Particle swarm with equilibrium strategy of selection for multi-objective optimization

A new ranking scheme based on equilibrium strategy of selection is proposed for multi-objective particle swarm optimization (MOPSO), and the preference ordering is used to identify the “best compromise” in the ranking stage. This scheme increases the selective pressure, especially when the number of objectives is very large. The proposed algorithm has been compared with other multi-objective evolutionary algorithms (MOEAs). The experimental results indicate that our algorithm produces better convergence performance.     

A cooperative swarm intelligence algorithm for multi-objective discrete optimization with application to the knapsack problem

We propose a novel cooperative swarm intelligence algorithm to solve multi-objective discrete optimization problems (MODP). Our algorithm combines a firefly algorithm (FA) and a particle swarm optimization (PSO). Basically, we address three main points: the effect of FA and PSO cooperation on the exploration of the search space, the discretization of the two algorithms using a transfer function, and finally, the use of the epsilon dominance relation to manage the size of the external archive and to guarantee the convergence and the diversity of Pareto optimal solutions.We compared the results of our algorithm with the results of five well-known meta-heuristics on nine multi-objective knapsack problem benchmarks. The experiments show clearly the ability of our algorithm to provide a better spread of solutions with a better convergence behavior.     

A hybrid multi-objective artificial bee colony algorithm for burdening optimization of copper strip production

To achieve burdening process optimization of copper strips effectively, a nonlinear constrained multi-objective model is established on the principle of the actual burdening. The problem is formulated with two objectives of minimizing the total cost of raw materials and maximizing the amount of waste material thrown into melting furnace. In this paper, a novel approach called “hybrid multi-objective artificial bee colony” (HMOABC) to solve this model is proposed. The HMOABC algorithm is new swarm intelligence based multi-objective optimization technique inspired by the intelligent foraging behavior of honey bees, summation of normalized objective values and diversified selection (SNOV-DS) and nondominated sorting approach. Two test examples were studied and the performance of HMOABC is evaluated in comparison with other nature inspired techniques which includes nondominated sorting genetic algorithm II (NSGAII) and multi-objective particle swarm optimization (MOPSO). The numerical results demonstrate HMOABC approach is a powerful search and optimization technique for burdening optimization of copper strips.     

合作博弈的粒子群算法求解

随着局中人人数的增加,利用传统的“占优”方法和“估值”方法进行合作博弈求解无论从逻辑上还是计算上都变得非常困难。针对此问题,将合作博弈的求解看作是局中人遵照有效性和个体理性提出分配方案,并按照一定规则不断迭代调整直至所有方案趋向一致的过程。依据该思路,对合作博弈粒子群算法模型进行构建,确定适应度函数,设置速度公式中的参数。通过算例分析,利用粒子群算法收敛快、精度高、容易实现的特点,可以迅速得到合作博弈的唯一分配值,这为求解合作博弈提供了新的方法和工具。     

混合变异粒子群优化算法及其应用

为改善粒子群优化算法在解决复杂优化问题时收敛质量不高的不足,提出了一种改进的粒子群优化算法,即混合变异粒子群优化算法(HMPSO).HMPSO算法采用了带有随机因子的惯性权重取值更新策略,降低了标准粒子群优化算法中由于粒子飞行速度过大而错过最优解的概率,从而加速了算法的收敛速度.此外,通过混合变异进化环节的引入,缓解了...     

一种改进粒子群优化算法及其在投资规划中的应用

粒子群优化算法(PSO)是模拟生物群体智能的优化算法,具有良好的优化性能.但是群体收缩过快和群体多样性降低导致早熟收敛.本文引入了多样性指标和收敛因子模型来改进PSO算法,形成多样性收敛因子PSO算法(DCPSO),并且对现代资产投资的多目标规划问题进行了优化,简化了多目标规划的问题,并且表现出了比传统PSO算法更好性能.     

Balanced fuzzy particle swarm optimization

In the present study an extension of particle swarm optimization (PSO) algorithm which is in conformity with actual nature is introduced for solving combinatorial optimization problems. Development of this algorithm is essentially based on balanced fuzzy sets theory. The classical fuzzy sets theory cannot distinguish differences between positive and negative information of membership functions, while in the new method both kinds of information “positive and negative” about membership function are equally important. The balanced fuzzy particle swarm optimization algorithm is used for fundamental optimization problem entitled traveling salesman problem (TSP). For convergence inspecting of new algorithm, method was used for TSP problems. Convergence curves were represented fast convergence in restricted and low iterations for balanced fuzzy particle swarm optimization algorithm (BF-PSO) comparison with fuzzy particle swarm optimization algorithm (F-PSO).     

A hybrid simplex search and particle swarm optimization for unconstrained optimization

This paper proposes the hybrid NM-PSO algorithm based on the Nelder–Mead (NM) simplex search method and particle swarm optimization (PSO) for unconstrained optimization. NM-PSO is very easy to implement in practice since it does not require gradient computation. The modification of both the Nelder–Mead simplex search method and particle swarm optimization intends to produce faster and more accurate convergence. The main purpose of the paper is to demonstrate how the standard particle swarm optimizers can be improved by incorporating a hybridization strategy. In a suite of 20 test function problems taken from the literature, computational results via a comprehensive experimental study, preceded by the investigation of parameter selection, show that the hybrid NM-PSO approach outperforms other three relevant search techniques (i.e., the original NM simplex search method, the original PSO and the guaranteed convergence particle swarm optimization (GCPSO)) in terms of solution quality and convergence rate. In a later part of the comparative experiment, the NM-PSO algorithm is compared to various most up-to-date cooperative PSO (CPSO) procedures appearing in the literature. The comparison report still largely favors the NM-PSO algorithm in the performance of accuracy, robustness and function evaluation. As evidenced by the overall assessment based on two kinds of computational experience, the new algorithm has demonstrated to be extremely effective and efficient at locating best-practice optimal solutions for unconstrained optimization.     

超越方程的优化解法

针对粒子群算法局部搜索能力差,后期收敛速度慢等缺点,提出了一种改进的粒子群算法,该算法是在粒子群算法后期加入拟牛顿方法,充分发挥了粒子群算法的全局搜索性和拟牛顿法的局部精细搜索性,从而克服了粒子群算法的不足,把超越方程转化为函数优化的问题,利用该算法求解,数值实验结果表明,算法有较高的收敛速度和求解精度。     

A new mechanism to maintain diversity in multi-objective metaheuristics

In this article, a new mechanism to spread the solutions generated by a multi-objective evolutionary algorithm is proposed. This approach is based on the use of stripes that are applied in objective function space and is independent of the search engine adopted. Additionally, it overcomes some of the drawbacks of other previous proposals such as the ?-dominance method. In order to validate the proposed approach, it is coupled to a multi-objective particle swarm optimizer and its performance is assessed with respect to that of state-of-the-art algorithms, using standard test problems and performance measures taken from the specialized literature. The results indicate that the proposed approach is a viable diversity maintenance mechanism that can be incorporated to any multi-objective metaheuristic used for multi-objective optimization.     

Evaluating selection methods on hyper-heuristic multi-objective particle swarm optimization

Multi-objective particle swarm optimization (MOPSO) is a promising meta-heuristic to solve multi-objective problems (MOPs). Previous works have shown that selecting a proper combination of leader and archiving methods, which is a challenging task, improves the search ability of the algorithm. A previous study has employed a simple hyper-heuristic to select these components, obtaining good results. In this research, an analysis is made to verify if using more advanced heuristic selection methods improves the search ability of the algorithm. Empirical studies are conducted to investigate this hypothesis. In these studies, first, four heuristic selection methods are compared: a choice function, a multi-armed bandit, a random one, and the previously proposed roulette wheel. A second study is made to identify if it is best to adapt only the leader method, the archiving method, or both simultaneously. Moreover, the influence of the interval used to replace the low-level heuristic is analyzed. At last, a final study compares the best variant to a hyper-heuristic framework that combines a Multi-Armed Bandit algorithm into the multi-objective optimization based on decomposition with dynamical resource allocation (MOEA/D-DRA) and a state-of-the-art MOPSO. Our results indicate that the resulting algorithm outperforms the hyper-heuristic framework in most of the problems investigated. Moreover, it achieves competitive results compared to a state-of-the-art MOPSO.     

Enhanced speciation in particle swarm optimization for multi-modal problems

In this paper, we present a novel multi-modal optimization algorithm for finding multiple local optima in objective function surfaces. We build from Species-based particle swarm optimization (SPSO) by using deterministic sampling to generate new particles during the optimization process, by implementing proximity-based speciation coupled with speciation of isolated particles, and by including “turbulence regions” around already found solutions to prevent unnecessary function evaluations. Instead of using error threshold values, the new algorithm uses the particle’s experience, geometric mean, and “exclusion factor” to detect local optima and stop the algorithm. The performance of each extension is assessed with leave-it-out tests, and the results are discussed. We use the new algorithm called Isolated-Speciation-based particle swarm optimization (ISPSO) and a benchmark algorithm called Niche particle swarm optimization (NichePSO) to solve a six-dimensional rainfall characterization problem for 192 rain gages across the United States. We show why it is important to find multiple local optima for solving this real-world complex problem by discussing its high multi-modality. Solutions found by both algorithms are compared, and we conclude that ISPSO is more reliable than NichePSO at finding optima with a significantly lower objective function value.     

A hybrid glowworm swarm optimization algorithm to solve constrained multimodal functions optimization

In this paper, a novel hybrid glowworm swarm optimization (HGSO) algorithm is proposed. The HGSO algorithm embeds predatory behaviour of artificial fish swarm algorithm (AFSA) into glowworm swarm optimization (GSO) algorithm and combines the GSO with differential evolution on the basis of a two-population co-evolution mechanism. In addition, to overcome the premature convergence, the local search strategy based on simulated annealing is applied to make the search of GSO approach the true optimum solution gradually. Finally, several benchmark functions show that HGSO has faster convergence efficiency and higher computational precision, and is more effective for solving constrained multi-modal function optimization problems.     

求解旅行商问题的一种改进粒子群算法

本文研究了求解旅行商问题的粒子群算法。针对标准粒子群算法在求解旅行商问题过程中容易出现早熟和停滞现象的缺点,提出了一种改进的粒子群算法。首先,在初始种群的选取过程中,利用改进的贪婪策略直接获得具有较高性能的初始种群以提高算法的搜索效率。其次,通过引入次优吸引子,使粒子在搜索过程中可以更加充分地利用群体的信息来提高自身的性能,有效抑制收敛过程中的停滞现象,提高算法的搜索能力。最后为了验证所提出的方法的有效性和可行性,对TSPLIB标准库中的多个实例进行了测试,并给出了数值结果。     

Modified particle swarm optimization algorithm with simulated annealing behavior and its numerical verification

The hybrid algorithm that combined particle swarm optimization with simulated annealing behavior (SA-PSO) is proposed in this paper. The SA-PSO algorithm takes both of the advantages of good solution quality in simulated annealing and fast searching ability in particle swarm optimization. As stochastic optimization algorithms are sensitive to their parameters, proper procedure for parameters selection is introduced in this paper to improve solution quality. To verify the usability and effectiveness of the proposed algorithm, simulations are performed using 20 different mathematical optimization functions with different dimensions. The comparative works have also been conducted among different algorithms under the criteria of quality of the solution, the efficiency of searching for the solution and the convergence characteristics. According to the results, the SA-PSO could have higher efficiency, better quality and faster convergence speed than compared algorithms.     

基于PSO-AFSA混合算法的模糊投资组合问题的研究

针对模糊不确定的证券市场,用可能性均值、下可能性方差和协方差分别替换了投资组合模型中概率均值、方差和协方差,构建了双目标均值-方差投资组合模型。然后采用线性加权法将双目标模型转化为单目标模型,进而提出了一个PSO-AFSA混合算法对其求解。该混合算法中,将粒子群算法搜索的结果作为人工鱼群算法初始鱼群,进一步搜索,这样能有效的避免粒子群算法陷入局部最优。同时,将人工鱼群中的最好位置反馈到粒子群算法的速度更新公式中,指引粒子运动,加快算法收敛。最后,进行实例分析,结果表明:PSO-AFSA混合算法是有效的,混合算法搜索到的全局最优值好于基本粒子群算法搜索到的全局最优值。     

Particle swarm optimization: Hybridization perspectives and experimental illustrations

Metaheuristic optimization algorithms have become popular choice for solving complex and intricate problems which are otherwise difficult to solve by traditional methods. In the present study an attempt is made to review the hybrid optimization techniques in which one main algorithm is a well known metaheuristic; particle swarm optimization or PSO. Hybridization is a method of combining two (or more) techniques in a judicious manner such that the resulting algorithm contains the positive features of both (or all) the algorithms. Depending on the algorithm/s used we made three classifications as (i) Hybridization of PSO and genetic algorithms (ii) Hybridization of PSO with differential evolution and (iii) Hybridization of PSO with other techniques. Where, other techniques include various local and global search methods. Besides giving the review we also show a comparison of three hybrid PSO algorithms; hybrid differential evolution particle swarm optimization (DE-PSO), adaptive mutation particle swarm optimization (AMPSO) and hybrid genetic algorithm particle swarm optimization (GA-PSO) on a test suite of nine conventional benchmark problems.     

Flying-V型仓储布局货位分配优化方法研究

Flying-V是一种典型的非传统布局方式,根据其布局方式的特性,针对仓储货位分配优化问题,以货物出入库效率最高和货物存放的重心最低为优化目标,建立了货位分配多目标优化模型,并采用自适应策略的遗传算法(GA),以及粒子群算法(PSO)进行求解。根据货位分配的优化特点,在GA算法的选择、交叉和变异环节均采用自适应策略, 同时采用惯性权重线性递减的方法设计了PSO算法,有效地解决了两种算法收敛速度慢和易“早熟”的问题,提高了算法的寻优性能。为了更好地表现两种优化求解算法的有效性和优越性,结合具体的货位分配实例利用MATLAB软件编程实现。通过对比分析优化结果表明,PSO算法在收敛速度和优化效果方面相比于自适应GA算法更具有优势,更加合适于解决Flying-V型仓储布局货位分配优化问题。     

Multi-objective open shop scheduling by considering human error and preventive maintenance

This study presents an open shop scheduling model by considering human error and preventive maintenance. The proposed mathematical model takes into account conflicting objective functions including makespan, human error and machine availability. In order to find the optimum scheduling, human error, maintenance and production factors are considered, simultaneously. Human error is measured by Human Error Assessment and Reduction Technique (HEART). Three metaheuristic methods including non-dominated sorting genetic algorithm-II (NSGA-II), multi-objective particle swarm optimization (MOPSO) and strength Pareto evolutionary algorithm II (SPEA-II) are developed to find near-optimal solution. The Taguchi method is applied by adjusting parameters of metaheuristic algorithms. Several illustrative examples and a real case study (auto spare parts manufacturer) are applied to show the applicability of the multi-objective mixed integer nonlinear programming model. The proposed approach of this study may be used for similar open shop problems with minor modifications.     

Structural learning of Bayesian networks by bacterial foraging optimization

Algorithms inspired by swarm intelligence have been used for many optimization problems and their effectiveness has been proven in many fields. We propose a new swarm intelligence algorithm for structural learning of Bayesian networks, BFO-B, based on bacterial foraging optimization. In the BFO-B algorithm, each bacterium corresponds to a candidate solution that represents a Bayesian network structure, and the algorithm operates under three principal mechanisms: chemotaxis, reproduction, and elimination and dispersal. The chemotaxis mechanism uses four operators to randomly and greedily optimize each solution in a bacterial population, then the reproduction mechanism simulates survival of the fittest to exploit superior solutions and speed convergence of the optimization. Finally, an elimination and dispersal mechanism controls the exploration processes and jumps out of a local optima with a certain probability. We tested the individual contributions of four algorithm operators and compared with two state of the art swarm intelligence based algorithms and seven other well-known algorithms on many benchmark networks. The experimental results verify that the proposed BFO-B algorithm is a viable alternative to learn the structures of Bayesian networks, and is also highly competitive compared to state of the art algorithms.