A metaheuristic approach to the dominating tree problem

This paper considers a recently introduced NP-hard problem on graphs, called the dominating tree problem. In order to solve this problem, we develop a variable neighborhood search (VNS) based heuristic. Feasible solutions are obtained by using the set of vertex permutations that allow us to implement standard neighborhood structures and the appropriate local search procedure. Computational experiments include two classes of randomly generated test instances and benchmark test instances from the literature. Optimality of VNS solutions on small size instances is verified with CPLEX.     

Adaptive perturbed neighbourhood search for the expanding capacity multiple-choice knapsack problem

In this paper, we develop a perturbed reactive-based neighbourhood search algorithm for the expanding constraint multiple-choice knapsack problem. It combines reactive tabu search with some specific neighbourhood search strategies to approximately solve the problem. The tests were conducted on randomly generated instances and executed in comparable benchmark scenarios to those of the literature. The results outperform those of the Cplex solver and demonstrate the high quality of the two approach versions.     

Cooperative Parallel Variable Neighborhood Search for the p-Median

We propose a cooperative multi-search method for the Variable Neighborhood Search (VNS) meta-heuristic based on the central-memory mechanism that has been successfully applied to a number of difficult combinatorial problems. In this approach, several independent VNS meta-heuristics cooperate by asynchronously exchanging information about the best solutions identified so far, thus conserving the simplicity of the original, sequential VNS ideas. The p-median problem (PM) serves as test case. Extensive experimentations have been conducted on the classical TSPLIB benchmark problem instances with up to 11948 customers and 1000 medians, without any particular calibration of the parallel method. The results indicate that, compared to sequential VNS, the cooperative strategy yields significant gains in terms of computation time without a loss in solution quality.     

Skewed VNS enclosing second order algorithm for the degree constrained minimum spanning tree problem

We develop ideas to enhance the performance of the variable neighborhood search (VNS) by guiding the search in the shaking phase, and by employing the Skewed strategy. For this purpose, Second Order algorithms and Skewed functions expressing structural differences are embedded in an efficient VNS proposed in the literature for the degree constrained minimum spanning tree problem. Given an undirected graph with weights associated with its edges, the degree constrained minimum spanning tree problem consists in finding a minimum spanning tree of the given graph, subject to constraints on node degrees. Computational experiments are conducted on the largest and hardest benchmark instances found in the literature to date. We report results showing that the VNS with the proposed strategies improved the best known solutions for all the hardest benchmark instances. Moreover, these new best solutions significantly reduced the gaps with respect to tight lower bounds reported in the literature.     

A variable neighborhood search for the capacitated arc routing problem with intermediate facilities

The capacitated arc routing problem (CARP) focuses on servicing edges of an undirected network graph. A wide spectrum of applications like mail delivery, waste collection or street maintenance outlines the relevance of this problem. A realistic variant of the CARP arises from the need of intermediate facilities (IFs) to load up or unload the service vehicle and from tour length restrictions. The proposed Variable Neighborhood Search (VNS) is a simple and robust solution technique which tackles the basic problem as well as its extensions. The VNS shows excellent results on four different benchmark sets. Particularly, for all 120 instances the best known solution could be found and in 71 cases a new best solution was achieved.     

时间窗约束下的车辆路径问题多目标优化算法

讨论了带时间窗约束的车辆路径问题(VRPTW)其数学模型,分析了以遗传算法求解该类问题时的染色体表示和有关遗传操作,将VRPTw视为一个多目标优化问题,用Pareto评等技术来求解最优解,并以Solomen基准问题为例验证了该方法的有效性.结果表明:该方法与以往文献中的最好结果具有竞争性.     

Metaheuristics for scheduling jobs with incompatible families on parallel batching machines

In this paper, we discuss the scheduling of jobs with incompatible families on parallel batching machines. The performance measure is total weighted tardiness. This research is motivated by a scheduling problem found in the diffusion and oxidation areas of semiconductor wafer fabrication where the machines can be modelled as parallel batch processors. Given that this scheduling problem is NP-hard, we suggest an ant colony optimization (ACO) and a variable neighbourhood search (VNS) approach. Both metaheuristics are hybridized with a decomposition heuristic and a local search scheme. We compare the performance of the two algorithms with that of a genetic algorithm (GA) based on extensive computational experiments. The VNS approach outperforms the ACO and GA approach with respect to time and solution quality.     

Greedy Randomized Adaptive Search and Variable Neighbourhood Search for the minimum labelling spanning tree problem

This paper studies heuristics for the minimum labelling spanning tree (MLST) problem. The purpose is to find a spanning tree using edges that are as similar as possible. Given an undirected labelled connected graph, the minimum labelling spanning tree problem seeks a spanning tree whose edges have the smallest number of distinct labels. This problem has been shown to be NP-hard. A Greedy Randomized Adaptive Search Procedure (GRASP) and a Variable Neighbourhood Search (VNS) are proposed in this paper. They are compared with other algorithms recommended in the literature: the Modified Genetic Algorithm and the Pilot Method. Nonparametric statistical tests show that the heuristics based on GRASP and VNS outperform the other algorithms tested. Furthermore, a comparison with the results provided by an exact approach shows that we may quickly obtain optimal or near-optimal solutions with the proposed heuristics.     

A basic variable neighborhood search heuristic for the uncapacitated multiple allocation <Emphasis Type="Italic">p</Emphasis>-hub center problem

The uncapacitated multiple allocation p-hub center problem (UMApHCP) consists of choosing p hub locations from a set of nodes with pairwise traffic demands in order to route the traffic between the origin-destination pairs such that the maximum cost between origin-destination pairs is minimum. It is assumed that transportation between non-hub nodes is possible only via chosen hub nodes. In this paper we propose a basic variable neighborhood search (VNS) heuristic for solving this NP hard problem. In addition we apply two mathematical formulations of the UMApHCP in order to detect limitations of the current state-of-the-art solver used for this problem. The heuristics are tested on benchmark instances for p-hub problems. The obtained results reveal the superiority of the proposed basic VNS over the state-of-the-art as well as over a multi-start local search heuristic developed by us in this paper.     

Graph Coloring with Adaptive Evolutionary Algorithms

This paper presents the results of an experimental investigation on solving graph coloring problems with Evolutionary Algorithms (EAs). After testing different algorithm variants we conclude that the best option is an asexual EA using order-based representation and an adaptation mechanism that periodically changes the fitness function during the evolution. This adaptive EA is general, using no domain specific knowledge, except, of course, from the decoder (fitness function). We compare this adaptive EA to a powerful traditional graph coloring technique DSatur and the Grouping Genetic Algorithm (GGA) on a wide range of problem instances with different size, topology and edge density. The results show that the adaptive EA is superior to the Grouping (GA) and outperforms DSatur on the hardest problem instances. Furthermore, it scales up better with the problem size than the other two algorithms and indicates a linear computational complexity.     

Variable neighbourhood search heuristics for the probabilistic multi-source Weber problem

The Multi-source Weber Problem (MWP) is concerned with locating m facilities in the Euclidean plane, and allocating these facilities to n customers at minimum total cost. The deterministic version of the problem, which assumes that customer locations and demands are known with certainty, is a non-convex optimization problem and difficult to solve. In this work, we focus on a probabilistic extension and consider the situation where customer locations are randomly distributed according to a bivariate distribution. We first present a mathematical programming formulation for the probabilistic MWP called the PMWP. For its solution, we propose two heuristics based on variable neighbourhood search (VNS). Computational results obtained on a number of test instances show that the VNS heuristics improve the performance of a probabilistic alternate location-allocation heuristic referred to as PALA. In its original form, the applicability of the new heuristics depends on the existence of a closed-form expression for the expected distances between facilities and customers. Unfortunately, such an expression exists only for a few distance function and probability distribution combinations. We therefore use two approximation methods for the expected distances, which make the VNS heuristics applicable for any distance function and bivariate distribution of customer locations.     

A Hybrid Taguchi–Immune approach to optimize an integrated supply chain design problem with multiple shipping

Supply chain network design is considered a strategic decision level problem that provides an optimal platform for the effective and efficient supply chain management. In this research, we have mathematically modeled an integrated supply chain design. To ensure high customer service levels, we propose the inclusion of multiple shipping/transportation options and distributed customer demands with fixed lead times into the supply chain distribution framework and formulated an integer-programming model for the five-tier supply chain design problem considered. The problem has been made additionally complex by including realistic assumptions of nonlinear transportation and inventory holding costs and the presence of economies of scale. In the light of aforementioned facts, this research proposes a novel solution methodology that amalgamates the features of Taguchi technique with Artificial Immune System (AIS) for the optimum or near optimum resolution of the problem at hand. The performance of the proposed solution methodology has been benchmarked against a set of test instances and the obtained results are compared against those obtained by Genetic Algorithm (GA), Hybrid Taguchi–Genetic Algorithm (HTGA) and AIS. Simulation results indicate that the proposed approach can not only search for optimal/near optimal solutions in large search spaces but also has good repeatability and convergence characteristics, thereby proving its superiority.     

A new population seeding technique for permutation-coded Genetic Algorithm: Service transfer approach

Genetic Algorithm (GA) is a popular heuristic method for dealing complex problems with very large search space. Among various phases of GA, the initial phase of population seeding plays an important role in deciding the span of GA to achieve the best fit w.r.t. the time. In other words, the quality of individual solutions generated in the initial population phase plays a critical role in determining the quality of final optimal solution. The traditional GA with random population seeding technique is quite simple and of course efficient to some extent; however, the population may contain poor quality individuals which take long time to converge with optimal solution. On the other hand, the hybrid population seeding techniques which have the benefit of good quality individuals and fast convergence lacks in terms of randomness, individual diversity and ability to converge with global optimal solution. This motivates to design a population seeding technique with multifaceted features of randomness, individual diversity and good quality. In this paper, an efficient Ordered Distance Vector (ODV) based population seeding technique has been proposed for permutation-coded GA using an elitist service transfer approach. One of the famous combinatorial hard problems of Traveling Salesman Problem (TSP) is being chosen as the testbed and the experiments are performed on different sized benchmark TSP instances obtained from standard TSPLIB [54]. The experimental results advocate that the proposed technique outperforms the existing popular initialization methods in terms of convergence rate, error rate and convergence time.     

EVE-OPT: a hybrid algorithm for the capacitated vehicle routing problem

This paper presents EVE-OPT, a Hybrid Algorithm based on Genetic Algorithms and Taboo Search for solving the Capacitated Vehicle Routing Problem. Several hybrid algorithms have been proposed in recent years for solving this problem. Despite good results, they usually make use of highly problem-dependent neighbourhoods and complex genetic operators. This makes their application to real instances difficult, as a number of additional constraints need to be considered. The algorithm described here hybridizes two very simple heuristics and introduces a new genetic operator, the Chain Mutation, as well as a new mutation scheme. We also apply a procedure, the k-chain-moves, able to increase the neighbourhood size, thereby improving the quality of the solution with negligible computational effort. Despite its simplicity, EVE-OPT is able to achieve the same results as very complex state-of-the art algorithms.     

A hybrid evolutionary algorithm for the job shop scheduling problem

In this paper, a hybrid metaheuristic method for the job shop scheduling problem is proposed. The optimization criterion is the minimization of makespan and the solution method consists of three components: a Differential Evolution-based algorithm to generate a population of initial solutions, a Variable Neighbourhood Search method and a Genetic Algorithm to improve the population; the latter two are interconnected. Computational experiments on benchmark data sets demonstrate that the proposed hybrid metaheuristic reaches high quality solutions in short computational times using fixed parameter settings.     

Metaheuristic algorithms hybridised with variable neighbourhood search for solving the response time variability problem

The response time variability problem (RTVP) is a scheduling problem with a wide range of real-world applications: mixed-model assembly lines, multi-threaded computer systems, network environments, broadcast of commercial videotapes and machine maintenance, among others. The RTVP arises whenever products, clients or jobs need to be sequenced in such a way that the variability in the time between the points at which they receive the necessary resources is minimised. Since the RTVP is NP-hard, several heuristic and metaheuristic techniques are needed to solve non-small instances. The published metaheuristic procedure that obtained the best solutions, on average, for non-small RTVP instances is an algorithm based on a variant of the variable neighbourhood search (VNS), called Reduced VNS (RVNS). We propose hybridising RVNS with three existing algorithms based on tabu search, multi-start and particle swarm optimisation. The aim is to combine the strengths of the metaheuristics. A computational experiment is carried out and it is shown that, on average, all proposed hybrid methods are able to improve the best published solutions.     

SASEGASA: A New Generic Parallel Evolutionary Algorithm for Achieving Highest Quality Results

This paper presents a new generic Evolutionary Algorithm (EA) for retarding the unwanted effects of premature convergence. This is accomplished by a combination of interacting generic methods. These generalizations of a Genetic Algorithm (GA) are inspired by population genetics and take advantage of the interactions between genetic drift and migration. In this regard a new selection scheme is introduced, which is designed to directedly control genetic drift within the population by advantageous self-adaptive selection pressure steering. Additionally this new selection model enables a quite intuitive heuristics to detect premature convergence. Based upon this newly postulated basic principle the new selection mechanism is combined with the already proposed Segregative Genetic Algorithm (SEGA), an advanced Genetic Algorithm (GA) that introduces parallelism mainly to improve global solution quality. As a whole, a new generic evolutionary algorithm (SASEGASA) is introduced. The performance of the algorithm is evaluated on a set of characteristic benchmark problems. Computational results show that the new method is capable of producing highest quality solutions without any problem-specific additions.     

A memetic algorithm based on a NSGAII scheme for the flexible job-shop scheduling problem

The Flexible Job-Shop Scheduling Problem is concerned with the determination of a sequence of jobs, consisting of many operations, on different machines, satisfying several parallel goals. We introduce a Memetic Algorithm, based on the NSGAII (Non-Dominated Sorting Genetic Algorithm II) acting on two chromosomes, to solve this problem. The algorithm adds, to the genetic stage, a local search procedure (Simulated Annealing). We have assessed its efficiency by running the algorithm on multiple objective instances of the problem. We draw statistics from those runs, which indicate that this Memetic Algorithm yields good and low-cost solutions.     

Simple ingredients leading to very efficient heuristics for the maximum clique problem

Starting from an algorithm recently proposed by Pullan and Hoos, we formulate and analyze iterated local search algorithms for the maximum clique problem. The basic components of such algorithms are a fast neighbourhood search (not based on node evaluation but on completely random selection) and simple, yet very effective, diversification techniques and restart rules. A detailed computational study is performed in order to identify strengths and weaknesses of the proposed algorithms and the role of the different components on several classes of instances. The tested algorithms are very fast and reliable: most of the DIMACS benchmark instances are solved within very short CPU times. For one of the hardest tests, a new putative optimum was discovered by one of our algorithms. Very good performances were also shown on recently proposed and more difficult instances. It is important to remark that the heuristics tested in this paper are basically parameter free (the appropriate value for the unique parameter is easily identified and was, in fact, the same value for all problem instances used in this paper).     

An integrated tabu search algorithm for the lot streaming problem in job shops

In this paper, we focus on solving the lot streaming problem in a job shop environment, where consistent sublots are considered. The presented three-phase algorithm incorporates the predetermination of sublot sizes, the determination of schedules based on tabu search and the variation of sublot sizes. With regard to tabu search implementation, a constructive multi-level neighbourhood is developed, which effectively connects three isolated neighbourhood functions. Moreover, enhancements of the basic version of tabu search are conducted. Combined with the procedure for varying sublot sizes, the algorithm further exploits the improvement potential. All tested instances show a rapid convergence to their lower bounds. The well-known difficult benchmark problems also achieve substantial makespan reduction. In addition, the performance of specific components is intensively examined in our study.