A tabu search/path relinking algorithm to solve the job shop scheduling problem

We present an algorithm that incorporates a tabu search procedure into the framework of path relinking to generate solutions to the job shop scheduling problem (JSP). This tabu search/path relinking (TS/PR) algorithm comprises several distinguishing features, such as a specific relinking procedure to effectively construct a path linking the initiating solution and the guiding solution, and a reference solution determination mechanism based on two kinds of improvement methods. We evaluate the performance of TS/PR on almost all of the benchmark JSP instances available in the literature. The test results show that TS/PR obtains competitive results compared with state-of-the-art algorithms for JSP in the literature, demonstrating its efficacy in terms of both solution quality and computational efficiency. In particular, TS/PR is able to improve the upper bounds for 49 out of the 205 tested instances and it solves a challenging instance that has remained unsolved for over 20 years.     

基于扩展状态任务网的制造供应链计划

制造供应链计划是制造供应链管理的关键问题,它不仅需要分配生产任务和控制库存,还需要解决不同工厂(企业)间的运输配套问题.为统一描述具有复杂产品生产过程(包括装配型、分解型和多输入多输出型等)的生产任务、存储任务和不同模式(包括单种物料独立运输模式和多种物料组合运输模式)的运输任务,提出了扩展状态任务网(extended state task network,简称ESTN).扩展状态任务网用比例转化任务统一描述生产任务、存储任务和单种物料独立运输任务,用虚比例转化任务和组合移动任务共同描述多种物料组合运输任务.应用扩展状态任务网,meta启发式方法在求解制造供应链问题时更容易编码和操作.为求解基于ESTN的制造供应链计划模型,提出了具有多样性检测的参考解集更新策略与分散性解变异策略的路径重连算法.路径重连算法维护一个由高质量解(精英解)组成的参考解集,将一个向导精英解的属性逐步引入一个起始精英解而形成的中间解序列(路径),并用此中间解序列更新参考解集以获得进化.计算实例表明,该路径重连算法比标准遗传算法、标准Tabu搜索算法以及普通路径重连算法能够获得更好的解,证明了多样性检测对参考解集更新的关键作用以及分散性解变异策略在提高解的质量上的能力.     

Local search algorithm with path relinking for single batch-processing machine scheduling problem

The single batch-processing machine problem is to minimize makespan, which has broad applications, including engineering fundamentals and theoretical background. The machine can process several jobs as a batch simultaneously, and every job has three different attributes: job size, processing time, and job arrival. In this paper, a hybrid local search algorithm with path relinking (LP) is devised to solve the problem. We not only generate an optimal initial solution firstly but also pay more attention to improving the solution quality. Three kinds of local searches are applied to enhance the diversity of solutions; the path relinking is adopted to explore better solutions through local tracks connecting the current solution and the best in the elite set. With these approaches, it can keep a balanced rate between exploratory and exploitative capacity. Computational experiments on 40 benchmark instances indicate that LP has the superior convergence and robust performance and it surpasses the current state-of-the-art methods such as genetic algorithm and ant colony optimization, especially for large instances.

     

A hybrid particle swarm optimization algorithm for the vehicle routing problem

This paper introduces a new hybrid algorithmic nature inspired approach based on particle swarm optimization, for successfully solving one of the most popular supply chain management problems, the vehicle routing problem. The vehicle routing problem is considered one of the most well studied problems in operations research. The proposed algorithm for the solution of the vehicle routing problem, the hybrid particle swarm optimization (HybPSO), combines a particle swarm optimization (PSO) algorithm, the multiple phase neighborhood search–greedy randomized adaptive search procedure (MPNS–GRASP) algorithm, the expanding neighborhood search (ENS) strategy and a path relinking (PR) strategy. The algorithm is suitable for solving very large-scale vehicle routing problems as well as other, more difficult combinatorial optimization problems, within short computational time. It is tested on a set of benchmark instances and produced very satisfactory results. The algorithm is ranked in the fifth place among the 39 most known and effective algorithms in the literature and in the first place among all nature inspired methods that have ever been used for this set of instances.     

A GRASP algorithm to solve the unicost set covering problem

The set covering problem (SCP) is a well-known combinatorial optimization problem. This paper presents a GRASP algorithm to solve a special SCP case known in the literature as the unicost set covering problem. The algorithm incorporates a local improvement procedure based on the heuristics to solve binary constraint satisfiability problems (SAT). The quality of the proposed algorithm is tested on a set of reference instances, comparing the obtained results with those found in the literature. Our algorithm improves the best-known solutions for many of these instances.     

A tabu search based hybrid evolutionary algorithm for the max-cut problem

This paper presents a tabu search based hybrid evolutionary algorithm (TSHEA) for solving the max-cut problem. The proposed algorithm integrates a distance-and-quality based solution combination operator and a tabu search procedure based on neighborhood combination of one-flip and constrained exchange moves. Comparisons with leading reference algorithms from the literature disclose that the proposed algorithm discovers new best solutions for 15 out of 91 instances, while matching the best known solutions on all but 4 instances. Analysis indicates that the neighborhood combination and the solution combination operator play key roles to the effectiveness of the proposed algorithm.     

Hybrid ensemble selection algorithm incorporating GRASP with path relinking

The greedy randomized adaptive search procedure (GRASP) is an iterative two-phase multi-start metaheuristic procedure for a combination optimization problem, while path relinking is an intensification procedure applied to the solutions generated by GRASP. In this paper, a hybrid ensemble selection algorithm incorporating GRASP with path relinking (PRelinkGraspEnS) is proposed for credit scoring. The base learner of the proposed method is an extreme learning machine (ELM). Bootstrap aggregation (bagging) is used to produce multiple diversified ELMs, while GRASP with path relinking is the approach for ensemble selection. The advantages of the ELM are inherited by the new algorithm, including fast learning speed, good generalization performance, and easy implementation. The PRelinkGraspEnS algorithm is able to escape from local optima and realizes a multi-start search. By incorporating path relinking into GRASP and using it as the ensemble selection method for the PRelinkGraspEnS the proposed algorithm becomes a procedure with a memory and high convergence speed. Three credit datasets are used to verify the efficiency of our proposed PRelinkGraspEnS algorithm. Experimental results demonstrate that PRelinkGraspEnS achieves significantly better generalization performance than the classical directed hill climbing ensemble pruning algorithm, support vector machines, multi-layer perceptrons, and a baseline method, the best single model. The experimental results further illustrate that by decreasing the average time needed to find a good-quality subensemble for the credit scoring problem, GRASP with path relinking outperforms pure GRASP (i.e., without path relinking).     

GRASP with path relinking for commercial districting

The problem of grouping basic units into larger geographic territories subject to dispersion, connectivity, and balance requirements is addressed. The problem is motivated by a real-world application from the bottled beverage distribution industry. Typically, a dispersion function is minimized as compact territories are sought. Existing literature reveals that practically all the works on commercial districting use center-based dispersion functions. These center-based functions yield mixed-integer programming models with some nice properties; however, they have the disadvantage of being very costly to be properly evaluated when used within heuristic frameworks. This is due to the center updating operations frequently needed through the heuristic search. In this work, a more robust dispersion measure based on the diameter of the formed territories is studied. This allows a more efficient heuristic search computation. For solving this particular territory design problem, a greedy randomized adaptive search procedure (GRASP) that incorporates a novel construction procedure where territories are formed simultaneously in two main stages using different criteria is proposed. This also differs from previous literature where GRASP was used to build one territory at a time. The GRASP is further enhanced with two variants of forward-backward path relinking, namely static and dynamic. Path relinking is a sophisticated and very successful search mechanism. This idea is novel in any districting or territory design application to the best of our knowledge. The proposed algorithm and its components have been extensively evaluated over a wide set of data instances. Experimental results reveal that the construction mechanism produces feasible solutions of acceptable quality, which are improved by an effective local search procedure. In addition, empirical evidence indicate that the two path relinking strategies have a significant impact on solution quality when incorporated within the GRASP framework. The ideas and components of the developed method can be further extended to other districting problems under balancing and connectivity constraints.     

A GRASP with evolutionary path relinking for the truck and trailer routing problem

In the truck and trailer routing problem (TTRP) a heterogeneous fleet composed of trucks and trailers has to serve a set of customers, some only accessible by truck and others accessible with a truck pulling a trailer. This problem is solved using a route-first, cluster-second procedure embedded within a hybrid metaheuristic based on a greedy randomized adaptive search procedure (GRASP), a variable neighborhood search (VNS) and a path relinking (PR). We test PR as a post-optimization procedure, as an intensification mechanism, and within evolutionary path relinking (EvPR). Numerical experiments show that all the variants of the proposed GRASP with path relinking outperform all previously published methods. Remarkably, GRASP with EvPR obtains average gaps to best-known solutions of less than 1% and provides several new best solutions.     

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.     

A GRASP with path‐relinking and restarts heuristic for the prize‐collecting generalized minimum spanning tree problem

Given a graph with its vertex set partitioned into a set of groups, nonnegative costs associated to its edges, and nonnegative prizes associated to its vertices, the prize‐collecting generalized minimum spanning tree problem consists in finding a subtree of this graph that spans exactly one vertex of each group and minimizes the sum of the costs of the edges of the tree less the prizes of the selected vertices. It is a generalization of the NP‐hard generalized minimum spanning tree optimization problem. We propose a GRASP (greedy randomized adaptive search procedure) heuristic for its approximate solution, incorporating path‐relinking for search intensification and a restart strategy for search diversification. The hybridization of the GRASP with path‐relinking and restarts heuristic with a data mining strategy that is applied along with the GRASP iterations, after the elite set is modified and becomes stable, contributes to making the heuristic more robust. The computational experiments show that the heuristic developed in this work found very good solutions for test problems with up to 439 vertices. All input data for the test instances and detailed numerical results are made available from Mendeley Data.     

A parallel algorithm for constrained two-staged two-dimensional cutting problems

In this paper, we solve the two-staged two-dimensional cutting problem using a parallel algorithm. The proposed approach combines two main features: beam search (BS) and strip generation solution procedures (SGSP). BS employs a truncated tree-search, where a selected subset of generated nodes are retuned for further search. SGSP, a constructive procedure, combines a (sub)set of strips for providing both partial lower and complementary upper bounds. The algorithm explores in parallel a subset of selected nodes following the master-slave paradigm. The master processor serves to guide the search-resolution and each slave processor develops its proper way, trying a global convergence. The aim of such an approach is to show how the parallelism is able to efficiently solve large-scale instances, by providing new solutions within a consistently reduced runtime. Extensive computational testing on instances, taken from the literature, shows the effectiveness of the proposed approach.     

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.     

Hybridizations of GRASP with path relinking for the far from most string problem

Among the sequence selection and comparison problems, the far from most string problem (FFMSP) is one of the computationally hardest with applications in several fields, including molecular biology where one is interested in creating diagnostic probes for bacterial infections or in discovering potential drug targets. In this paper, we describe several heuristics that hybridize GRASP with different path‐relinking strategies, such as forward, backward, mixed, greedy randomized adaptive forward, and evolutionary path relinking. Experiments on a large set of both real‐world and randomly generated test instances indicate that these hybrid heuristics are both effective and efficient. In particular, the hybrid GRASP with evolutionary path relinking finds slightly better quality solutions compared to the other variants when running for the same number of iterations, while the hybrid with backward path relinking finds better quality solution within a fixed running time.     

GRASP and path relinking for the max–min diversity problem

The max–min diversity problem (MMDP) consists in selecting a subset of elements from a given set in such a way that the diversity among the selected elements is maximized. The problem is NP-hard and can be formulated as an integer linear program. Since the 1980s, several solution methods for this problem have been developed and applied to a variety of fields, particularly in the social and biological sciences. We propose a heuristic method—based on the GRASP and path relinking methodologies—for finding approximate solutions to this optimization problem. We explore different ways to hybridize GRASP and path relinking, including the recently proposed variant known as GRASP with evolutionary path relinking. Empirical results indicate that the proposed hybrid implementations compare favorably to previous metaheuristics, such as tabu search and simulated annealing.     

The fixed set search applied to the power dominating set problem

In this article, we focus on solving the power dominating set problem and its connected version. These problems are frequently used for finding optimal placements of phasor measurement units in power systems. We present an improved integer linear program (ILP) for both problems. In addition, a greedy constructive algorithm and a local search are developed. A greedy randomised adaptive search procedure (GRASP) algorithm is created to find near optimal solutions for large scale problem instances. The performance of the GRASP is further enhanced by extending it to the novel fixed set search (FSS) metaheuristic. Our computational results show that the proposed ILP has a significantly lower computational cost than existing ILPs for both versions of the problem. The proposed FSS algorithm manages to find all the optimal solutions that have been acquired using the ILP. In the last group of tests, it is shown that the FSS can significantly outperform the GRASP in both solution quality and computational cost.     

A water-flow algorithm for flexible flow shop scheduling with intermediate buffers

We investigate the flexible flow shop scheduling problem with limited or unlimited intermediate buffers. A common objective of the problem is to find a production schedule that minimizes the completion time of jobs. Other objectives that we also consider are minimizing the total weighted flow time of jobs and minimizing the total weighted tardiness time of jobs. We propose a water-flow algorithm to solve this scheduling problem. The algorithm is inspired by the hydrological cycle in meteorology and the erosion phenomenon in nature. In the algorithm, we combine the amount of precipitation and its falling force to form a flexible erosion capability. This helps the erosion process of the algorithm to focus on exploiting promising regions strongly. To initiate the algorithm, we use a constructive procedure to obtain a seed permutation. We also use an improvement procedure for constructing a complete schedule from a permutation that represents the sequence of jobs in the first stage of the scheduling problem. To evaluate the proposed algorithm, we use benchmark instances taken from the literature and randomly generated instances of the scheduling problem. The computational results demonstrate the efficacy of the algorithm. We have also obtained several improved solutions for the benchmark instances using the proposed algorithm. We further illustrate the algorithm’s capability for solving problems in practical applications by applying it to a maltose syrup production problem.     

Parallel island based Memetic Algorithm with Lin–Kernighan local search for a real-life Two-Echelon Heterogeneous Vehicle Routing Problem based on Brazilian wholesale companies

This paper deals with a Two-Echelon Fixed Fleet Heterogeneous Vehicle Routing Problem (2E-HVRP) faced by Brazilian wholesale companies. Vehicle routing problems with more than one phase are known as Multi-Echelon VRP and consider situations in which freight is moved through some intermediate facilities (e.g., cross-docks or distribution centers) before reaching its destination. The first phase of the problem dealt here is to choose a first-level vehicle, from an heterogeneous set, that will leave a depot and reach an intermediate uncapacitated facility (satellite) to serve a set of second-level vehicles. After that, it is necessary to define routes for smaller vehicles, also from an heterogeneous set, that will visit a set of customers departing from and returning to a satellite. The solution proposed here is an efficient island based memetic algorithm with a local search procedure based on Lin–Kernighan heuristic (IBMA-LK). In order to attest the algorithm’s efficiency, first it was tested in single echelon HVRP benchmark instances. After that the instances were adapted for two-echelon context and used for 2E-HVRP validation and, finally, it was tested on 2E-HVRP instances created using real world normalized data. Localsolver tool was also executed for comparison purposes. Promising results (which corroborate results obtained on the real problem) and future works are presented and discussed.     

求解最大割问题的多启动禁忌搜索算法

为了增强局部搜索算法在求解最大割问题上的寻优能力,提高解质量,提出了一种多启动禁忌搜索（MSTS）算法。算法主要包括两个重要组件:一是用于搜索高质量局部优化解的禁忌搜索算法;二是具有全局搜索能力的重启策略。算法首先通过禁忌搜索组件获取局部优化解;然后应用设计的重启策略重新生成初始解并重启禁忌搜索过程。重启策略基于随机贪心的思想,综合利用了“构造”和“扰动”这两种方法生成新的起始解,来逃离局部最优的陷阱从而找到更高优度的解。采用了国际文献中公认的21个算例作为本算法的测试实验集并进行实算, 并与多个先进算法进行比较,MSTS算法在18个算例上得到最好解值,高于其他对比算法。实验结果表明,MSTS算法具有更强的寻优能力和更高的解质量。     

Using a greedy random adaptative search procedure to solve the cover printing problem

In this paper, the cover printing problem, which consists in the grouping of book covers on offset plates in order to minimize the total production cost, is discussed. As the considered problem is hard, we discuss and propose a greedy random adaptative search procedure (GRASP) to solve the problem. The quality of the proposed procedure is tested on a set of reference instances, comparing the obtained results with those found in the literature. Our procedure improves the best known solutions for some of these instances. Results are also presented for larger, randomly generated problems.