Solving shortest path problem using particle swarm optimization

This paper presents the investigations on the application of particle swarm optimization (PSO) to solve shortest path (SP) routing problems. A modified priority-based encoding incorporating a heuristic operator for reducing the possibility of loop-formation in the path construction process is proposed for particle representation in PSO. Simulation experiments have been carried out on different network topologies for networks consisting of 15–70 nodes. It is noted that the proposed PSO-based approach can find the optimal path with good success rates and also can find closer sub-optimal paths with high certainty for all the tested networks. It is observed that the performance of the proposed algorithm surpasses those of recently reported genetic algorithm based approaches for this problem.     

Constrained particle swarm optimization using a bi-objective formulation

This paper introduces an approach for dealing with constraints when using particle swarm optimization. The constrained, single objective optimization problem is converted into an unconstrained, bi-objective optimization problem that is solved using a multi-objective implementation of the particle swarm optimization algorithm. A specialized bi-objective particle swarm optimization algorithm is presented and an engineering example problem is used to illustrate the performance of the algorithm. An additional set of 13 test problems from the literature is used to further validate the performance of the newly proposed algorithm. For the example problems considered here, the proposed algorithm produced promising results, indicating that it is an approach that deserves further consideration. The newly proposed algorithm provides performance similar to that of a tuned penalty function approach, without having to tune any penalty parameters.     

基于离散微粒群算法求解背包问题研究

微粒群算法(PSO)是一种新的演化算法,主要用于求解数值优化问题.基于离散微粒群算法(DPSO)分别与处理约束问题的罚函数法和贪心变换方法相结合,提出了求解背包问题的两个算法:基于罚函数策略的离散微粒群算法(PFDPSO)和基于贪心变换策略的离散微粒群算法(GDPSO).通过将这两个算法与文献[7]中的混合微粒群算法(Hybrid_PSO)进行数值计算比较发现:对于求解大规模的背包问题,GDPSO非常优秀,其求解能力优于Hybrid_PSO和PFDPSO,是求解背包问题的一种非常有效的方法.     

Solving the multi-stage portfolio optimization problem with a novel particle swarm optimization

Solving the multi-stage portfolio optimization (MSPO) problem is very challenging due to nonlinearity of the problem and its high consumption of computational time. Many heuristic methods have been employed to tackle the problem. In this paper, we propose a novel variant of particle swarm optimization (PSO), called drift particle swarm optimization (DPSO), and apply it to the MSPO problem solving. The classical return-variance function is employed as the objective function, and experiments on the problems with different numbers of stages are conducted by using sample data from various stocks in S&P 100 index. We compare performance and effectiveness of DPSO, particle swarm optimization (PSO), genetic algorithm (GA) and two classical optimization solvers (LOQO and CPLEX), in terms of efficient frontiers, fitness values, convergence rates and computational time consumption. The experiment results show that DPSO is more efficient and effective in MSPO problem solving than other tested optimization tools.     

基于OpenMP求解QAP的并行粒子群优化算法

提出了一种基于OpenMP求解QAP的并行粒子群优化算法.该算法将遗传算法的交叉策略引入PSO算法中,同时采用禁忌搜索算法作为局部搜索算法.在QAPLIB实例上的测试结果表明,并行PSO算法在所有测试实例上都获得了超线性加速比,且运行结果优于串行算法.     

Multi-objective reliability-redundancy allocation problem using particle swarm optimization

This paper considers the multi-objective reliability redundancy allocation problem of a series system where the reliability of the system and the corresponding designing cost are considered as two different objectives. Due to non-stochastic uncertain and conflicting factors it is difficult to reduce the cost of the system and improve the reliability of the system simultaneously. In such situations, the decision making is difficult, and the presence of multi-objectives gives rise to multi-objective optimization problem (MOOP), which leads to Pareto optimal solutions instead of a single optimal solution. However in order to make the model more flexible and adaptable to human decision process, the optimization model can be expressed as fuzzy nonlinear programming problems with fuzzy numbers. Thus in a fuzzy environment, a fuzzy multi-objective optimization problem (FMOOP) is formulated from the original crisp optimization problem. In order to solve the resultant problem, a crisp optimization problem is reformulated from FMOOP by taking into account the preference of decision maker regarding cost and reliability goals and then particle swarm optimization is applied to solve the resulting fuzzified MOOP under a number of constraints. The approach has been demonstrated through the case study of a pharmaceutical plant situated in the northern part of India.     

Unit commitment problem using enhanced particle swarm optimization algorithm

This paper proposes an enhanced PSO (EPSO) approach to solve the unit commitment (UC) problem in electric power system, which is an integrated improved discrete binary particle swarm optimization (DBPSO) with the Lambda-iteration method. The EPSO is enhanced by priority list based on the unit characteristics and heuristic search strategies to repair the spinning reserve and minimum up/down time constraints. The implementation of EPSO for UC problem consists of three stages. First, the DBPSO based on priority list is applied for unit scheduling when neglecting the minimum up/down time constraints. Second, heuristic search strategies are used to handle the minimum up/down time constraints and decommit excess spinning reserve units. Finally, Lambda-iteration method is adopted to solve economic load dispatch based on the obtained unit schedule. To verify the advantages of the EPSO method, the EPSO is tested and compared to the other methods on the systems with the number of units in the range of 10 to 100. Numerical results demonstrate that the EPSO is superior to other methods reported in the literature in terms of lower production cost and shorter computational time.     

Multi-objective optimization problem under fuzzy rule constraints using particle swarm optimization

In this paper, a fuzzy multi-objective programming problem is considered where functional relationships between decision variables and objective functions are not completely known to us. Due to uncertainty in real decision situations sometimes it is difficult to find the exact functional relationship between objectives and decision variables. It is assumed that information source from where some knowledge may be obtained about the objective functions consists of a block of fuzzy if-then rules. In such situations, the decision making is difficult and the presence of multiple objectives gives rise to multi-objective optimization problem under fuzzy rule constraints. In order to tackle the problem, appropriate fuzzy reasoning schemes are used to determine crisp functional relationship between the objective functions and the decision variables. Thus a multi-objective optimization problem is formulated from the original fuzzy rule-based multi-objective optimization model. In order to solve the resultant problem, a deterministic single-objective non-linear optimization problem is reformulated with the help of fuzzy optimization technique. Finally, PSO (Particle Swarm Optimization) algorithm is employed to solve the resultant single-objective non-linear optimization model and the computation procedure is illustrated by means of numerical examples.     

Robust optimization using multi-objective particle swarm optimization

This article proposes an algorithm to search for solutions which are robust against small perturbations in design variables. The proposed algorithm formulates robust optimization as a bi-objective optimization problem, and fi nds solutions by multi-objective particle swarm optimization (MOPSO). Experimental results have shown that MOPSO has a better performance at fi nding multiple robust solutions than a previous method using a multi-objective genetic algorithm.     

Solution to profit based unit commitment problem using particle swarm optimization

In this paper, an algorithm to solve the profit based unit commitment problem (PBUCP) under deregulated environment has been proposed using Particle Swarm Optimization (PSO) intelligent technique to maximize the GENCOs profit. Deregulation in power sector increases the efficiency of electricity production and distribution, offer lower prices, higher quality, a secure and a more reliable product. The proposed algorithm has been developed from the view point of a generation company wishing to maximize its profit in the deregulated power and reserve markets. UC schedule depends on the market price in the deregulated market. In deregulated environment utilities are not required to meet the demand. GENCO can consider a schedule that produce less than the predicted load demand and reserve but creates maximum profit. More number of units are committed when the market price is higher. When more number of generating units are brought online more power is generated and participated in the deregulated market to get maximum profit. This paper presents a new approach of GENCOs profit based unit commitment using PSO technique in a day ahead competitive electricity markets. The profit based unit commitment problem is solved using various PSO techniques such as Chaotic PSO (CPSO), New PSO (NPSO) and Dispersed PSO (DPSO) and the results are compared. Generation, spinning reserve, non-spinning reserve, and system constraints are considered in proposed formulation. The proposed approach has been tested on IEEE-30 bus system with 6 generating units as an individual GENCO. The results obtained are quite encouraging and useful in deregulated market. The algorithm and simulation are carried out using Matlab software.     

A fuzzy multi-criteria decision making approach for solving a bi-objective personnel assignment problem

Effective personnel assignment is one of the most crucial tasks performed by the decision makers of a company. This paper proposes a systematic approach with a feedback mechanism in which the interdependences among positions and the differences among the selected employees are considered simultaneously. Unfortunately, the two combined considerations have rarely been discussed in the literature. The purpose of this approach is to obtain the best matching of candidates and positions in order to organize a collaboratively cross-functional team. In a fuzzy environment and, then, in the proposed approach, a bi-objective binary integer programming (BOBIP) model is formulated. Based on the weighted composite scores determined in the third step of the proposed procedure, the BOBIP model is transformed into a fuzzy bi-objective goal programming (FBOGP) model. An elaborately designed heuristic algorithm is developed to determine the appropriate values of several important parameters in the FBOGP model, which is solved using LINDO 8.0. An application example is illustrated, and two additional examples are tested. The results indicate that the proposed approach achieves the acceptable satisfaction level and requires less computation time than the brute force enumerative method.     

QPSO算法与PSO算法求解二维热传导反问题

热传导反问题在国内研究起步较晚,研究方法有很多,但通常方法很难较好地接近全局最优.在介绍经典的微粒群优化算法(PSO)的基础上,研究基于量子行为的微粒群优化算法(QPSO)的二维热传导参数优化方法,具体介绍依据目标函数如何利用上述的算法去寻找最优参数组合.为了提高算法的收敛性和稳定性,在具体应用中对算法进行了改进,并进行了大量实验,结果显示在解决热传导反问题优化问题中,基于QPSO算法的性能比经典PSO算法更加优越,证明QPSO在热传导领域具有很大的实际应用价值.     

Solving multiobjective problems using cat swarm optimization

This paper proposes a new multiobjective evolutionary algorithm (MOEA) by extending the existing cat swarm optimization (CSO). It finds the nondominated solutions along the search process using the concept of Pareto dominance and uses an external archive for storing them. The performance of our proposed approach is demonstrated using standard test functions. A quantitative assessment of the proposed approach and the sensitivity test of different parameters is carried out using several performance metrics. The simulation results reveal that the proposed approach can be a better candidate for solving multiobjective problems (MOPs).     

Solving the high school timetabling problem using a hybrid cat swarm optimization based algorithm

In this contribution we present the application of a hybrid cat swarm optimization (CSO) based algorithm for solving the school timetabling problem. This easy to use, efficient and fast algorithm is a hybrid variation of the classic CSO algorithm. Its efficiency and performance is demonstrated by conducting experiments with real-world input data. This data, collected from various high schools in Greece, has also been used as test instances by many other researchers in their publications. Results reveal that this hybrid CSO based algorithm, applied to the same school timetabling test instances using the same evaluation criteria, exhibits better performance in less computational time compared to the majority of other existing approaches, such as Genetic Algorithms (GAs), Evolutionary Algorithms (EAs), Simulated Annealing (SA), Particle Swarm Optimization (PSO) and Artificial Fish Swarm (AFS). The algorithm's main process constitutes a variation of the classic CSO algorithm, properly altered so as to be applied for solving the school timetabling problem. This process contains the main algorithmic differences of the proposed approach compared to other algorithms presented in the respective literature.     

Solving uncapacitated multilevel lot-sizing problems using a particle swarm optimization with flexible inertial weight

The multilevel lot-sizing (MLLS) problem is a key production planning problem in materials requirements planning (MRP) system. The MLLS problem deals with determining the production lot-sizes of various items appearing in the product structure over a given finite planning horizon to minimize the production cost, the inventory carrying cost, the back ordering cost and etc. This paper proposed a particle swarm optimization (PSO) algorithm for solving the uncapacitated MLLS problem with assembly structure. All the mathematical operators in our algorithm are redefined and the inertial weight parameter can be either a negative real number or a positive one. The feasibility and effectiveness of our algorithm are investigated by comparing the experimental results with those of a genetic algorithm (GA).     

Multiobjective clustering analysis using particle swarm optimization

Clustering is a significant data mining task which partitions datasets based on similarities among data. This technique plays a very important role in the rapidly growing field known as exploratory data analysis. A key difficulty of effective clustering is to define proper grouping criteria that reflect fundamentally different aspects of a good clustering solution such as compactness and separation of clusters. Moreover, in the conventional clustering algorithms only a single criterion is considered that may not conform to the diverse and complex shapes of the underlying clusters. In this study, partitional clustering is defined as a multiobjective optimization problem. The aim is to obtain well-separated, connected, and compact clusters and for this purpose, two objective functions have been defined based on the concepts of data connectivity and cohesion. These functions are the core of an efficient multiobjective particle swarm optimization algorithm, which has been devised for and applied to automatic grouping of large unlabeled datasets. A comprehensive experimental study is conducted and the obtained results are compared with the results of four other state-of-the-art clustering techniques. It is shown that the proposed algorithm can achieve the optimal number of clusters, is robust and outperforms, in most cases, the other methods on the selected benchmark datasets.     

Dynamic clustering using combinatorial particle swarm optimization

Combinatorial Particle Swarm Optimization (CPSO) is a relatively recent technique for solving combinatorial optimization problems. CPSO has been used in different applications, e.g., partitional clustering and project scheduling problems, and it has shown a very good performance. In partitional clustering problem, CPSO needs to determine the number of clusters in advance. However, in many clustering problems, the correct number of clusters is unknown, and it is usually impossible to estimate. In this paper, an improved version, called CPSOII, is proposed as a dynamic clustering algorithm, which automatically finds the best number of clusters and simultaneously categorizes data objects. CPSOII uses a renumbering procedure as a preprocessing step and several extended PSO operators to increase population diversity and remove redundant particles. Using the renumbering procedure increases the diversity of population, speed of convergence and quality of solutions. For performance evaluation, we have examined CPSOII using both artificial and real data. Experimental results show that CPSOII is very effective, robust and can solve clustering problems successfully with both known and unknown number of clusters. Comparing the obtained results from CPSOII with CPSO and other clustering techniques such as KCPSO, CGA and K-means reveals that CPSOII yields promising results. For example, it improves 9.26 % of the value of DBI criterion for Hepato data set.     

基于QPSO算法的单阶段投资组合优化

投资组合优化问题是NP难解问题,通常的方法很难较好地接近全局最优.在经典微粒群算法(PSO)的基础上,研究了基于量子行为的微粒群算法(QPSO)的单阶段投资组合优化方法,具体介绍了依据目标函数如何利用QPSO算法去寻找最优投资组合.在具体应用中,为了提高算法的收敛性和稳定性对算法进行了改进.利用真实历史数据进行验证,结果表明在解决单阶段投资组合优化问题时,基于QPSO算法的投资组合优化的性能比PSO算法更加优越,且QPSO算法在投资组合优化领域具有很大的实际应用价值.     

A multi-objective particle swarm optimization for project selection problem

Selecting the most appropriate projects out of a given set of investment proposals is recognized as a critical issue for which the decision maker takes several aspects into consideration. Since many of these aspects may be conflicting, the problem is rendered as a multi-objective one. Consequently, we consider a multi-objective project selection problem in this study where total benefits are to be maximized while total risk and total coat must be minimized, simultaneously. Since solving an NP-hard problem becomes demanding as the number of projects grows, a multi-objective particle swarm with new selection regimes for global best and personal best for swarm members is designed to find the locally Pareto-optimal frontier and is compared with a salient multi-objective genetic algorithm, i.e. SPEAII, based on some comparison metrics with random instances.     

利用免疫粒子群算法解决排课问题

为解决排课当中的资源合理分配问题,寻求一种合理的解决方案,提出一种带免疫量子行为的粒子群智能优化算法.将粒子群中的粒子当作抗体,给粒子的生成加入免疫记忆机制,迭代开始后,使用抗体浓度指导粒子种群向更优方向移动.改进后的方法能避免粒子陷入局部最优和早熟收敛,用以解决这种多约束、多目标的组合排课问题.最后进行实验仿真,仿真结果表明了该新算法在解决实际问题中的有效性与优越性.