Capacitated Clustering Problems by Hybrid Simulated Annealing and Tabu Search

The capacitated clustering problem (CCP) is the problem in which a given set of weighted objects is to be partitioned into clusters so that the total weight of objects in each cluster is less than a given value (cluster ‘capacity’). The objective is to minimize the total scatter of objects from the ‘centre’ of the cluster to which they have been allocated. A simple constructive heuristic, a R-interchange generation mechanism, a hybrid simulated annealing (SA) and tabu search (TS) algorithm which has computationally desirable features using a new non-monotonic cooling schedule, are developed. A classification of the existing SA cooling schedules is presented. The effects on the final solution quality of the initial solutions, the cooling schedule parameters and the neighbourhood search strategies are investigated. Computational results on randomly generated problems with size ranging from 50 to 100 customers indicate that the hybrid SA/TS algorithm out-performs previous simulated annealing algorithms, a simple tabu search and local descent algorithms.     

An evolution-based tabu search approach to codebook design

This paper presents an evolution-based tabu search approach (ETSA) to design codebooks with smaller distortion values in vector quantization. In the ETSA, there is no need for users to determine the size of a tabu memory and to specifically define a set of tabu restrictions and a set of aspiration criteria. During iterations, only the best solution visited is memorized as a tabu point in the search space and the distance from each trial solution to the tabu point is an important factor in the fitness evaluation. In population competition, the new fitness function plays the roles of the tabu restrictions and the aspiration criteria. Based on the new fitness function and a parallel evolutionary mechanism, the ETSA can prevent premature convergence and eventually find a good solution. Seven grayscale images are used to test the performance of the ETSA. Experimental results show that the ETSA performs better than several existing algorithms in terms of the distortion and robustness measures.     

Artificial intelligence search methods for multi-machine two-stage scheduling with due date penalty,inventory, and machining costs

This paper evaluates artificial intelligence search methods for multi-machine two-stage scheduling problems with due date penalty, inventory, and machining costs. We compare four search methods: tabu search, simulated annealing, genetic algorithm, and neighborhood search. Computational results show that the tabu search performs best in terms of solution quality. The tabu search also requires much less computational time than the genetic algorithm and simulated annealing. As expected, the neighborhood search needs the smallest computational time, but gives the worst solution quality. To further improve the solution quality and computational time, this paper proposes a two-phase tabu search. The two-phase tabu search sequentially addresses two aspects of sequencing for the same problem, order- and component-based sequencing. The order-based tabu search identifies a sequence for customers’ orders. Starting from the sequence identified for customers’ orders, the component-based tabu search fine-tunes the sequence for components produced at the fabrication stage. The results show that the two-phase tabu search is better in solution quality and computational time than the one-phase tabu search. The difference in solution quality is more pronounced at the early stage of the search.Scope and purposeMost manufacturing firms have some form of separate fabrication and assembly stages. Raw materials are transformed into components at the fabrication stage and the components are then assembled into finished products at the assembly stage. The components and assembly items are typically routed in batch quantities through several machines/work centers in a predetermined order before the finished products are delivered to customers.In this study, we model fabrication and assembly work centers as multi-machine two-stage manufacturing systems where a given machine is used to assemble/produce at least one component/product. The scheduling problem considered in this study involves a scheduling decision that achieves three objectives concurrently: (1) meeting customers’ due dates, (2) minimizing inventory cost, and (3) minimizing machining cost. Each order is an indivisible scheduling element that needs to be delivered to customers on the due date. Each order triggers successive production events from upstream to downstream according to the bill-of-material structure between components and end products.The objective of this paper are three-fold: (1) to present a solution representation for the multi-machine two-stage scheduling problem, (2) to identify the best artificial intelligence search method for this problem based on extensive computational experiments, and (3) to propose a modified tabu search method to further improve the solution quality and computational time.     

Parallel machine total tardiness scheduling with a new hybrid metaheuristic approach

This work proposes a hybrid metaheuristic (HMH) approach which integrates several features from tabu search (TS), simulated annealing (SA) and variable neighbourhood search (VNS) in a new configurable scheduling algorithm. In particular, either a deterministic or a random candidate list strategy can be used to generate the neighbourhood of a solution, both a tabu list mechanism and the SA probabilistic rule can be adopted to accept solutions, and the dimension of the explored neighbourhood can be dynamically modified. The considered class of scheduling problems is characterized by a set of independent jobs to be executed on a set of parallel machines with non-zero ready times and sequence dependent setups. In particular, the NP-hard generalized parallel machine total tardiness problem (GPMTP) recently defined by Bilge et al. [A tabu search algorithm for parallel machine total tardiness problem. Computers & Operations Research 2004;31:397–414], is faced. Several alternative configurations of the HMH have been tested on the same benchmark set used by Bilge et al. The results obtained highlight the appropriateness of the proposed approach.     

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。     

Lateness minimization with Tabu search for job shop scheduling problem with sequence dependent setup times

We tackle the job shop scheduling problem with sequence dependent setup times and maximum lateness minimization by means of a tabu search algorithm. We start by defining a disjunctive model for this problem, which allows us to study some properties of the problem. Using these properties we define a new local search neighborhood structure, which is then incorporated into the proposed tabu search algorithm. To assess the performance of this algorithm, we present the results of an extensive experimental study, including an analysis of the tabu search algorithm under different running conditions and a comparison with the state-of-the-art algorithms. The experiments are performed across two sets of conventional benchmarks with 960 and 17 instances respectively. The results demonstrate that the proposed tabu search algorithm is superior to the state-of-the-art methods both in quality and stability. In particular, our algorithm establishes new best solutions for 817 of the 960 instances of the first set and reaches the best known solutions in 16 of the 17 instances of the second set.     

Metaheuristics for the waste collection vehicle routing problem with time windows,driver rest period and multiple disposal facilities

In this problem there is a set of waste disposal facilities, a set of customers at which waste is collected and an unlimited number of homogeneous vehicles based at a single depot. Empty vehicles leave the depot and collect waste from customers, emptying themselves at the waste disposal facilities as and when necessary. Vehicles return to the depot empty. We take into consideration time windows associated with customers, disposal facilities and the depot. We also have a driver rest period. The problem is solved heuristically. A neighbour set is defined for each customer as the set of customers that are close, but with compatible time windows. A procedure that attempts to fully utilise a vehicle is used to obtain an initial solution, with this initial solution being improved using an interchange procedure. We present two metaheuristic algorithms using tabu search and variable neighbourhood search that are based around the neighbour sets. We also present a metaheuristic based on variable neighbourhood tabu search, where the variable neighbourhood is searched via tabu search. Computational results are presented for publicly available waste collection problems involving up to 2092 customers and 19 waste disposal facilities, which indicate that our algorithms produce better quality solutions than previous work presented in the literature.     

最小赋权支配集的迭代禁忌搜索算法

最小赋权支配集是一个NP困难的组合优化问题,有着广泛的应用背景。提出了一个高效的求解最小赋权支配集的迭代禁忌搜索算法。该算法采用随机贪心构造算法构造初始解,并利用快速的局部禁忌搜索算法寻找局部最优解,通过随机扰动和修复策略来搜索新的区域,以期跳出当前的局部最优解。用顶点数为800到1 000的大规模标准测试例子测试提出的算法。数值实验结果和与现存的启发式算法比较结果表明了算法是有效的。     

Tabu搜索在特征选择中的应用

研究利用Tabu搜索从大特征集中选择一组有效特征的问题.分析了Tabu搜索中表长、邻域大小和候选解数量等参数对Tabu搜索的影响.对两种特征选择的问题,与经典及最近新提出的一些特征选择方法如SFS,SBS,GSFS,GSBS,PTA,BB,GA和SFFS,SFBS等算法的实验比较表明,Tabu搜索在求解时间和解的质量上都取得了满意的结果.     

A variable neighbourhood search for fast train scheduling and routing during disturbed railway traffic situations

This paper focuses on the development of metaheuristic algorithms for the real-time traffic management problem of scheduling and routing trains in complex and busy railway networks. This key optimization problem can be formulated as a mixed integer linear program. However, since the problem is strongly NP-hard, heuristic algorithms are typically adopted in practice to compute good quality solutions in a short computation time. This paper presents a number of algorithmic improvements implemented in the AGLIBRARY optimization solver in order to improve the possibility of finding good quality solutions quickly. The optimization solver manages trains at the microscopic level of block sections and at a precision of seconds. The solver outcome is a detailed conflict-free train schedule, being able to avoid deadlock situations and to minimize train delays. The proposed algorithmic framework starts from a good initial solution for the train scheduling problem with fixed routes, obtained via a truncated branch-and-bound algorithm. Variable neighbourhood search or tabu search algorithms are then applied to improve the solution by re-routing some trains. The neighbourhood of a solution is characterized by the set of candidate trains to be re-routed and the available routes. Computational experiments are performed on railway networks from different countries and various sources of disturbance. The new algorithms often outperform a state-of-the-art tabu search algorithm and a commercial solver in terms of reduced computation times and/or train delays.     

A tabu search based approach for graph layout

This paper describes an automated tabu search based method for drawing general graph layouts with straight lines. To our knowledge, this is the first time tabu methods have been applied to graph drawing. We formulated the task as a multi-criteria optimization problem with a number of metrics which are used in a weighted fitness function to measure the aesthetic quality of the graph layout. The main goal of this work is to speed up the graph layout process without sacrificing layout quality. To achieve this, we use a tabu search based method that goes through a predefined number of iterations to minimize the value of the fitness function. Tabu search always chooses the best solution in the neighbourhood. This may lead to cycling, so a tabu list is used to store moves that are not permitted, meaning that the algorithm does not choose previous solutions for a set period of time. We evaluate the method according to the time spent to draw a graph and the quality of the drawn graphs. We give experimental results applied on random graphs and we provide statistical evidence that our method outperforms a fast search-based drawing method (hill climbing) in execution time while it produces comparably good graph layouts. We also demonstrate the method on real world graph datasets to show that we can reproduce similar results in a real world setting.     

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.     

A graph coloring heuristic using partial solutions and a reactive tabu scheme

Most of the recent heuristics for the graph coloring problem start from an infeasible k-coloring (adjacent vertices may have the same color) and try to make the solution feasible through a sequence of color exchanges. In contrast, our approach (called FOO-PARTIALCOL), which is based on tabu search, considers feasible but partial solutions and tries to increase the size of the current partial solution. A solution consists of k disjoint stable sets (and, therefore, is a feasible, partial k-coloring) and a set of uncolored vertices. We introduce a reactive tabu tenure which substantially enhances the performance of both our heuristic as well as the classical tabu algorithm (called TABUCOL) proposed by Hertz and de Werra [Using tabu search techniques for graph coloring, Computing 1987;39:345–51]. We will report numerical results on different benchmark graphs and we will observe that FOO-PARTIALCOL, though very simple, outperforms TABUCOL on some instances, provides very competitive results on a set of benchmark graphs which are known to be difficult, and outperforms the best-known methods on the graph flat300_28_0. For this graph, FOO-PARTIALCOL finds an optimal coloring with 28 colors. The best coloring achieved to date uses 31 colors. Algorithms very close to TABUCOL are still used as intensification procedures in the best coloring methods, which are evolutionary heuristics. FOO-PARTIALCOL could then be a powerful alternative. In conclusion FOO-PARTIALCOL is one of the most efficient simple local search coloring methods yet available.     

铁路行包基地及配送点选址问题禁忌搜索算法

分析了铁路行包运输物流化发展背景及行包运输物流配送的特点,给出了铁路行包基地及配送点选址的数学模型,应用改进的扫描法构造问题尽可能好的初始解,并通过巧妙地设计罚函数、合理构造邻域及随机选取禁忌长度的一种禁忌搜索算法对初始解优化．计算结果表明,扫描法和禁忌搜索算法结合的两阶段法,不仅可以得到良好的计算结果,而且具有搜索空间小、求解速度快的优点,该方法是有效、可行的．     

片上网络映射问题的改进禁忌搜索算法

为求解通信时延受约束的低能耗片上网络(NoC)映射问题,提出一种改进禁忌搜索算法.该算法由局部搜索和精英重组2个步骤经过多次迭代完成,局部搜索采用简化的robust tabu search (RoTS),精英重组步骤选用COHX交叉操作.实验结果表明:文中算法与RoTS相比具有优化性能好、搜索空间小的优点,映射结果比分支限界法平均节能16.1%,适于求解大规模NoC映射问题.     

A tabu search algorithm for order acceptance and scheduling

We consider a make-to-order production system, where limited production capacity and order delivery requirements necessitate selective acceptance of the orders. Since tardiness penalties cause loss of revenue, scheduling and order acceptance decisions must be taken jointly to maximize total revenue. We present a tabu search algorithm that solves the order acceptance and scheduling problem on a single machine with release dates and sequence dependent setup times. We analyze the performance of the tabu search algorithm on an extensive set of test instances with up to 100 orders and compare it with two heuristics from the literature. In the comparison, we report optimality gaps which are calculated with respect to bounds generated from a mixed integer programming formulation. The results show that the tabu search algorithm gives near optimal solutions that are significantly better compared to the solutions given by the two heuristics. Furthermore, the run time of the tabu search algorithm is very small, even for 100 orders. The success of the proposed heuristic largely depends on its capability to incorporate in its search acceptance and scheduling decisions simultaneously.     

Improved Tabu search heuristics for the dynamic space allocation problem

The dynamic space allocation problem (DSAP) presented in this paper considers the task of assigning items (resources) to locations during a multi-period planning horizon such that the cost of rearranging the items is minimized. Three tabu search heuristics are presented for this problem. The first heuristic is a simple basic tabu search heuristic. The second heuristic adds diversification and intensification strategies to the first, and the third heuristic is a probabilistic tabu search heuristic. To test the performances of the heuristics, a set of test problems from the literature is used in the analysis. The results show that the tabu search heuristics are efficient techniques for solving the DSAP. More importantly, the proposed tabu search heuristic with diversification/intensification strategies found new best solutions using less computation time for one-half of all the test problems.     

Adaptive memory search for multidemand multidimensional knapsack problems

We describe a simple adaptive memory search method for the 0/1 Multidemand Multidimensional Knapsack Problem (0/1 MDMKP). The search balances the level of infeasibility against the quality of the solution, and uses a simple dynamic tabu search mechanism. A weighting scheme to balance out the differences in the tightness of the constraints is also implemented. Computational results on a portfolio of test problems taken from the literature are reported, showing very favorable results, both in terms of solution quality and the ability of the search to find feasible solutions.     

A hybrid genetic algorithm and tabu search approach for post enrolment course timetabling

The post enrolment course timetabling problem (PECTP) is one type of university course timetabling problems, in which a set of events has to be scheduled in time slots and located in suitable rooms according to the student enrolment data. The PECTP is an NP-hard combinatorial optimisation problem and hence is very difficult to solve to optimality. This paper proposes a hybrid approach to solve the PECTP in two phases. In the first phase, a guided search genetic algorithm is applied to solve the PECTP. This guided search genetic algorithm, integrates a guided search strategy and some local search techniques, where the guided search strategy uses a data structure that stores useful information extracted from previous good individuals to guide the generation of offspring into the population and the local search techniques are used to improve the quality of individuals. In the second phase, a tabu search heuristic is further used on the best solution obtained by the first phase to improve the optimality of the solution if possible. The proposed hybrid approach is tested on a set of benchmark PECTPs taken from the international timetabling competition in comparison with a set of state-of-the-art methods from the literature. The experimental results show that the proposed hybrid approach is able to produce promising results for the test PECTPs.     

A very fast TS/SA algorithm for the job shop scheduling problem

The job shop scheduling problem (JSP) is one of the most notoriously intractable NP-complete optimization problems. Over the last 10–15 years, tabu search (TS) has emerged as an effective algorithmic approach for the JSP. However, the quality of solutions found by tabu search approach depends on the initial solution. To overcome this problem and provide a robust and efficient methodology for the JSP, the heuristics search approach combining simulated annealing (SA) and TS strategy is developed. The main principle of this approach is that SA is used to find the elite solutions inside big valley (BV) so that TS can re-intensify search from the promising solutions. This hybrid algorithm is tested on the standard benchmark sets and compared with the other approaches. The computational results show that the proposed algorithm could obtain the high-quality solutions within reasonable computing times. For example, 17 new upper bounds among the unsolved problems are found in a short time.