An improved global-best harmony search algorithm for faster optimization

In this paper, an improved global-best harmony search algorithm, named IGHS, is proposed. In the IGHS algorithm, initialization based on opposition-based learning for improving the solution quality of the initial harmony memory, a new improvisation scheme based on differential evolution for enhancing the local search ability, a modified random consideration based on artificial bee colony algorithm for reducing randomness of the global-best harmony search (GHS) algorithm, as well as two perturbation schemes for avoiding premature convergence, are integrated. In addition, two parameters of IGHS, harmony memory consideration rate and pitch adjusting rate, are dynamically updated based on a composite function composed of a linear time-varying function, a periodic function and a sign function in view of approximate periodicity of evolution in nature. Experimental results tested on twenty-eight benchmark functions indicate that IGHS is far better than basic harmony search (HS) algorithm and GHS. In further study, IGHS has also been compared with other eight well known metaheuristics. The results show that IGHS is better than or at least similar to those approaches on most of test functions.     

单纯形法的布谷鸟搜索算法及其在约束优化问题中的应用

为求解约束优化问题,针对布谷鸟搜索算法(CS)后期收敛速度慢,求解精度不高等不足,利用单纯形法局部搜索能力强的特点,提出了基于单纯形法的布谷鸟搜索算法(SMCS)。算法首先用CS算法进行全局搜索,再用单纯形法进行局部搜索。10个标准测试函数的实验结果表明,SMCS算法相对于CS算法有更强的寻优能力,再将算法用于求解减速器设计、伸缩绳设计、焊接条设计等约束优化问题。实验结果表明,CS算法和SMCS算法均能求出比其他文献更优的解,且SMCS算法求出的解更优、稳定性更强。     

Multiobjective cuckoo search for design optimization

Many design problems in engineering are typically multiobjective, under complex nonlinear constraints. The algorithms needed to solve multiobjective problems can be significantly different from the methods for single objective optimization. Computing effort and the number of function evaluations may often increase significantly for multiobjective problems. Metaheuristic algorithms start to show their advantages in dealing with multiobjective optimization. In this paper, we formulate a new cuckoo search for multiobjective optimization. We validate it against a set of multiobjective test functions, and then apply it to solve structural design problems such as beam design and disc brake design. In addition, we also analyze the main characteristics of the algorithm and their implications.     

An improved vector particle swarm optimization for constrained optimization problems

Increasing attention is being paid to solve constrained optimization problems (COP) frequently encountered in real-world applications. In this paper, an improved vector particle swarm optimization (IVPSO) algorithm is proposed to solve COPs. The constraint-handling technique is based on the simple constraint-preserving method. Velocity and position of each particle, as well as the corresponding changes, are all expressed as vectors in order to present the optimization procedure in a more intuitively comprehensible manner. The NVPSO algorithm [30], which uses one-dimensional search approaches to find a new feasible position on the flying trajectory of the particle when it escapes from the feasible region, has been proposed to solve COP. Experimental results showed that searching only on the flying trajectory for a feasible position influenced the diversity of the swarm and thus reduced the global search capability of the NVPSO algorithm. In order to avoid neglecting any worthy position in the feasible region and improve the optimization efficiency, a multi-dimensional search algorithm is proposed to search within a local region for a new feasible position. The local region is composed of all dimensions of the escaped particle’s parent and the current positions. Obviously, the flying trajectory of the particle is also included in this local region. The new position is not only present in the feasible region but also has a better fitness value in this local region. The performance of IVPSO is tested on 13 well-known benchmark functions. Experimental results prove that the proposed IVPSO algorithm is simple, competitive and stable.     

A novel global harmony search algorithm for task assignment problem

The objective of task assignment problem (TAP) is to minimize the sum of interprocessor communication and task processing costs for a distributed system which subjects to several resource constraints. We use a novel global harmony search algorithm (NGHS) to solve this problem, and the NGHS algorithm has demonstrated higher efficiency than the improved harmony search algorithm (IHS) on finding the near optimal task assignment. We also devise a new method called normalized penalty function method to tradeo^® the costs and the constraints. A large number of experiments show that our algorithm performs well on finding the near optimal task assignment, and it is a viable approach for the task assignment problem.     

Improving a model for the dynamic modulus of asphalt using the modified harmony search algorithm

We report the improvement of a dynamic modulus model using a modified harmony search (MHS) algorithm to describe the resistance to rutting and fatigue cracking of asphalt concrete mixtures. The MHS algorithm was reformulated to improve the harmony search (HS) algorithm by introducing minimum and maximum bandwidths. Using the MHS algorithm, model parameters for lime-modified asphalt concrete mixtures were extracted and a good fit to the dynamic modulus data obtained from laboratory tests was achieved.     

A coevolutionary differential evolution with harmony search for reliability-redundancy optimization

Solving reliability-redundancy optimization problems via meta-heuristic algorithms has attracted increasing attention in recent years. In this paper, an effective coevolutionary differential evolution with harmony search algorithm (CDEHS) is proposed to solve the reliability-redundancy optimization problem by dividing the problem into a continuous part and an integer part. In CDEHS, two populations evolve simultaneously and cooperatively, where one population for the continuous part evolves by means of differential evolution while another population for the integer part evolves by means of harmony search. After half of the whole evolving process, the integer part stops evolving and provides the best solution to the other part for further evolving with differential evolution. Simulations results based on three typical problems and comparisons with some existing algorithms show that the proposed CDEHS is effective, efficient and robust for solving the reliability-redundancy optimization problem.     

BSTBGA: A hybrid genetic algorithm for constrained multi-objective optimization problems

Most of the existing multi-objective genetic algorithms were developed for unconstrained problems, even though most real-world problems are constrained. Based on the boundary simulation method and trie-tree data structure, this paper proposes a hybrid genetic algorithm to solve constrained multi-objective optimization problems (CMOPs). To validate our approach, a series of constrained multi-objective optimization problems are examined, and we compare the test results with those of the well-known NSGA-II algorithm, which is representative of the state of the art in this area. The numerical experiments indicate that the proposed method can clearly simulate the Pareto front for the problems under consideration.     

A restarted and modified simplex search for unconstrained optimization

In this paper we propose a simple but efficient modification of the well-known Nelder–Mead (NM) simplex search method for unconstrained optimization. Instead of moving all n simplex vertices at once in the direction of the best vertex, our “shrink” step moves them in the same direction but one by one until an improvement is obtained. In addition, for solving non-convex problems, we simply restart the so-modified NM (MNM) method by constructing an initial simplex around the solution obtained in the previous phase. We repeat restarts until there is no improvement in the objective function value. Thus, our restarted modified NM (RMNM) is a descent and deterministic method and may be seen as an extended local search for continuous optimization. In order to improve computational complexity and efficiency, we use the heap data structure for storing and updating simplex vertices. Extensive empirical analysis shows that: our modified method outperforms in average the original version as well as some other recent successful modifications; in solving global optimization problems, it is comparable with the state-of-the-art heuristics.     

Biogeography-based optimization for constrained optimization problems

Biogeography-based optimization (BBO) has been recently proposed as a viable stochastic optimization algorithm and it has so far been successfully applied in a variety of fields, especially for unconstrained optimization problems. The present paper shows how BBO can be applied for constrained optimization problems, where the objective is to find a solution for a given objective function, subject to both inequality and equality constraints.     

Discrete cost optimization of composite floor system using social harmony search model

This paper presents a social harmony search algorithm model for the cost optimization of composite floor system with discrete variables. The total cost function includes the costs of concrete, steel beam and shear studs. The design is based on AISC load and resistance factor design specifications and plastic design concepts. Here, six decision variables are considered for the objective function. In order to demonstrate the capabilities of the proposed model in optimizing composite floor system designs, two design examples taken from the literature are studied. It is shown that use of the presented model results in significant cost saving. Hence, it can be of practical value to structural designers. Also the proposed model is compared to the original harmony search, its recently developed variants, and other meta-heuristic algorithms to illustrate the superiority of the present method in convergence and leading to better solutions. In order to investigate the effects of beam spans and loadings on the cost optimization of composite floor system a parametric study is also conducted.     

Tournament-based harmony search algorithm for non-convex economic load dispatch problem

This paper proposes a tournament-based harmony search (THS) algorithm for economic load dispatch (ELD) problem. The THS is an efficient modified version of the harmony search (HS) algorithm where the random selection process in the memory consideration operator is replaced by the tournament selection process to activate the natural selection of the survival-of-the-fittest principle and thus improve the convergence properties of HS. The performance THS is evaluated with ELD problem using five different test systems: 3-units generator system; two versions of 13-units generator system; 40-units generator system; and large-scaled 80-units generator system. The effect of tournament size (t) on the performance of THS is studied. A comparative evaluation between THS and other existing methods reported in the literature are carried out. The simulation results show that the THS algorithm is capable of achieving better quality solutions than many of the well-popular optimization methods.     

Co-evolutionary particle swarm optimization to solve constrained optimization problems

This paper presents a co-evolutionary particle swarm optimization (CPSO) algorithm to solve global nonlinear optimization problems. A new co-evolutionary PSO (CPSO) is constructed. In the algorithm, a deterministic selection strategy is proposed to ensure the diversity of population. Meanwhile, based on the theory of extrapolation, the induction of evolving direction is enhanced by adding a co-evolutionary strategy, in which the particles make full use of the information each other by using gene-adjusting and adaptive focus-varied tuning operator. Infeasible degree selection mechanism is used to handle the constraints. A new selection criterion is adopted as tournament rules to select individuals. Also, the infeasible solution is properly accepted as the feasible solution based on a defined threshold of the infeasible degree. This diversity mechanism is helpful to guide the search direction towards the feasible region. Our approach was tested on six problems commonly used in the literature. The results obtained are repeatedly closer to the true optimum solution than the other techniques.     

改进的蚁群算法求解连续函数约束优化问题

对基本蚁群算法框架进行了改进,采用轮盘赌选择代替了基本框架中通过启发式函数和信息素选择路径,同时对信息素的更新方式也做出调整,提出了一种新的蚁群算法,使得其更适合解决连续函数问题.将这种改进的蚁群算法应用于带有约束条件的连续函数问题中,在典型实例中进行仿真测试,实验结果表明,提出的改进蚁群算法可以很好地解决带有约束条件的连续函数问题,并能迅速找到最优解.     

混合变邻域和声搜索的独立任务调度问题研究

结合和声搜索和变邻域搜索算法的特点,提出混合的和声变邻域搜索算法,并将混合算法用于解决多处理机独立任务调度问题.混合算法采用列表调度方法对和声解进行编码,把和声分量转换为基于优先级的独立任务调度模型,利用变邻域搜索算法对和声解进行局部搜索以提高和声算法的搜索效率和解质量,利用模拟退火算法中的Metropolis准则作为新解接受准则,防止算法陷入局部极值.仿真实验对比结果表明,混合算法在解决独立任务的多处理机调度中具有更强的全局搜索能力和更快的收敛速度,并且能够跳出局部极小获得更高质量的解.     

Gaussian variable neighborhood search for continuous optimization

Variable Neighborhood Search (VNS) has shown to be a powerful tool for solving both discrete and box-constrained continuous optimization problems. In this note we extend the methodology by allowing also to address unconstrained continuous optimization problems.Instead of perturbing the incumbent solution by randomly generating a trial point in a ball of a given metric, we propose to perturb the incumbent solution by adding some noise, following a Gaussian distribution. This way of generating new trial points allows one to give, in a simple and intuitive way, preference to some directions in the search space, or, contrarily, to treat uniformly all directions. Computational results show some advantages of this new approach.     

折半查找算法在最优化问题中的应用

折半查找是一种常见的静态查找方法,在特定的、有序的查找区间内,通过折半方式不断地缩小查找区间,将区间中间位置的元素与给定元素加以比较,最终确定查找结果.在此传统折半查找基础上,总结了一种抽象化的改进方法,并将此改进后的折半查找算法应用于最优化问题的求解.     

A trust-region algorithm combining line search filter technique for nonlinear constrained optimization

In this paper, we propose a trust-region algorithm in association with line search filter technique for solving nonlinear equality constrained programming. At current iteration, a trial step is formed as the sum of a normal step and a tangential step which is generated by trust-region subproblem and the step size is decided by interior backtracking line search together with filter methods. Then, the next iteration is determined. This is different from general trust-region methods in which the next iteration is determined by the ratio of the actual reduction to the predicted reduction. The global convergence analysis for this algorithm is presented under some reasonable assumptions and the preliminary numerical results are reported.     

基于Powell局部搜索策略的全局优化布谷鸟算法

为了解决布谷鸟搜索算法后期收敛速度慢、求解精度不高、易陷入局部最优等缺陷,提出了一种基于Powell局部搜索策略的全局优化布谷鸟搜索算法.算法将布谷鸟全局搜索能力与Powell方法的局部寻优性能有机地结合,并根据适应度值逐步构建精英种群候选解池在迭代后期牵引Powell搜索的局部优化,在保证求解速度、尽可能找到全局极值点的同时提高算法的求解精度.对52个典型测试函数实验结果表明,该算法相比于传统的布谷鸟搜索算法不仅寻优精度和寻优率有所提高,并且适应能力强、鲁棒性好,与最新提出的其他改进算法相比也具有一定的竞争优势.     

求解函数优化问题的改进布谷鸟搜索算法

为了提高布谷鸟搜索算法求解函数优化问题的求精能力和收敛速度,提出了一种基于自适应机制的改进算法.自适应机制用于控制缩放因子和发现概率,以提高种群的多样性,避免早熟,从而使更多的个体参与演化,达到提高求精能力和收敛速度的效果.仿真实验结果表明,与标准的布谷鸟搜索算法相比,基于自适应机制缩放因子的改进算法(rCS)和基于自适应机制发现概率的改进算法(paCS)在求精能力和收敛速度上都有明显的提高;同时具有自适应缩放因子和自适应发现概率的改进算法(iCS)比rCS和paCS具有更优的求精能力和收敛速度.