A discrete particle swarm optimization algorithm for the no-wait flowshop scheduling problem

In this paper, a discrete particle swarm optimization (DPSO) algorithm is presented to solve the no-wait flowshop scheduling problem with both makespan and total flowtime criteria. The main contribution of this study is due to the fact that particles are represented as discrete job permutations and a new position update method is developed based on the discrete domain. In addition, the DPSO algorithm is hybridized with the variable neighborhood descent (VND) algorithm to further improve the solution quality. Several speed-up methods are proposed for both the swap and insert neighborhood structures. The DPSO algorithm is applied to both 110 benchmark instances of Taillard [Benchmarks for basic scheduling problems. European Journal of Operational Research 1993;64:278–85] by treating them as the no-wait flowshop problem instances with the total flowtime criterion, and to 31 benchmark instances provided by Carlier [Ordonnancements a contraintes disjonctives. RAIRO Recherche operationelle 1978;12:333–51], Heller [Some numerical experiments for an M×J$\mathrm{M}\times \mathrm{J}$ flow shop and its decision-theoretical aspects. Operations Research 1960;8:178–84], and Revees [A genetic algorithm for flowshop sequencing. Computers and Operations Research 1995;22:5–13] for the makespan criterion. For the makespan criterion, the solution quality is evaluated according to the reference makespans generated by Rajendran [A no-wait flowshop scheduling heuristic to minimize makespan. Journal of the Operational Research Society 1994;45:472–8] whereas for the total flowtime criterion, it is evaluated with the optimal solutions, lower bounds and best known solutions provided by Fink and Voß [Solving the continuous flow-shop scheduling problem by metaheuristics. European Journal of Operational Research 2003;151:400–14]. The computational results show that the DPSO algorithm generated either competitive or better results than those reported in the literature. Ultimately, 74 out of 80 best known solutions provided by Fink and Voß [Solving the continuous flow-shop scheduling problem by metaheuristics. European Journal of Operational Research 2003;151:400–14] were improved by the VND version of the DPSO algorithm.     

A revised discrete particle swarm optimization algorithm for permutation flow-shop scheduling problem

This research proposes a revised discrete particle swarm optimization (RDPSO) to solve the permutation flow-shop scheduling problem with the objective of minimizing makespan (PFSP-makespan). The candidate problem is one of the most studied NP-complete scheduling problems. RDPSO proposes new particle swarm learning strategies to thoroughly study how to properly apply the global best solution and the personal best solution to guide the search of RDPSO. A new filtered local search is developed to filter the solution regions that have been reviewed and guide the search to new solution regions in order to keep the search from premature convergence. Computational experiments on Taillard’s benchmark problem sets demonstrate that RDPSO significantly outperforms all the existing PSO algorithms.     

A discrete shuffled frog optimization algorithm

The shuffled frog leaping (SFL) optimization algorithm has been successful in solving a wide range of real-valued optimization problems. In this paper we present a discrete version of this algorithm and compare its performance with a SFL algorithm, a binary genetic algorithm (BGA), and a discrete particle swarm optimization (DPSO) algorithm on seven low dimensional and five high dimensional benchmark problems. The obtained results demonstrate that our proposed algorithm, i.e. the DSFL, outperforms the BGA and the DPSO in terms of both success rate and speed. On low dimensional functions and for large values of tolerance the DSFL is slower than the SFL, but their success rates are equal. Part of this slowness could be attributed to the extra bits used for data coding. By increasing number of variables and the required precision of answer, the DSFL performs very well in terms of both speed and success rate. For high dimensional problems, for intrinsically discrete problems, also when the required precision of answer is high, the DSFL is the most efficient method.     

Multiheuristic approach to discrete optimization problems

In this paper, some heuristic decision-making techniques (methods) are considered that are used in various discrete optimization problems. The objective of each of these problems is the construction of anytime algorithms. The considered methods for solving these problems are constructed on the basis of a combination of some heuristics that belong to different areas of the theory of artificial intelligence. A brief variant of the present article is presented in [1]. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 32–42, May–June 2006.     

A graph theoretic approach to problem formulation for multidisciplinary design analysis and optimization

The formulation of multidisciplinary design, analysis, and optimization (MDAO) problems has become increasingly complex as the number of analysis tools and design variables included in typical studies has grown. This growth in the scale and scope of MDAO problems has been motivated by the need to incorporate additional disciplines and to expand the parametric design space to enable the exploration of unconventional design concepts. In this context, given a large set of disciplinary analysis tools, the problem of determining a feasible data flow between tools to produce a specified set of system-level outputs is combinatorially challenging. The difficulty is compounded in multi-fidelity problems, which are of increasing interest to the MDAO community. In this paper, we propose an approach for addressing this problem based on the formalism of graph theory. The approach begins by constructing the maximal connectivity graph (MCG) describing all possible interconnections between a set of analysis tools. Graph operations are then conducted to reduce the MCG to a fundamental problem graph (FPG) that describes the connectivity of analysis tools needed to solve a specified system-level design problem. The FPG does not predispose a particular solution procedure; any relevant MDO solution architecture could be selected to implement the optimization. Finally, the solution architecture can be represented in a problem solution graph (PSG). The graph approach is applied to an example problem based on a commercial aircraft MDAO study.     

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.     

A new PSO-based algorithm for multi-objective optimization with continuous and discrete design variables

This paper presents a new multi-objective optimization algorithm called FC-MOPSO for optimal design of engineering problems with a small number of function evaluations. The proposed algorithm expands the main idea of the single-objective particle swarm optimization (PSO) algorithm to deal with constrained and unconstrained multi-objective problems (MOPs). FC-MOPSO employs an effective procedure in selection of the leader for each particle to ensure both diversity and fast convergence. Fifteen benchmark problems with continuous design variables are used to validate the performance of the proposed algorithm. Finally, a modified version of FC-MOPSO is introduced for handling discrete optimization problems. Its performance is demonstrated by optimizing five space truss structures. It is shown that the FC-MOPSO can effectively find acceptable approximations of Pareto fronts for structural MOPs within very limited number of function evaluations.     

解决TSP问题的局部调整离散微粒群算法

微粒群算法提出以来一直不能较好的解决离散及组合优化问题,针对这个问题,通过对微粒群算法的优化机理的分析,对原有的微粒群进化方程中的速度和位置的更新等进行重新的定义,同时提出一种具有自适应能力的惯性因子,使其适合解决TSP这样的组合优化问题.针对过去的离散算法整体调整容易形成对路径的破坏这一缺点,在重新定义的算法上加入局部调整的策略,形成一种局部调整的离散微粒群算法(local adjustive discrete PSO,LADPSO),通过在ch31和ei151上的试验,证明了该算法在解决这一问题上是可行的.     

A novel discrete particle swarm optimization algorithm for solving bayesian network structures learning problem

ABSTRACT

Bayesian network is an effective representation tool to describe the uncertainty of the knowledge in artificial intelligence. One important method to learning Bayesian network from data is to employ a search procedure to explore the space of networks and a scoring metric to evaluate each candidate structure. In this paper, a novel discrete particle swarm optimization algorithm has been designed to solve the problem of Bayesian network structures learning. The proposed algorithm not only maintains the search advantages of the classical particle swarm optimization but also matches the characteristics of Bayesian networks. Meanwhile, mutation and neighbor searching operators have been used to overcome the drawback of premature convergence and balance the exploration and exploitation abilities of the particle swarm optimization. The experimental results on benchmark networks illustrate the feasibility and effectiveness of the proposed algorithm, and the comparative experiments indicate that our algorithm is highly competitive compared to other algorithms.     

A reduction approach to the two-campus transport problem

The two-campus transport problem (TCTP) is a dial-a-ride problem with only two destinations. The problem is motivated by a transport problem between two campuses of an academic college. The two campuses are located in two different cities. Lecturers living in one city are sometimes asked to teach at the other city’s campus. The problem is that of transporting the lecturers from one campus to the other, using a known set of vehicles, so as to minimize the time the lecturers wait for their transport. We mathematically model the general TCTP, and provide an algorithm that solves it, which is polynomial in the number of lecturers. The algorithm is based on a reduction to a shortest path problem.     

A particle swarm optimization algorithm for the multiple-level warehouse layout design problem

Warehouse operation and management is one of the essential parts of manufacturing and service operations. The warehouse layout problem is a key to warehouse operations. Generally, warehouse layout design models attempt to optimize different objectives such as the orientation of storage racks, the allocation of space among competing uses, the number of cranes, the overall configuration of the facility, etc. The warehousing strategies can be classified as distribution-type, production-type and contract-type warehouse strategies. In this study, a distribution-type warehouse considered that various type products are collected from different suppliers for storing in the warehouse for a determined period and for delivery to different customers. The aim of the study is to design a multiple-level warehouse shelf configuration which minimizes the annual carrying costs. The turnover rates of the products are classified and they are considered while putting/picking them to/from shelves regarding the distances between the shelves and docks. Since proposed mathematical model was shown to be NP-hard, a particle swarm optimization algorithm (PSO) as a novel heuristic was developed for determining the optimal layout.     

A hybrid continuous-discrete approach to large discrete structural optimization problems

Many optimum structural designs are based on searching for the best of all combinations, arising from the number of structural members, and parameters of listed rolled profiles. Even, in a relatively simple design, the number of such combinations is of an order higher than ten. All known methods of finding discrete minimum of structural weight require very large number of analyses often of an order of four. In this study, a relatively simple method of solving such problems is presented. It is based on a tree graph, representing discrete values of the structural volume. The structure can be subjected to multi static loadings with constraints imposed on displacements and stresses. The number of analyses, in the proposed algorithm, is limited to the order of two. The knowledge needed to apply the method is limited to FEM and graph representation. The paper is illustrated with two examples with numbers of combinations up to 42³⁸.     

A relative difference quotient algorithm for discrete optimization

According to the characteristics of discrete optimization, the concept of a relative difference quotient is proposed, and a highly accurate heuristic algorithm, a relative difference quotient algorithm, is developed for a class of discrete optimization problems with monotonic objective functions and constraint functions. The algorithm starts from the minimum point of the objective function outside the feasible region and advances along the direction of minimum increment of the objective function and maximum decrement of constraint functions to find a better approximate optimum solution. In order to evaluate the performance of the algorithm, a stochastic numerical test and a statistical analysis for the test results are also completed. The algorithm has been successfully applied to the discrete optimization of structures.     

Adaptive heuristic search algorithm for discrete variables based multi-objective optimization

Although metamodel technique has been successfully used to enhance the efficiency of the multi-objective optimization (MOO) with black-box objective functions, the metamodel could become less accurate or even unavailable when the design variables are discrete. In order to overcome the bottleneck, this work proposes a novel random search algorithm for discrete variables based multi-objective optimization with black-box functions, named as k-mean cluster based heuristic sampling with Utopia-Pareto directing adaptive strategy (KCHS-UPDA). This method constructs a few adaptive sampling sets in the solution space and draws samples according to a heuristic probability model. Several benchmark problems are supplied to test the performance of KCHS-UPDA including closeness, diversity, efficiency and robustness. It is verified that KCHS-UPDA can generally converge to the Pareto frontier with a small quantity of number of function evaluations. Finally, a vehicle frontal member crashworthiness optimization is successfully solved by KCHS-UPDA.     

A hyper-heuristic approach to aircraft structural design optimization

The conceptual design of an aircraft is a challenging problem in which optimization can be of great importance to the quality of design generated. Mass optimization of the structural design of an aircraft aims to produce an airframe of minimal mass whilst maintaining satisfactory strength under various loading conditions due to flight and ground manoeuvres. Hyper-heuristic optimization is an evolving field of research wherein the optimization process is continuously adapted in order to provide greater improvements in the quality of the solution generated. The relative infancy of hyper-heuristic optimization has resulted in limited application within the field of aerospace design. This paper describes a framework for the mass optimization of the structural layout of an aircraft at the conceptual level of design employing a novel hyper-heuristic approach. This hyper-heuristic approach encourages solution space exploration, thus reducing the likelihood of premature convergence, and improves the feasibility of and convergence upon the best solution found. A case study is presented to illustrate the effects of hyper-heuristics on the problem for a large commercial aircraft. Resulting solutions were generated of considerably lighter mass than the baseline aircraft. A further improvement in solution quality was found with the use of the hyper-heuristics compared to that obtained without, albeit with a penalty on computation time.     

A novel approach to design optimal 2-D digital differentiator using vortex search optimization algorithm

Multimedia Tools and Applications - The designing of 2-D digital differentiator is multimodal and high dimensional problem which requires large number of differentiator coefficients to be...     

A convex optimization approach to the mode acceleration problem

The purpose of this note is to introduce an alternative procedure to the mode acceleration method when the underlying structure model includes damping. We will show that the problem can be cast as a convex optimization problem that can be solved via linear matrix inequalities.