Orthogonal Methods Based Ant Colony Search for Solving Continuous Optimization Problems

Research into ant colony algorithms for solving continuous optimization problems forms one of the most significant and promising areas in swarm computation. Although traditional ant algorithms are designed for combinatorial optimization, they have shown great potential in solving a wide range of optimization problems, including continuous optimization. Aimed at solving continuous problems effectively, this paper develops a novel ant algorithm termed ＂continuous orthogonal ant colony＂ （COAC）, whose pheromone deposit mechanisms would enable ants to search for solutions collaboratively and effectively. By using the orthogonal design method, ants in the feasible domain can explore their chosen regions rapidly and efficiently. By implementing an ＂adaptive regional radius＂ method, the proposed algorithm can reduce the probability of being trapped in local optima and therefore enhance the global search capability and accuracy. An elitist strategy is also employed to reserve the most valuable points. The performance of the COAC is compared with two other ant algorithms for continuous optimization -API and CACO by testing seventeen functions in the continuous domain. The results demonstrate that the proposed COAC algorithm outperforms the others.     

Combinations of Estimation of Distribution Algorithms and Other Techniques

This paper summaries our recent work on combining estimation of distribution algorithms (EDA) and other techniques for solving hard search and optimization problems:a) guided mutation,an offspring generator in which the ideas from EDAs and genetic algorithms are combined together,we have shown that an evolutionary algorithm with guided mutation outperforms the best GA for the maximum clique problem,b)evolutionary algorithms refining a heuristic,we advocate a strategy for solving a hard optimization problem with complicated data structure,and c) combination of two different local search techniques and EDA for numerical global optimization problems,its basic idea is that not all the new generated points are needed to be improved by an expensive local search.     

SSTT: Efficient local search for GSI global routing

In this paper, a novel global routing algorithm is presented for congestion opti-mization based on efficient local search, named SSTT (search space traversing technology). This method manages to traverse the whole search space. A hybrid optimization strategy is adopted,consisting of three optimization sub-strategies: stochastic optimization, deterministic optimiza-tion and local enumeration optimization, to dynamically reconstruct the problem structure. Thus,“transition” can be made from a local minimum point to reach other parts of the search space,traverse the whole search space, and obtain the global (approximate) optimal routing solution.Since any arbitrary initial routing solution can be used as the start point of the search, the initial-ization in SSTT algorithm is greatly simplified. SSTT algorithm has been tested on both MCNC benchmark circuits and industrial circuits, and the experimental results were compared with those of typical existing algorithms. The experimental results show that SSTT algorithm can obtain the global (approximate) optimal routing solution easily and quickly. Moreover, it can meet the needs of practical applications. The SSTT global routing algorithm gives a general-purpose routing solution.     

具有适应性突变和惯性权重的粒子群优化(PSO)算法及其在动态系统参数估计中的应用

An important problem in engineering is the unknown parameters estimation in nonlinear systems. In this paper, a novel adaptive particle swarm optimization (APSO) method is proposed to solve this problem. This work considers two new aspects, namely an adaptive mutation mechanism and a dynamic inertia weight into the conventional particle swarm optimization (PSO) method. These mechanisms are employed to enhance global search ability and to increase accuracy. First, three well-known benchmark functions namely Griewank, Rosenbrock and Rastrigrin are utilized to test the ability of a search algorithm for identifying the global optimum. The performance of the proposed APSO is compared with advanced algorithms such as a nonlinearly decreasing weight PSO (NDWPSO) and a real-coded genetic algorithm (GA), in terms of parameter accuracy and convergence speed. It is confirmed that the proposed APSO is more successful than other aforementioned algorithms. Finally, the feasibility of this algorithm is demonstrated through estimating the parameters of two kinds of highly nonlinear systems as the case studies.     

An improved fireworks algorithm for the capacitated vehicle routing problem

The capacitated vehicle routing problem (CVRP), which aims at minimizing travel costs, is a wellknown NP-hard combinatorial optimization. Owing to its hardness, many heuristic search algorithms have been proposed to tackle this problem. This paper explores a recently proposed heuristic algorithm named the fireworks algorithm (FWA), which is a swarm intelligence algorithm. We adopt FWA for the combinatorial CVRP problem with several modifications of the original FWA: it employs a new method to generate "sparks" according to the selection rule, and it uses a new method to determine the explosion amplitude for each firework. The proposed algorithm is compared with several heuristic search methods on some classical benchmark CVRP instances. The experimental results show a promising performance of the proposed method. We also discuss the strengths and weaknesses of our algorithm in contrast to traditional algorithms.     

An optimization algorithm employing multiple metamodels and optimizers

Modern engineering design optimization often relies on computer simulations to evaluate candidate designs, a setup which results in expensive black-box optimization problems. Such problems introduce unique challenges, which has motivated the application of metamodel-assisted computational intelligence algorithms to solve them. Such algorithms combine a computational intelligence optimizer which employs a population of candidate solutions, with a metamodel which is a computationally cheaper approximation of the expensive computer simulation. However, although a variety of metamodels and optimizers have been proposed, the optimal types to employ are problem dependant. Therefore, a priori prescribing the type of metamodel and optimizer to be used may degrade its effectiveness. Leveraging on this issue, this study proposes a new computational intelligence algorithm which autonomously adapts the type of the metamodel and optimizer during the search by selecting the most suitable types out of a family of candidates at each stage. Performance analysis using a set of test functions demonstrates the effectiveness of the proposed algorithm, and highlights the merit of the proposed adaptation approach.     

An evolutionary multiobjective method based on dominance and decomposition for feature selection in classification

Feature selection in classification can be considered a multiobjective problem with the objectives of increasing classification accuracy and decreasing the size of the selected feature subset. Dominance-based and decomposition-based multiobjective evolutionary algorithms(MOEAs) have been extensively used to address the feature selection problem due to their strong global search capability. However, most of them face the problem of not effectively balancing convergence and diversity during the ev...     

New Meta-Heuristic for Combinatorial Optimization Problems: Intersection Based Scaling

Combinatorial optimization problems are found in many application fields such as computer science,engineering and economy. In this paper, a new efficient meta-heuristic, Intersection-Based Scaling (IBS for abbreviation), is proposed and it can be applied to the combinatorial optimization problems. The main idea of IBS is to scale the size of the instance based on the intersection of some local optima, and to simplify the search space by extracting the intersection from the instance, which makes the search more efficient. The combination of IBS with some local search heuristics of different combinatorial optimization problems such as Traveling Salesman Problem (TSP) and Graph Partitioning Problem (GPP) is studied, and comparisons are made with some of the best heuristic algorithms and meta-heuristic algorithms. It is found that it has significantly improved the performance of existing local search heuristics and significantly outperforms the known best algorithms.     

Evolutionary multi-objective portfolio optimization in practical context

This paper addresses evolutionary multi-objective portfolio optimization in the practical context by incorporating realistic constraints into the problem model and preference criterion into the optimization search process. The former is essential to enhance the realism of the classical mean-variance model proposed by Harry Markowitz, since portfolio managers often face a number of realistic constraints arising from business and industry regulations, while the latter reflects the fact that portfolio managers are ultimately interested in specific regions or points along the efficient frontier during the actual execution of their investment orders. For the former, this paper proposes an order-based representation that can be easily extended to handle various realistic constraints like floor and ceiling constraints and cardinality constraint. An experimental study, based on benchmark problems obtained from the OR-library, demonstrates its capability to attain a better approximation of the efficient frontier in terms of proximity and diversity with respect to other conventional representations. The experimental results also illustrated its viability and practicality in handling the various realistic constraints. A simple strategy to incorporate preferences into the multi-objective optimization process is highlighted and the experimental study demonstrates its capability in driving the evolutionary search towards specific regions of the efficient frontier.     

Dynamic PSO method for nonlinear constrained programming problems

A new approach is presented to solve the nonlinear constrained programming problems. Firstly, the nonlinear constrained programming problem is transformed into a bi-ohjective optimization problem. Based on the reasonable design of the searching operation and different parameters, a new dynamic particle swarm optimization algorithm （TS-MC） is proposed. The numerical experiments show that the proposed algorithm is effective in dealing with the nonlinear constrained programming problems.     

A parallel boundary search particle swarm optimization algorithm for constrained optimization problems

During the past decade, considerable research has been conducted on constrained optimization problems (COPs) which are frequently encountered in practical engineering applications. By introducing resource limitations as constraints, the optimal solutions in COPs are generally located on boundaries of feasible design space, which leads to search difficulties when applying conventional optimization algorithms, especially for complex constraint problems. Even though penalty function method has been frequently used for handling the constraints, the adjustment of control parameters is often complicated and involves a trial-and-error approach. To overcome these difficulties, a modified particle swarm optimization (PSO) algorithm named parallel boundary search particle swarm optimization (PBSPSO) algorithm is proposed in this paper. Modified constrained PSO algorithm is adopted to conduct global search in one branch while Subset Constrained Boundary Narrower (SCBN) function and sequential quadratic programming (SQP) are applied to perform local boundary search in another branch. A cooperative mechanism of the two branches has been built in which locations of the particles near boundaries of constraints are selected as initial positions of local boundary search and the solutions of local boundary search will lead the global search direction to boundaries of active constraints. The cooperation behavior of the two branches effectively reinforces the optimization capability of the PSO algorithm. The optimization performance of PBSPSO algorithm is illustrated through 13 CEC06 test functions and 5 common engineering problems. The results are compared with other state-of-the-art algorithms and it is shown that the proposed algorithm possesses a competitive global search capability and is effective for constrained optimization problems in engineering applications.     

采用不可微精确罚函数的约束优化演化算法

针对多数已有的采用罚函数的约束优化遗传算法存在优化效果差的问题 ,提出了一种新的求解约束优化问题的演化算法 .借助不可微精确罚函数把约束问题转化为单个无约束问题来处理 .采用混合杂交和间歇变异来提高算法的搜索能力 .数值实验结果表明了新算法的优化效果远远优于已有的几种采用罚函数的遗传算法     

修正免疫克隆约束多目标优化算法

针对约束多目标优化问题,提出修正免疫克隆约束多目标优化算法.该算法通过引进一个约束处理策略,用一个修正算法对个体的目标函数值进行修正,并对修正后的目标函数值采用免疫克隆算法进行优化,用一个精英种群对可行非支配解进行存储.该算法在优化过程中,既保留了非支配可行解,也充分利用了约束偏离值小的非可行解,同时引进整体克隆策略来提高解分布的多样性.通过对约束多目标问题的各项性能指标的测试以及和对比算法的比较可以看出:该算法在处理约束多目标优化测试问题时,所得解的多样性得到了一定的提高.同时,解的收敛性和均匀性也得到了一定的改进.     

Artificial bee colony algorithm for large-scale problems and engineering design optimization

Engineering design problems are generally large scale or nonlinear or constrained optimization problems. The Artificial Bee Colony (ABC) algorithm is a successful tool for optimizing unconstrained problems. In this work, the ABC algorithm is used to solve large scale optimization problems, and it is applied to engineering design problems by extending the basic ABC algorithm simply by adding a constraint handling technique into the selection step of the ABC algorithm in order to prefer the feasible regions of entire search space. Nine well-known large scale unconstrained test problems and five well-known constrained engineering problems are solved by using the ABC algorithm and the performance of ABC algorithm is compared against those of state-of-the-art algorithms.     

A new algorithm inspired in the behavior of the social-spider for constrained optimization

During the past decade, solving constrained optimization problems with swarm algorithms has received considerable attention among researchers and practitioners. In this paper, a novel swarm algorithm called the Social Spider Optimization (SSO-C) is proposed for solving constrained optimization tasks. The SSO-C algorithm is based on the simulation of cooperative behavior of social-spiders. In the proposed algorithm, individuals emulate a group of spiders which interact to each other based on the biological laws of the cooperative colony. The algorithm considers two different search agents (spiders): males and females. Depending on gender, each individual is conducted by a set of different evolutionary operators which mimic different cooperative behaviors that are typically found in the colony. For constraint handling, the proposed algorithm incorporates the combination of two different paradigms in order to direct the search towards feasible regions of the search space. In particular, it has been added: (1) a penalty function which introduces a tendency term into the original objective function to penalize constraint violations in order to solve a constrained problem as an unconstrained one; (2) a feasibility criterion to bias the generation of new individuals toward feasible regions increasing also their probability of getting better solutions. In order to illustrate the proficiency and robustness of the proposed approach, it is compared to other well-known evolutionary methods. Simulation and comparisons based on several well-studied benchmarks functions and real-world engineering problems demonstrate the effectiveness, efficiency and stability of the proposed method.     

A Generic Framework for Constrained Optimization Using Genetic Algorithms

In this paper, we propose a generic, two-phase framework for solving constrained optimization problems using genetic algorithms. In the first phase of the algorithm, the objective function is completely disregarded and the constrained optimization problem is treated as a constraint satisfaction problem. The genetic search is directed toward minimizing the constraint violation of the solutions and eventually finding a feasible solution. A linear rank-based approach is used to assign fitness values to the individuals. The solution with the least constraint violation is archived as the elite solution in the population. In the second phase, the simultaneous optimization of the objective function and the satisfaction of the constraints are treated as a biobjective optimization problem. We elaborate on how the constrained optimization problem requires a balance of exploration and exploitation under different problem scenarios and come to the conclusion that a nondominated ranking between the individuals will help the algorithm explore further, while the elitist scheme will facilitate in exploitation. We analyze the proposed algorithm under different problem scenarios using Test Case Generator-2 and demonstrate the proposed algorithm's capability to perform well independent of various problem characteristics. In addition, the proposed algorithm performs competitively with the state-of-the-art constraint optimization algorithms on 11 test cases which were widely studied benchmark functions in literature.     

求解约束优化问题的自适应人工蜂群算法

针对约束优化问题，提出一种自适应人工蜂群算法。算法采用反学习初始化方法使初始种群均匀分布于搜索空间。为了平衡搜索过程中可行个体和不可行个体的数量，算法使用自适应选择策略。在跟随蜂阶段，采用最优引导搜索方程来增强算法的开采能力。通过对13个标准测试问题进行实验并与其他算法比较，发现自适应人工蜂群算法具有较强的寻优能力和较好的稳定性。     

面向复杂约束优化问题的进化算法综述

约束优化是多数实际工程应用优化问题的呈现方式.进化算法由于其高效的表现,近年来被广泛应用于约束优化问题求解.但约束条件使得问题解空间离散、缩小、改变,给进化算法求解约束优化问题带来极大挑战.在此背景下,融合约束处理技术的进化算法成为研究热点.此外,随着研究的深入,近年来约束处理技术在复杂工程应用问题优化中得到了广泛发展,例如多目标、高维、等式优化等.根据复杂性的缘由,将面向复杂约束优化问题的进化优化分为面向复杂目标的进化约束优化算法和面向复杂约束场景的进化算法两种类别进行综述,其中,重点探讨了实际工程应用的复杂性对约束处理技术的挑战和目前研究的最新进展,并最后总结了未来的研究趋势与挑战.     

一种新型约束多目标帝国竞争算法

针对约束多目标优化问题，提出了一种基于约束违背程度和Pareto支配的有效约束处理策略，并设计了一种新型多目标帝国竞争算法（MOICA）.该算法采用一种简化的初始帝国构建过程，在同化过程引入了向外部档案内非劣解学习的机制，并基于帝国势力新定义的帝国竞争新方法以获取问题高质量的解.选用了7个测试问题CF1~CF7进行计算实验并和多种算法进行对比.计算结果表明， MOICA在求解约束多目标优化问题方面具有较强的搜索能力和优势.     

A Multiobjective Optimization-Based Evolutionary Algorithm for Constrained Optimization

A considerable number of constrained optimization evolutionary algorithms (COEAs) have been proposed due to increasing interest in solving constrained optimization problems (COPs) by evolutionary algorithms (EAs). In this paper, we first review existing COEAs. Then, a novel EA for constrained optimization is presented. In the process of population evolution, our algorithm is based on multiobjective optimization techniques, i.e., an individual in the parent population may be replaced if it is dominated by a nondominated individual in the offspring population. In addition, three models of a population-based algorithm-generator and an infeasible solution archiving and replacement mechanism are introduced. Furthermore, the simplex crossover is used as a recombination operator to enrich the exploration and exploitation abilities of the approach proposed. The new approach is tested on 13 well-known benchmark functions, and the empirical evidence suggests that it is robust, efficient, and generic when handling linear/nonlinear equality/inequality constraints. Compared with some other state-of-the-art algorithms, our algorithm remarkably outperforms them in terms of the best, mean, and worst objective function values and the standard deviations. It is noteworthy that our algorithm does not require the transformation of equality constraints into inequality constraints