An improved memetic algorithm using ring neighborhood topology for constrained optimization

This paper proposes an improved memetic algorithm relying on ring neighborhood topology for constrained optimization problems based on our previous work in Cai et al. (Soft Comput (in press), 2013). The main motivation of using ring neighborhood topology is to provide a good balance between effective exploration and efficient exploitation, which is a very important design issue for memetic algorithms. More specifically, a novel variant of invasive weed optimization (IWO) as the local refinement procedure is proposed in this paper. The proposed IWO variant adopts a neighborhood-based dispersal operator to achieve more fine-grained local search through the estimation of neighborhood fitness information relying on the ring neighborhood topology. Furthermore, a modified version of differential evolution (DE), known as “DE/current-to-best/1”, is integrated into the improved memetic algorithm with the aim of providing a more effective exploration. Performance of the improved memetic algorithm has been comprehensively tested on 13 well-known benchmark test functions and four engineering constrained optimization problems. The experimental results show that the improved memetic algorithm obtains greater competitiveness when compared with the original memetic approach Cai et al. in (Soft Comput (in press), 2013) and other state-of-the-art algorithms. The effectiveness of the modification of each component in the proposed approach is also discussed in the paper.     

求解约束优化问题的中心引力优化算法及其工程应用

为了平衡算法的全局探测能力和局部搜索能力,提出一种基于交叉与变异的中心引力优化算法用于求解约束优化问题。该算法首先利用佳点集方法构造初始种群以保证粒子的多样性。以一定概率随机选择粒子与当前最优粒子进行算术交叉操作,引导粒子向全局最优解靠拢。对当前最优粒子进行多样性变异以避免算法陷入局部最优。标准测试函数和工程优化应用问题的实验结果表明,新算法能有效求解不同的约束优化问题。     

动态分级中心引力约束优化算法及工程应用

结合非固定多段罚函数处理约束条件,提出一种动态分级中心引力优化算法用于求解约束优化问题。该算法利用佳点集初始化个体以保证种群的多样性。在每次迭代过程中将种群分为两个子种群,分别用于全局搜索和局部搜索,根据搜索阶段动态调整子种群个体数目。对几个标准的测试问题和工程优化问题进行数值实验,结果表明该算法能处理不同的约束优化问题。     

ε constrained differential evolution with pre-estimated comparison using gradient-based approximation for constrained optimization problems

Many real-world problems can be categorized as constrained optimization problems. So, designing effective algorithms for constrained optimization problems become more and more important. In designing algorithms, how to guide the individuals moving more efficiently towards the feasible region is one of the most important aspects on finding the optimum of constrained optimization problems. In this paper, we propose an improved ε constrained differential evolution, which combines with pre-estimated comparison gradient based approximation. The proposed algorithm uses gradient matrix to determine whether the trail vector generated by differential evolution algorithm is worth using the fitness function to evaluate it or not. Pre-estimated comparison gradient based approximation is used as a detector to find the promising offspring and in this way can we guide the individuals moving towards the feasible region. The proposed method is tested both on twenty-four benchmark functions and four well-known engineering optimization problems. Experimental results show that the proposed algorithm is highly competitive in comparing with other state-of-the-art algorithms. The proposed algorithm offers higher accuracy in engineering optimization problems for constrained optimization problems.     

A particle swarm optimization based memetic algorithm for dynamic optimization problems

Recently, there has been an increasing concern from the evolutionary computation community on dynamic optimization problems since many real-world optimization problems are dynamic. This paper investigates a particle swarm optimization (PSO) based memetic algorithm that hybridizes PSO with a local search technique for dynamic optimization problems. Within the framework of the proposed algorithm, a local version of PSO with a ring-shape topology structure is used as the global search operator and a fuzzy cognition local search method is proposed as the local search technique. In addition, a self-organized random immigrants scheme is extended into our proposed algorithm in order to further enhance its exploration capacity for new peaks in the search space. Experimental study over the moving peaks benchmark problem shows that the proposed PSO-based memetic algorithm is robust and adaptable in dynamic environments.     

A modified augmented Lagrangian with improved grey wolf optimization to constrained optimization problems

This paper presents a novel constrained optimization algorithm named MAL-IGWO, which integrates the benefit of the improved grey wolf optimization (IGWO) capability for discovering the global optimum with the modified augmented Lagrangian (MAL) multiplier method to handle constraints. In the proposed MAL-IGWO algorithm, the MAL method effectively converts a constrained problem into an unconstrained problem and the IGWO algorithm is applied to deal with the unconstrained problem. This algorithm is tested on 24 well-known benchmark problems and 3 engineering applications, and compared with other state-of-the-art algorithms. Experimental results demonstrate that the proposed algorithm shows better performance in comparison to other approaches.

     

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.     

AMA: a new approach for solving constrained real-valued optimization problems

Memetic algorithms (MA) have recently been applied successfully to solve decision and optimization problems. However, selecting a suitable local search technique remains a critical issue of MA, as this significantly affects the performance of the algorithms. This paper presents a new agent based memetic algorithm (AMA) for solving constrained real-valued optimization problems, where the agents have the ability to independently select a suitable local search technique (LST) from our designed set. Each agent represents a candidate solution of the optimization problem and tries to improve its solution through co-operation with other agents. Evolutionary operators consist of only crossover and one of the self-adaptively selected LSTs. The performance of the proposed algorithm is tested on five new benchmark problems along with 13 existing well-known problems, and the experimental results show convincing performance.     

求解约束优化问题的改进灰狼优化算法

针对基本灰狼优化(GWO)算法存在求解精度低、收敛速度慢、局部搜索能力差的问题,提出一种改进灰狼优化(IGWO)算法用于求解约束优化问题。该算法采用非固定多段映射罚函数法处理约束条件,将原约束优化问题转化为无约束优化问题,然后利用IGWO算法对转换后的无约束优化问题进行求解。在IGWO算法中,引入佳点集理论生成初始种群,为算法全局搜索奠定基础;为了提高局部搜索能力和加快收敛,对当前最优灰狼个体执行Powell局部搜索。采用几个标准约束优化测试问题进行仿真实验,结果表明该算法不仅克服了基本GWO的缺点,而且性能优于差分进化和粒子群优化算法。     

Multimodal optimization by artificial weed colonies enhanced with localized group search optimizers

Multimodal optimization aims at finding multiple global and local optima (as opposed to a single solution) of a function, so that the user can have a better knowledge about different optimal solutions in the search space and as and when needed, the current solution may be switched to another suitable one while still maintaining the optimal system performance. Evolutionary Algorithms (EAs) due to their population-based approach are able to detect multiple solutions within a population in a single simulation run and have a clear advantage over the classical optimization techniques, which need multiple restarts and multiple runs in the hope that a different solution may be discovered every run, with no guarantee however. This article proposes a hybrid two-stage optimization technique that firstly employs Invasive Weed Optimization (IWO), an ecologically inspired algorithm to find the promising Euclidean sub-regions surrounding multiple global and local optima. IWO is run for 80% of the total budget of function evaluations (FEs), and consecutively the search is intensified by using a modified Group Search Optimizer (GSO), in each detected sub-region. GSO, invoked in each sub-region discovered with IWO, is continued for 20% of the total budget of FEs. Both IWO and GSO have been modified from their original forms to meet the demands of the multimodal problems used in this work. Performance of the proposed algorithm is compared with a number of state-of-the-art multimodal optimization algorithms over a benchmark-suite comprising of 21 basic multimodal problems and 7 composite multimodal problems. A practical multimodal optimization problem concerning the design of dielectric composites has also been used to test the performance of the algorithm. Experimental results suggest that the proposed technique is able to provide better and more consistent performance over the existing well-known multimodal algorithms for majority of the test problems without incurring any serious computational burden.     

一种求解动态优化问题的免疫文化基因算法

针对传统免疫网络动态优化算法局部寻优能力弱、寻优精度低及易早熟收敛的缺点,提出一种求解动态优化问题的免疫文化基因算法。基于文化基因算法基本框架,将人工免疫网络算法作为全局搜索算法,采用禁忌搜索算法作为局部搜索算子;同时引入柯西变异加强算法的全局搜索能力,并有效防止早熟收敛。通过对经典动态优化函数测试集在相同条件下的实验表明,该免疫文化基因算法相较于其他同类算法具有较好的搜索精度和收敛速度。     

求解约束优化问题的改进果蝇优化算法及其工程应用

针对基本果蝇优化算法收敛速度慢、求解精度低、易于陷入局部极值以及算法候选解不能取负值等不足,提出一种用于解决约束优化问题的改进果蝇优化算法.该算法利用果蝇个体历史最佳记忆信息和种群全局历史最佳记忆信息构建多策略混合协同进化的搜索机制,以达到有效平衡算法的全局探索与局部开发的目的,同时也能够较好地避免算法的早熟收敛问题;...     

求解约束化工优化问题的混合布谷鸟搜索算法

针对布谷鸟搜索算法存在收敛速度慢和易陷入局部最优等缺陷,提出一种基于Rosenbrock搜索和柯西变异的混合布谷鸟搜索算法用于求解约束化工优化问题。该算法首先采用佳点集方法对鸟窝位置进行初始化,为全局搜索的多样性奠定基础;然后利用Rosenbrock搜索算法对当前最优位置进行局部搜索,以提高算法的收敛速度;最后对当前最优解进行柯西变异以避免算法陷入局部最优。两个约束化工优化问题的实验结果表明了该混合算法的有效性。     

动态分级的并行约束优化进化算法

提出一种动态分级的并行进化算法用于求解约束优化问题。该算法首先利用佳点集方法初始化种群。在进化过程中,将种群个体分为两个子种群,分别用于全局和局部搜索,并根据不同的搜索阶段动态调整各种级别中并行变量的数目。标准测试问题的实验结果表明了该算法的可行性和有效性。     

Multiobjective invasive weed optimization: Application to analysis of Pareto improvement models in electricity markets

This paper presents a proposal for multiobjective Invasive Weed Optimization (IWO) based on nondominated sorting of the solutions. IWO is an ecologically inspired stochastic optimization algorithm which has shown successful results for global optimization. In the present work, performance of the proposed nondominated sorting IWO (NSIWO) algorithm is evaluated through a number of well-known benchmarks for multiobjective optimization. The simulation results of the test problems show that this algorithm is comparable with other multiobjective evolutionary algorithms and is also capable of finding better spread of solutions in some cases. Next, the proposed algorithm is employed to study the Pareto improvement model in two complex electricity markets. First, the Pareto improvement solution set is obtained for a three-player oligopolistic electricity market with a nonlinear demand function. Then, the IEEE 30-bus power system with transmission constraints is considered, and the Pareto improvement solutions are found for the model with deterministic cost functions. In addition, NSIWO algorithm is used to analyze this system with stochastic cost data in a risk management problem which maximizes the expected total profit but minimizes the profit risk in the market.     

A hybrid differential evolution augmented Lagrangian method for constrained numerical and engineering optimization

We present a new hybrid method for solving constrained numerical and engineering optimization problems in this paper. The proposed hybrid method takes advantage of the differential evolution (DE) ability to find global optimum in problems with complex design spaces while directly enforcing feasibility of constraints using a modified augmented Lagrangian multiplier method. The basic steps of the proposed method are comprised of an outer iteration, in which the Lagrangian multipliers and various penalty parameters are updated using a first-order update scheme, and an inner iteration, in which a nonlinear optimization of the modified augmented Lagrangian function with simple bound constraints is implemented by a modified differential evolution algorithm. Experimental results based on several well-known constrained numerical and engineering optimization problems demonstrate that the proposed method shows better performance in comparison to the state-of-the-art algorithms.     

An interval space reducing method for constrained problems with particle swarm optimization

In this paper, we propose a method for solving constrained optimization problems using interval analysis combined with particle swarm optimization. A set inverter via interval analysis algorithm is used to handle constraints in order to reduce constrained optimization to quasi unconstrained one. The algorithm is useful in the detection of empty search spaces, preventing useless executions of the optimization process. To improve computational efficiency, a space cleaning algorithm is used to remove solutions that are certainly not optimal. As a result, the search space becomes smaller at each step of the optimization procedure. After completing pre-processing, a modified particle swarm optimization algorithm is applied to the reduced search space to find the global optimum. The efficiency of the proposed approach is demonstrated through comprehensive experimentation involving 100 000 runs on a set of well-known benchmark constrained engineering design problems. The computational efficiency of the new method is quantified by comparing its results with other PSO variants found in the literature.     

A memetic algorithm with adaptive hill climbing strategy for dynamic optimization problems

Dynamic optimization problems challenge traditional evolutionary algorithms seriously since they, once converged, cannot adapt quickly to environmental changes. This paper investigates the application of memetic algorithms, a class of hybrid evolutionary algorithms, for dynamic optimization problems. An adaptive hill climbing method is proposed as the local search technique in the framework of memetic algorithms, which combines the features of greedy crossover-based hill climbing and steepest mutation-based hill climbing. In order to address the convergence problem, two diversity maintaining methods, called adaptive dual mapping and triggered random immigrants, respectively, are also introduced into the proposed memetic algorithm for dynamic optimization problems. Based on a series of dynamic problems generated from several stationary benchmark problems, experiments are carried out to investigate the performance of the proposed memetic algorithm in comparison with some peer evolutionary algorithms. The experimental results show the efficiency of the proposed memetic algorithm in dynamic environments.     

Memetic algorithm with Preferential Local Search using adaptive weights for multi-objective optimization problems

Evolutionary multi-objective optimization algorithms are generally employed to generate Pareto optimal solutions by exploring the search space. To enhance the performance, exploration by global search can be complemented with exploitation by combining it with local search. In this paper, we address the issues in integrating local search with global search such as: how to select individuals for local search; how deep the local search is performed; how to combine multiple objectives into single objective for local search. We introduce a Preferential Local Search mechanism to fine tune the global optimal solutions further and an adaptive weight mechanism for combining multi-objectives together. These ideas have been integrated into NSGA-II to arrive at a new memetic algorithm for solving multi-objective optimization problems. The proposed algorithm has been applied on a set of constrained and unconstrained multi-objective benchmark test suite. The performance was analyzed by computing different metrics such as Generational distance, Spread, Max spread, and HyperVolume Ratio for the test suite functions. Statistical test applied on the results obtained suggests that the proposed algorithm outperforms the state-of-art multi-objective algorithms like NSGA-II and SPEA2. To study the performance of our algorithm on a real-world application, Economic Emission Load Dispatch was also taken up for validation. The performance was studied with the help of measures such as Hypervolume and Set Coverage Metrics. Experimental results substantiate that our algorithm has the capability to solve real-world problems like Economic Emission Load Dispatch and is able to produce better solutions, when compared with NSGA-II, SPEA2, and traditional memetic algorithms with fixed local search steps.     

Memetic algorithm using multi-surrogates for computationally expensive optimization problems

In this paper, we present a multi-surrogates assisted memetic algorithm for solving optimization problems with computationally expensive fitness functions. The essential backbone of our framework is an evolutionary algorithm coupled with a local search solver that employs multi-surrogate in the spirit of Lamarckian learning. Inspired by the notion of ‘blessing and curse of uncertainty’ in approximation models, we combine regression and exact interpolating surrogate models in the evolutionary search. Empirical results are presented for a series of commonly used benchmark problems to demonstrate that the proposed framework converges to good solution quality more efficiently than the standard genetic algorithm, memetic algorithm and surrogate-assisted memetic algorithms.