Self-adaptive check and repair operator-based particle swarm optimization for the multidimensional knapsack problem

The multidimensional knapsack problem (MKP) is a combinatorial optimization problem belonging to the class of NP-hard problems. This study proposes a novel self-adaptive check and repair operator (SACRO) combined with particle swarm optimization (PSO) to solve the MKP. The traditional check and repair operator (CRO) uses a unique pseudo-utility ratio, whereas SACRO dynamically and automatically changes the alternative pseudo-utility ratio as the PSO algorithm runs. Two existing PSO algorithms are used as the foundation to support the novel SACRO methods, the proposed SACRO-based algorithms were tested using 137 benchmark problems from the OR-Library to validate and demonstrate the efficiency of SACRO idea. The results were compared with those of other population-based algorithms. Simulation and evaluation results show that SACRO is more competitive and robust than the traditional CRO. The proposed SACRO-based algorithms rival other state-of-the-art PSO and other algorithms. Therefore, changing different types of pseudo-utility ratios produces solutions with better results in solving MKP. Moreover, SACRO can be combined with other population-based optimization algorithms to solve constrained optimization problems.     

A comparative study of the improvement of performance using a PSO modified by ACO applied to TSP

Swarm-inspired optimization has become very popular in recent years. Particle swarm optimization (PSO) and Ant colony optimization (ACO) algorithms have attracted the interest of researchers due to their simplicity, effectiveness and efficiency in solving complex optimization problems. Both ACO and PSO were successfully applied for solving the traveling salesman problem (TSP). Performance of the conventional PSO algorithm for small problems with moderate dimensions and search space is very satisfactory. As the search, space gets more complex, conventional approaches tend to offer poor solutions. This paper presents a novel approach by introducing a PSO, which is modified by the ACO algorithm to improve the performance. The new hybrid method (PSO–ACO) is validated using the TSP benchmarks and the empirical results considering the completion time and the best length, illustrate that the proposed method is efficient.     

A novel combination of Particle Swarm Optimization and Genetic Algorithm for Pareto optimal design of a five-degree of freedom vehicle vibration model

In this paper, at first, a novel combination of Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) is introduced. This hybrid algorithm uses the operators such as mutation, traditional or classical crossover, multiple-crossover, and PSO formula. The selection of these operators in each iteration for each particle or chromosome is based on a fuzzy probability. The performance of the proposed hybrid algorithm for solving both single and multi-objective optimization problems is challenged by using of some well-known benchmark problems. Obtained numerical results are compared with those of other optimization algorithms. At the end, the proposed multi-objective hybrid algorithm is used for the Pareto optimal design of a five-degree of freedom vehicle vibration model. The comparison of the obtained results with it in the literature demonstrates the superiority of this work.     

A DAG scheduling scheme on heterogeneous computing systems using double molecular structure-based chemical reaction optimization

A new meta-heuristic method, called Chemical Reaction Optimization (CRO), has been proposed very recently. The method encodes solutions as molecules and mimics the interactions of molecules in chemical reactions to search the optimal solutions. The CRO method has demonstrated its capability in solving NP-hard optimization problems. In this paper, the CRO scheme is used to formulate the scheduling of Directed Acyclic Graph (DAG) jobs in heterogeneous computing systems, and a Double Molecular Structure-based Chemical Reaction Optimization (DMSCRO) method is developed. There are two molecular structures in DMSCRO: one is used to encode the execution order of the tasks in a DAG job, and the other to encode the task-to-computing-node mapping. The DMSCRO method also designs four elementary chemical reaction operations and the fitness function suitable for the scenario of DAG scheduling. In this paper, we have also conducted the simulation experiments to verify the effectiveness and efficiency of DMSCRO over a large set of randomly generated graphs and the graphs for real-world problems.     

实值化学反应优化算法

化学反应优化（CRO）是近年来提出的一个基于种群的元启发式算法,而实数编码化学反应优化（RCCRO）是CRO的一个变体,针对该算法存在的不足提出了一个新的实值化学反应优化（RVCRO）算法求解全局数值优化问题。该算法改进了传统CRO的框架和搜索模式,将控制参数从8个减少到5个;采用一组常用的基准函数来测试其性能,比较结果表明,该算法在最终误差值和收敛速度方面,性能有较大提升。     

A hybrid multi-objective PSO–EDA algorithm for reservoir flood control operation

Reservoir flood control operation (RFCO) is a complex multi-objective optimization problem (MOP) with interdependent decision variables. Traditionally, RFCO is modeled as a single optimization problem by using a certain scalar method. Few works have been done for solving multi-objective RFCO (MO-RFCO) problems. In this paper, a hybrid multi-objective optimization approach named MO-PSO–EDA which combines the particle swarm optimization (PSO) algorithm and the estimation of distribution algorithm (EDA) is developed for solving the MO-RFCO problem. MO-PSO–EDA divides the particle population into several sub-populations and builds probability models for each of them. Based on the probability model, each sub-population reproduces new offspring by using PSO based and EDA methods. In the PSO based method, a novel global best position selection method is designed. With the help of the EDA based reproduction, the algorithm can lean linkage between decision variables and hence have a good capability of solving complex multi-objective optimization problems, such as the MO-RFCO problem. Experimental studies on six benchmark problems and two typical multi-objective flood control operation problems of Ankang reservoir have indicated that the proposed MO-PSO–EDA performs as well as or superior to the other three competitive multi-objective optimization algorithms. MO-PSO–EDA is suitable for solving MO-RFCO problems.     

基于模糊物元PSO混合优化算法的客户创意挖掘*

针对具有模糊性、缺乏系统性和主题性的新产品开发模糊前端客户创意,提出一种基于模糊物元和改进微粒群算法的混合启发式挖掘方法。首先将模糊理论引入物元分析,将客户的个性化要求、特征及相应的模糊量值结合起来建立其形式化模糊物元模型, 应用模糊物元优化方法将客户多需求优化问题转换为单需求优化问题;然后给出了最优客户创意的自适应变异微粒群（AMPSO）算法的求解方法,并与遗传算法加以比较,证明该算法的有效性和先进性。最后将该算法应用于某型号汽车外观造型设计的客户创意挖掘中,有效指导了产品创新的实施。     

基于混沌搜索的粒子群优化算法

粒子群优化算法(PSO)是一种有效的随机全局优化技术。文章把混沌优化搜索技术引入到PSO算法中,提出了基于混沌搜索的粒子群优化算法。该算法保持了PSO算法结构简单的特点,改善了PSO算法的全局寻优能力,提高的算法的收敛速度和计算精度。仿真计算表明,该算法的性能优于基本PSO算法。     

Chemical reaction optimization with greedy strategy for the 0–1 knapsack problem

The 0–1 knapsack problem (KP01) is a well-known combinatorial optimization problem. It is an NP-hard problem which plays important roles in computing theory and in many real life applications. Chemical reaction optimization (CRO) is a new optimization framework, inspired by the nature of chemical reactions. CRO has demonstrated excellent performance in solving many engineering problems such as the quadratic assignment problem, neural network training, multimodal continuous problems, etc. This paper proposes a new chemical reaction optimization with greedy strategy algorithm (CROG) to solve KP01. The paper also explains the operator design and parameter turning methods for CROG. A new repair function integrating a greedy strategy and random selection is used to repair the infeasible solutions. The experimental results have proven the superior performance of CROG compared to genetic algorithm (GA), ant colony optimization (ACO) and quantum-inspired evolutionary algorithm (QEA).     

求解优化问题的混合PSO-Solver算法

融合了粒子群算法(PSO) 和Solver 加载宏,形成混合PSO-Solver算法进行优化问题的求解。PSO作为全局搜索算法首先给出问题的全局可行解,Solver则是基于梯度信息的局部搜索工具,对粒子群算法得出的解再进行改进,二者互相结合,既加快了全局搜索的速度,又有效地避免了陷入局部最优。算法用VBA语言进行编程,简单且易于实现。通过对无约束优化问题和约束优化问题的求解,以及和标准PSO、其他一些混合算法的比较表明,PSO-Solver算法能够有效地提高求解过程的收敛速度和解的精确性。     

一种新的混合杂交方法及其在约束优化中的应用

为进一步提高基于混合杂交与间歇变异的约束优化演化算法的求解性能,提出了一种新的混合杂交方法。该方法主要是在混合算术杂交算子中引入离散均匀重组算子,并组成一个离散——算术混合杂交算子网,其中离散均匀重组算子起到协助调整子代分布、增强混合算术杂交算子局部搜索能力的作用。数值实验和比较表明所提的混合杂交方法可有效改善算法求解不等式约束优化问题的性能。     

LADPSO: using fuzzy logic to conduct PSO algorithm

Optimization plays a critical role in human modern life. Nowadays, optimization is used in many aspects of human modern life including engineering, medicine, agriculture and economy. Due to the growing number of optimization problems and their growing complexity, we need to improve and develop theoretical and practical optimization methods. Stochastic population based optimization algorithms like genetic algorithms and particle swarm optimization are good candidates for solving complex problems efficiently. Particle swarm optimization (PSO) is an optimization algorithm that has received much attention in recent years. PSO is a simple and computationally inexpensive algorithm inspired by the social behavior of bird flocks and fish schools. However, PSO suffers from premature convergence, especially in high dimensional multi-modal functions. In this paper, a new method for improving PSO has been introduced. The Proposed method which has been named Light Adaptive Particle Swarm Optimization is a novel method that uses a fuzzy control system to conduct the standard algorithm. The suggested method uses two adjunct operators along with the fuzzy system in order to improve the base algorithm on global optimization problems. Our approach is validated using a number of common complex uni-modal/multi-modal benchmark functions and results have been compared with the results of Standard PSO (SPSO2011) and some other methods. The simulation results demonstrate that results of the proposed approach is promising for improving the standard PSO algorithm on global optimization problems and also improving performance of the algorithm.     

An effective hybrid particle swarm optimization algorithm for multi-objective flexible job-shop scheduling problem

Flexible job-shop scheduling problem (FJSP) is an extension of the classical job-shop scheduling problem. Although the traditional optimization algorithms could obtain preferable results in solving the mono-objective FJSP. However, they are very difficult to solve multi-objective FJSP very well. In this paper, a particle swarm optimization (PSO) algorithm and a tabu search (TS) algorithm are combined to solve the multi-objective FJSP with several conflicting and incommensurable objectives. PSO which integrates local search and global search scheme possesses high search efficiency. And, TS is a meta-heuristic which is designed for finding a near optimal solution of combinatorial optimization problems. Through reasonably hybridizing the two optimization algorithms, an effective hybrid approach for the multi-objective FJSP has been proposed. The computational results have proved that the proposed hybrid algorithm is an efficient and effective approach to solve the multi-objective FJSP, especially for the problems on a large scale.     

基于群体爬山策略的混合粒子群优化算法

针对粒子群优化算法（PSO）在求解高维复杂优化问题时存在搜索精度不高和易陷入局部最优解的缺陷,借鉴混合蛙跳算法（SFLA）的群体爬山思想,提出一种基于群体爬山策略的混合粒子群优化算法（CMCPSO）,并证明了CMCPSO算法的全局收敛性。对四个典型高维连续优化函数的求解表明,该算法不仅保持了PSO算法的快速收敛能力,而且吸收了SFLA算法局部精细搜索和保持种群多样性的优点,具有良好的全局收敛性。     

求解工程约束优化问题的PSO-ABC混合算法*

针对包含约束条件的工程优化问题,提出了基于人工蜂群的粒子群优化PSO-ABC算法。将PSO中较优的粒子作为ABC算法的蜜源,并使用禁忌表存储其局部极值,克服粒子群优化算法易陷入局部最优的缺陷。采用可行性规则进行约束处理,将粒子种群分为可行子群和不可行子群,并在ABC算法产生蜜源的过程中保留部分较优的可行解和不可行解的信息,弥补了可行性规则处理最优点位于约束边界附近的问题时存在的不足。四个典型工程优化设计的实验结果表明,该算法能够寻得更优的约束最优化解,且稳健性更强。     

一种求解作业车间调度的混合粒子群算法*

针对车间作业调度问题,提出了一种混合了知识进化算法和粒子群优化的算法。算法主要是结合知识进化算法的进化选择机制和粒子群优化的局部快速收敛性特性,首先让粒子替代知识进化算法中的进化个体,在群体空间中按粒子群优化规则寻找局部最优,然后根据知识进化算法的全局选择机制寻找全局最优,最后,将车间作业调度问题的特点融入到所提出的混合算法中求解问题。采用基准数据进行测试的仿真实验,并比对标准遗传算法,结果表明所提算法的有效性。     

最优化问题全局寻优的PSO BFGS混合算法*

针对利用粒子群优化算法进行多极值函数优化时存在早熟收敛和搜索效率低的问题,提出混合的PSO-BFGS算法,并增强了混合算法的变异能力使算法能逃出局部极值点.通过对三种Benchmark函数的测试结果表明,PSO-BFGS算法不仅具有有效的全局收敛性能,而且还具有较快的收敛速度,是求解最优化问题的一种有效算法.     

A hybrid PSO-GA algorithm for optimization of laminated composites

This paper presents a new hybrid Particle Swarm Algorithm (PSO) for optimization of laminated composite structures. The method combines the standard PSO heuristics with Genetic Algorithm operators in order to improve the algorithm performance. Thus, operations that are important to the optimization of laminated composites such as mutation and layer swap are incorporated into the method. A specially designed encoding scheme is used to represent the laminate variables and the associated velocities. A study is carried-out to select the best variant of the proposed method for the optimization of laminated composites, considering different swarm topologies and genetic operators. Both strength maximization and weight minimization problems are considered. A meta-optimization procedure is used to tune the parameters of each variant in order to avoid biased results. The results showed that the proposed method led to excellent results for both traditional and dispersed laminates, representing a significant improvement over the standard PSO algorithm.     

一种催化粒子群算法及其性能分析

针对粒子群算法（PSO）在解决高维、多模复杂问题时容易陷入局部最优的问题,提出了一种新颖的混合算法—催化粒子群算法（CPSO）。在CPSO优化过程中,种群中的粒子始终保持其个体历史最优值pbests。CPSO种群更新由改造PSO、横向交叉以及垂直交叉三个搜索算子交替进行,其中,每个算子产生的中庸解均通过贪婪思想产生占优解pbests,并作为下一个算子的父代种群。在CPSO中,纵横交叉算法（CSO）作为PSO的加速催化剂,一方面通过横向交叉改善PSO的全局收敛性能,另一方面通过纵向交叉维持种群的多样性。对6个典型benchmark函数的仿真结果表明,相比其它主流PSO变体,CPSO在全局收敛能力和收敛速率方面具有明显优势。     

基数约束投资组合问题的一种混合元启发式算法求解

针对资产数目和投资资金比例受约束的投资组合选择这一NP难问题,基于混沌搜索、粒子群优化和引力搜索算法提出了一种新的混合元启发式搜索算法。该算法能很好地平衡开发能力和勘探能力,有效抑制了算法早熟收敛现象。标准测试函数的测试结果表明混合算法与标准的粒子群优化和引力搜索算法相比具有更好的寻优效率;实证分析进一步对混合算法与遗传算法及粒子群优化算法在求解这类投资组合选择问题的性能进行了比较。数值结果表明,混合算法在搜索具有高预期回报的非支配投资组合方面表现更好,取得了更为满意的结果。