representation, fitness function, crossover and mutation, provided they use tournament selection. We analyse their behaviour and benefits both theoretically, using Markov chain theory and space/time complexity analysis, and empirically, by performing a variety of experiments with standard and back-ward chaining versions of genetic algorithms and genetic programming.     

On-the-fly calibrating strategies for evolutionary algorithms

The issue of controlling values of various parameters of an evolutionary algorithm is one of the most important and interesting areas of research in evolutionary computation. In this paper we propose two new parameter control strategies for evolutionary algorithms based on the ideas of reinforcement learning. These strategies provide efficient and low-cost adaptive techniques for parameter control and they preserve the original design of the evolutionary algorithm, as they can be included without changing either the structure of the algorithm nor its operators design.     

Distributed evolutionary algorithms for simulation optimization

The optimization of such complex systems as manufacturing systems often necessitates the use of simulation. In this paper, the use of evolutionary algorithms is suggested for the optimization of simulation models. Several types of variables are taken into account. The reduction of computing cost is achieved through the parallelization of this method, which allows several simulation experiments to be run simultaneously. Emphasis is put on a distributed approach where several computers manage both their own local population of solutions and their own simulation experiments, exchanging solutions using a migration operator. After a first evaluation through a mathematical function with a known optimum, the benefits of this new approach are demonstrated through the example of a transport lot sizing and transporter allocation problem in a manufacturing flow shop system, which is solved using a distributed software implemented on a network of eight Sun workstations     

Performance evaluation of evolutionary multiobjective optimization algorithms for multiobjective fuzzy genetics-based machine learning

Recently, evolutionary multiobjective optimization (EMO) algorithms have been utilized for the design of accurate and interpretable fuzzy rule-based systems. This research area is often referred to as multiobjective genetic fuzzy systems (MoGFS), where EMO algorithms are used to search for non-dominated fuzzy rule-based systems with respect to their accuracy and interpretability. In this paper, we examine the ability of EMO algorithms to efficiently search for Pareto optimal or near Pareto optimal fuzzy rule-based systems for classification problems. We use NSGA-II (elitist non-dominated sorting genetic algorithm), its variants, and MOEA/D (multiobjective evolutionary algorithm based on decomposition) in our multiobjective fuzzy genetics-based machine learning (MoFGBML) algorithm. Classification performance of obtained fuzzy rule-based systems by each EMO algorithm is evaluated for training data and test data under various settings of the available computation load and the granularity of fuzzy partitions. Experimental results in this paper suggest that reported classification performance of MoGFS in the literature can be further improved using more computation load, more efficient EMO algorithms, and/or more antecedent fuzzy sets from finer fuzzy partitions.     

Fitness inheritance in multiple objective evolutionary algorithms: A test bench and real-world evaluation

In many real-world applications of evolutionary algorithms, the fitness of an individual has to be derived using complex models and time-consuming computations. Especially in the case of multiple objective optimisation problems, the time needed to evaluate these individuals increases exponentially with the number of objectives due to the ‘curse of dimensionality’ [J. Chen, D.E. Goldberg, S. Ho, K. Sastry, Fitness inheritance in multi-objective optimization, in: W.B. Langdon et al. (Eds.), GECCO 2002: Proceedings of the Genetic and Evolutionary Computation Conference, July 9–13, Morgan Kaufmann Publishers, New York, 2002, pp. 319–326]. This in turn leads to a slower convergence of the evolutionary algorithms. It is not feasible to use time-consuming models with large population sizes unless the time to evaluate the objective functions is reduced. Fitness inheritance is an efficiency enhancement technique that was originally proposed by Smith et al. [R.E. Smith, B.A. Dike, S.A. Stegmann, Fitness inheritance in genetic algorithms, in: Proceedings of the 1995 ACM Symposium on Applied Computing, February 26–28, ACM, Nashville, TN, USA, 1995] to improve the performance of genetic algorithms. Sastry et al. [K. Sastry, D.E. Goldberg, M. Pelikan, Don’t evaluate, inherit, in: L. Spector et al. (Eds.), GECCO 2001: Proceedings of the Genetic and Evolutionary Computation Conference, Morgan Kaufmann Publishers, San Francisco, 2001, pp. 551–558] and Chen et al. [J. Chen, D.E. Goldberg, S. Ho, K. Sastry, Fitness inheritance in multi-objective optimization, in: W.B. Langdon et al. (Eds.), GECCO 2002: Proceedings of the Genetic and Evolutionary Computation Conference, July 9–13, Morgan Kaufmann Publishers, New York, 2002, pp. 319–326] have developed analytical models for fitness inheritance. In this paper, the usefulness of fitness inheritance for a set of popular and separable multiple objective test functions as well as a non-separable real-world problem is evaluated based on unary performance measures testing closeness to the Pareto-optimal front, uniform distribution along and extent of the obtained Pareto front. A statistical evaluation of the performance of an NSGA-II like algorithm on the basis of these unary performance measures suggests that especially for non-convex or non-continuous problems the use of fitness inheritance negatively affects the closeness to the Pareto-optimal front.