Path Relinking Method Research Articles

A fast path relinking algorithm for the min–max edge crossing problem

The min–max edge crossing problem (MMECP) is a challenging and important problem arising in integrated-circuit design, information visualization, and software engineering. Drawing edges as straight lines in accordance with the hierarchical graph drawing standard, the goal is to reduce the maximum number of edge crossings in graphs. In this study, we propose a fast path relinking (FPR) method based on dynamic-programming local search to tackle the MMECP, where an efficient neighborhood reduction mechanism is employed to evaluate only the so-called critical vertices instead of all the vertices. Moreover, the proposed FPR can simultaneously manage a number of neighborhood moves at each search iteration, which is significantly different from all the previous approaches based on one neighborhood in the literature. Extensive computational experiments on MMECP instances show that our proposed FPR approach is relatively competitive compared to the best-performing heuristics and the optimization Gurobi solver. In particular, our algorithm improved the best-known solutions for 104 of the 301 publicly available benchmark instances. Additional experiments were conducted to elucidate the key elements and search parameters of the proposed FPR. Furthermore, we made the source code of the algorithm publicly available to facilitate its use in real applications and future research.

An effective water wave optimization algorithm with problem-specific knowledge for the distributed assembly blocking flow-shop scheduling problem

The distributed assembly blocking flow-shop scheduling problem (DABFSP), which is a promising area in modern supply chains and manufacturing systems, has attracted great attention from researchers and practitioners. However, minimizing the total tardiness in DABFSP has not captured much attention so far. For solving the DABFSP with the total tardiness criterion, a mixed integer linear programming method is utilized to model the problem, wherein the total tardiness during the production process and assembly process are optimized simultaneously. A constructive heuristic (KBNEH) and a water wave optimization algorithm with problem-specific knowledge (KWWO) are presented. KBNEH is designed by combining a new dispatching rule with an insertion-based improvement procedure to obtain solutions with high quality. In KWWO, effective technologies, such as the re-developed destruction–construction​ operator, four local search methods under the framework of the variable neighborhood search strategy (VNS), the path-relinking method are applied to improve the performance of the algorithm. Comprehensive numerical experiments based on 900 small-scale benchmark instances and 810 large-scale benchmark instances are conducted to evaluate the performance of the presented algorithm. The experimental results obtained by KWWO are 1 to 4 times better than those obtained by the other comparison algorithms, which demonstrate that the effectiveness of KWWO is superior to the compared state-of-the-art algorithms for the considered problem.

Multi- and many-objective path-relinking: A taxonomy and decomposition approach

This paper proposes a decomposition-based path-relinking method for multi- and many-objective combinatorial optimization problems. The proposed approach, referred to as MOPR/D, considers the localization of solutions in the objective space and can handle this information to make choices regarding intermediate solutions in the path-relinking trajectory. Because it does not require aggregation functions, it does not suffer from a tendency to introduce search bias to specific regions of the Pareto front. The proposed approach was compared with seven path-relinking techniques from the literature on three differently structured combinatorial optimization problems: 0/1 multidimensional knapsack, quadratic assignment, and spanning tree. Experiments were conducted on sets of benchmark instances with up to five objectives. This study also reviewed multi-objective path generation strategies, investigated their behaviors, and a taxonomy is proposed for standardizing and classifying them.

Efficient incrementing heuristics for generalized p-location problems

This paper studies effective solving techniques for large p-location problems, in which generalized disutility is applied to incorporate stochastic behavior of real service system. The concept of generalized disutility follows the idea that the nearest located service center may be temporarily unavailable at the moment of currently arisen demand and the demand is serviced from a more distant service center with given probability. The more complex approach to the real p-location asks for enormous computational time of exact solving tools and thus evokes the question whether the faster heuristics can compete with the exact approaches in accuracy of results obtained. To answer the question, two heuristics were proposed for the studied problem. The first of them is a common swap local search with the best-admissible strategy and the second is based on the path-relinking method. The both heuristics make use of so called uniformly deployed sets used for preliminary mapping of the feasible solutions to accelerate the performance of the heuristics. As uniformly deployed set construction can be done in two modes, the paper is also focused on finding the most effective combination of the mode and heuristic. A real case study was performed with seven road networks with number of nodes varying from 250 to 660. In addition, ten different families of uniformly deployed sets were generated for each network and mode. The results of the case study confirm that the suggested approaches are able to produce the solutions of the same quality as the exact approaches. Furthermore, the study indicates drawbacks, which can be met in connection with usage of specific combinations of heuristic and the mode of uniformly deployed set construction.

Discrete self-organizing migration algorithm and p-location problems

Mathematical modelling, and integer programming generally, has many practical applications in different areas of human life. Effective and fast solving approaches for various optimization problems play an important role in the decision-making process and therefore, big attention is paid to the development of many exact and approximate algorithms. This paper deals only with a special class of location problems in which given number of facilities are to be chosen to minimize the objective function value. Since the exact methods are not suitable for their unpredictable computational time or memory demands, we focus here on possible usage of a special type of a particle swarm optimization algorithm transformed by discretization and meme usage into so-called discrete self-organizing migrating algorithm. In the paper, there is confirmed that it is possible to suggest a sophisticated heuristic for zero-one programming problem, which can produce near-to-optimal solution in much smaller time than the time demanded by exact methods. We introduce a special adaptation of the discrete self-organizing migration algorithm to the $p$-location problem making use of the path-relinking method. In the theoretical part of this paper, we introduce several strategies of the migration process. To verify their features and effectiveness, a computational study with real-sized benchmarks was performed. The main goal of the experiments was to find the most efficient version of the suggested solving tool.

A discrete oppositional multi-verse optimization algorithm for multi-skill resource constrained project scheduling problem

In this paper, a discrete oppositional multi-verse optimization (DOMVO) algorithm is proposed to address multi-skill resource constrained project scheduling problem (MS-RCPSP). Firstly, the black/white holes phase in DOMVO algorithm is designed by integrating path relinking technique. Secondly, two improved path relinking methods are presented and embedded into the proposed scheme to enhance search abilities. Thirdly, the opposition-based learning (OBL) method is employed as a hybrid strategy to improve the quality of solutions. Moreover, a repair-based decoding scheme is developed to generate schedules more efficiently. Additionally, the design-of-experiment (DOE) method is carried out to investigate the influence of parameters setting. Finally, the effectiveness of DOMVO is evaluated on the intelligent multi-objective project scheduling environment (iMOPSE) benchmark dataset and the computational comparisons indicate the superiority of the proposed DOMVO over the state-of-the-art algorithms in solving MS-RCPSP.

An iterative Path-Breaking approach with mutation and restart strategies for the MAX-SAT problem

Although Path-Relinking is an effective local search method for many combinatorial optimization problems, its application is not straightforward in solving the MAX-SAT, an optimization variant of the satisfiability problem (SAT) that has many real-world applications and has gained more and more attention in academy and industry. Indeed, it was not used in any recent competitive MAX-SAT algorithms in our knowledge. In this paper, we propose a new local search algorithm called IPBMR for the MAX-SAT, that remedies the drawbacks of the Path-Relinking method by using a careful combination of three components: A new strategy named Path-Breaking to avoid unpromising regions of the search space when generating trajectories between an elite solution and its inverse solution; a weak and a strong mutation strategies, together with restarts, to diversify the search; and stochastic path generating steps to avoid premature local optimum solutions. We then present experimental results to show that IPBMR outperforms two of the best state-of-the-art MAX-SAT local search solvers, and an empirical investigation to identify and explain the effect of the three components in IPBMR.

APaRT: A Fast Meta-Heuristic Algorithm using Path-Relinking and Tabu Search for Allocating Machines to Operations in FJSP Problem

This paper proposes a multi-start local search algorithm that solves the flexible job-shop scheduling (FJSP) problem to minimize makespan. The proposed algorithm uses a path-relinking method to generate near optimal solutions. A heuristic parameter, $\alpha$, is used to assign machines to operations.Also, a tabu list is applied to avoid getting stuck at local optimums.The proposed algorithm is tested on two sets of benchmark problems (BRdata and Kacem) to make a comparison with the variable neighborhood search.The experimental results show that the proposed algorithm can produce promising solution in a shorter amount of time.

Graph drawing using tabu search coupled with path relinking.

Graph drawing, or the automatic layout of graphs, is a challenging problem. There are several search based methods for graph drawing which are based on optimizing an objective function which is formed from a weighted sum of multiple criteria. In this paper, we propose a new neighbourhood search method which uses a tabu search coupled with path relinking to optimize such objective functions for general graph layouts with undirected straight lines. To our knowledge, before our work, neither of these methods have been previously used in general multi-criteria graph drawing. Tabu search uses a memory list to speed up searching by avoiding previously tested solutions, while the path relinking method generates new solutions by exploring paths that connect high quality solutions. We use path relinking periodically within the tabu search procedure to speed up the identification of good solutions. We have evaluated our new method against the commonly used neighbourhood search optimization techniques: hill climbing and simulated annealing. Our evaluation examines the quality of the graph layout (objective function’s value) and the speed of layout in terms of the number of evaluated solutions required to draw a graph. We also examine the relative scalability of each method. Our experimental results were applied to both random graphs and a real-world dataset. We show that our method outperforms both hill climbing and simulated annealing by producing a better layout in a lower number of evaluated solutions. In addition, we demonstrate that our method has greater scalability as it can layout larger graphs than the state-of-the-art neighbourhood search methods. Finally, we show that similar results can be produced in a real world setting by testing our method against a standard public graph dataset.

Relaxation heuristics for the set multicover problem with generalized upper bound constraints

We consider an extension of the set covering problem (SCP) introducing (i) multicover and (ii) generalized upper bound (GUB) constraints. For the conventional SCP, the pricing method has been introduced to reduce the size of instances, and several efficient heuristic algorithms based on such reduction techniques have been developed to solve large-scale instances. However, GUB constraints often make the pricing method less effective, because they often prevent solutions from containing highly evaluated variables together. To overcome this problem, we develop heuristic algorithms to reduce the size of instances, in which new evaluation schemes of variables are introduced taking account of GUB constraints. We also develop an efficient implementation of a 2-flip neighborhood local search algorithm that reduces the number of candidates in the neighborhood without sacrificing the solution quality. In order to guide the search to visit a wide variety of good solutions, we also introduce a path relinking method that generates new solutions by combining two or more solutions obtained so far. According to computational comparison on benchmark instances, the proposed method succeeds in selecting a small number of promising variables properly and performs quite effectively even for large-scale instances having hard GUB constraints.

A path relinking-based scatter search for the resource-constrained project scheduling problem

Project scheduling has received growing attention from researchers in recent decades in order to recommend models and methods to tackle problems for real-size projects. In this paper, we consider the resource-constrained project scheduling problem (RCPSP), which consists of scheduling activities in order to minimise the project duration in presence of precedence and resource constraints. We propose a hybrid metaheuristic based on scatter search that involves forward-backward improvement and reversing the project network at each iteration of the search. A bidirectional path relinking method with a new move is used as a solution combination method and a new improvement procedure is proposed in the reference set update method. The proposed method is applied to the standard benchmark projects from the PSPLIB library. The computational results show that the proposed scatter search produces high-quality solutions in a reasonable computational time and is among the best performing metaheuristics.

An evolutionary path relinking approach for the quadratic multiple knapsack problem

The quadratic multiple knapsack problem (QMKP) is a challenging combinatorial optimization problem with numerous applications. In this paper, we propose the first evolutionary path relinking approach (EPR) for solving the QMKP approximately. This approach combines advanced features both from the path relinking (PR) method and the responsive threshold search algorithm. Thanks to the tunneling property which allows a controlled exploration of infeasible regions, the proposed EPR algorithm is able to identify very high quality solutions. Experimental studies on the set of 60 well-known benchmarks and a new set of 30 large-sized instances show that EPR outperforms several state-of-the-art algorithms. In particular, for the 60 conventional benchmarks, it discovers 10 improved results (new lower bounds) and matches the best known result for the remaining 50 cases. More significantly, EPR demonstrates remarkable efficacy on the 30 new larger instances by easily dominating the current best performing algorithms across the whole instance set. Key components of the algorithm are analyzed to shed lights on their impact on the proposed approach.

An MILP model and clustering heuristics for LED assembly optimisation on high-speed hybrid pick-and-place machines

This paper deals with a scheduling optimisation problem arising in printed circuit board (PCB) assembly. In one class of PCB assembly, light-emitting diodes are to be assembled into the placement locations on PCBs by a machine with multiple pick-and-place heads. The scheduling optimisation problem is to determine the assembly sequence of placement locations and the assignment of pick-and-place heads for locations so as to minimise the assembly time. We formulate it as a mixed integer linear programming model. To solve the problem efficiently, we classify the PCBs into two types. For the first type of PCBs, on which the locations are linearly arranged, a constructive heuristic is proposed based on the analysis of the best next location after a location is assembled. For the second type of PCBs, on which the locations are circularly arranged, a heuristic based on clustering strategy and path relinking method is proposed. Computational experiments show that the solutions obtained by the two heuristics make 2.32 and 6.82% improvements averagely for the PCBs with linearly and circularly arranged locations, respectively, as compared to the solutions used in real production, and they are also better than those obtained by a hybrid genetic algorithm.

A hybrid column generation with GRASP and path relinking for the network load balancing problem

In this paper, a hybrid meta-heuristic is proposed which combines the GRASP with path relinking method and Column Generation. The key idea of this method is to run a GRASP with path relinking search on a restricted search space, defined by Column Generation, instead of running the search on the complete search space of the problem. Moreover, column generation is used not only to compute the initial restricted search space but also to modify it during the whole algorithm. The proposed heuristic is used to solve the network load balancing problem: given a capacitated telecommunications network with single path routing and an estimated traffic demand matrix, the network load balancing problem is the determination of a routing path for each traffic commodity such that the network load balancing is optimized, i.e., the worst link load is minimized, among all such solutions, the second worst link load is minimized, and continuing in this way until all link loads are minimized. The computational results presented in this paper show that, for the network load balancing problem, the proposed heuristic is effective in obtaining better quality solutions in shorter running times.

An iterated sample construction with path relinking method: Application to switch allocation in electrical distribution networks

We present a metaheuristic approach which combines constructive heuristics and local searches based on sampling with path relinking. Its effectiveness is demonstrated by an application to the problem of allocating switches in electrical distribution networks to improve their reliability. Our approach also treats the service restoration problem, which has to be solved as a subproblem, to evaluate the reliability benefit of a given switch allocation proposal. Comparisons with other metaheuristics and with a branch-and-bound procedure evaluate its performance.

Path Relinking Scheme for the Max-Cut Problem within Global Equilibrium Search

In this paper, the potential of the path relinking method for the maximum cut problem is investigated. This method is embedded within global equilibrium search to utilize the set of high quality solutions provided by the latter. The computational experiment on a set of standard benchmark problems is provided to study the proposed approach. The empirical experiments reveal that the large sizes of the elite set lead to restart distribution of the running times, i.e., the algorithm can be accelerated by simply removing all of the accumulated data (set P) and re-initiating its execution after a certain number of elite solutions is obtained.

A hybrid scatter search meta-heuristic for delay-constrained multicast routing problems

This paper investigates the first hybrid scatter search and path relinking meta-heuristic for the Delay-Constrained Least-Cost (DCLC) multicast routing problem. The underpinning mathematic model of the DCLC multicast routing problem is the constrained Steiner tree problem in graphs, a well known NP-complete problem. After combining a path relinking method as the solution combination method in scatter search, we further explore two improvement strategies: tabu search and variable neighborhood search, to intensify the search in the hybrid scatter search algorithm. A large number of simulations on some benchmark instances from the OR-library and a group of random graphs of different characteristics demonstrate that the improvement strategy greatly affects the performance of the proposed scatter search algorithm. The hybrid scatter search algorithm intensified by a variable neighborhood descent search is highly efficient in solving the DCLC multicast routing problem in comparison with other algorithms and heuristics in the literature.

Parallel path relinking method for the single machine total weighted tardiness problem with sequence-dependent setups

We propose a new method of sequential and parallel speeding up of the process of solving a single machine scheduling problem with total tardiness cost function. This improvement is done on two levels: generating a neighborhood inside path relinking method (basing on new approach--blocks in solutions) and parallelization of generating paths. The obtained results are compared to the benchmark ones taken from the literature. It was possible to find new the best solutions for many benchmark instances by using the proposed method.

Multi-start and path relinking methods to deal with multiobjective knapsack problems

This paper deals with a multiobjective combinatorial optimization problem called Extended Knapsack Problem. By applying multi-start search and path relinking we rapidly guide the search toward the most balanced zone of the Pareto-optimal front. The Pareto relation is applied in order to designate a subset of the best generated solutions to be the current efficient set of solutions. The max-min criterion with the Hamming distance is used as a measure of dissimilarity in order to find diverse solutions to be combined. The performance of our approach is compared with several state-of-the-art MOEAs for a suite test problems taken from the literature.

Optimizing production smoothing decisions via batch selection for mixed-model just-in-time manufacturing systems with arbitrary setup and processing times

This paper is concerned with the production smoothing problem that arises in the context of just-in-time manufacturing systems. The production smoothing problem can be solved by employing a two-phase solution methodology, where optimal batch sizes for the products and a sequence for these batches are specified in the first and second phases, respectively. In this paper, we focus on the problem of selecting optimal batch sizes for the products. We propose a dynamic programming (DP) algorithm for the exact solution of the problem. Our computational experiments demonstrate that the DP approach requires significant computational effort, rendering its use in a real environment impractical. We develop three meta-heuristics for the near-optimal solution of the problem, namely strategic oscillation, scatter search and path relinking. The efficiency and efficacy of the methods are tested via a computational study. The computational results show that the meta-heuristic methods considered in this paper provide near-optimal solutions for the problem within several minutes. In particular, the path relinking method can be used for the planning of mixed-model manufacturing systems in real time with its negligible computational requirement and high solution quality.