A tabu search algorithm for the pallet loading problem

This paper presents a new heuristic algorithm for the pallet loading problem, the problem of packing the maximum number of identical rectangular boxes onto a rectangular pallet. The problem arises in distribution and logistics and has many practical applications. We have developed a tabu search algorithm based on new types of moves. Instead of moving individual boxes, we propose moving blocks, sets of boxes with the same orientation. We have tested our algorithm on the whole sets Cover I and Cover II, usually taken as a reference for this problem, and we obtain excellent results in very short computing times.This complete issue was revised and published online in November 2004. The previous version contained a false date. Correspondence to: R. Alvarez-ValdesThis paper has been partially supported by the Project PBC-02-002, Consejeria de Ciencia y Tecnologia, JCCM, the Spanish Ministry of Science and Technology, DPI2002-02553 and the Valencian Science and Technology Agency, GRUPOS03/174     

基于连续函数优化的禁忌搜索算法

提出了一种连续禁忌搜索算法,用于求解连续函数优化问题.邻域规则及禁忌规则是禁忌搜索算法的核心,针对连续函数解空间的连续性,提出了一种邻域分割法来进行邻域搜索,并对禁忌规则进行了设计.通过经典函数测试可以看出,禁忌搜索算法在连续函数优化问题中显示出很强的"爬山"能力,优化结果与实际最优值非常接近,是一种有效的全局优化算法.     

集装箱装箱问题的同质块禁忌搜索算法

为保证集装箱装入物体的稳定性和减少装满后箱内的零碎剩余空间,提出了由同种规格物体组合成同质块的思想,利用局部启发规则构造同质块.设计了有效的剩余空间划分与合并处理方法,以便最大程度利用剩余空间.基于同质块生成和剩余空间处理方法,给出了禁忌搜索算法及其在编码、解码、邻域解构造以及解的评估函数等技术中的实现方法.通过标准实...     

A multilevel tabu search algorithm for balanced partitioning of unstructured grids

This paper presents a multilevel algorithm for balanced partitioning of unstructured grids. The grid is partitioned such that the number of interface elements is minimized and each partition contains an equal number of grid elements. The partition refinement of the proposed multilevel algorithm is based on iterative tabu search procedure. In iterative partition refinement algorithms, tie‐breaking in selection of maximum gain vertices affects the performance considerably. A new tie‐breaking strategy in the iterative tabu search algorithm is proposed that leads to improved partitioning quality. Numerical experiments are carried out on various unstructured grids in order to evaluate the performance of the proposed algorithm. The partition results are compared with those produced by the well‐known partitioning package Metis and k‐means clustering algorithm and shown to be superior in terms of edge cut, partition balance, and partition connectivity. Copyright © 2015 John Wiley & Sons, Ltd.     

A tabu search algorithm for simultaneous machine/AGV scheduling problem

Machines and automated guided vehicles (AGVs) scheduling problems are two essential issues that need to be addressed for the efficiency of the overall production system. The purpose of this paper is to study the simultaneous scheduling problem of machines and AGVs in a flexible manufacturing system (FMS) since the global optimum cannot be reached by considering each of them individually. In this paper, a mixed integer linear programming (MILP) model is developed with the objective of makespan minimisation. The MILP model consists of the following two constraint sets: machines and AGVs scheduling sub-problems. As both sub-problems are known to be NP-hard, a heuristic algorithm based on tabu search (TS) is proposed to get optimal or near to optimal solution for large-size problems within reasonable computation time. The proposed algorithm includes a novel two-dimensional solution representation and the generation of two neighbour solutions, which are alternately and iteratively applied to improve solutions. Moreover, an improved lower bound calculation method is introduced for the large-size problems. Computational results show the superior performance of the TS algorithm for the simultaneous scheduling problem.     

A solution to the hub center problem via a single-relocation algorithm with tabu search

Network designers for many transportation or telecommunication applications need to minimize the maximum (weighted) interaction time or distance in the networks, i.e., to solve the p-hub center problems. This study addresses the p-hub center problem. A single-relocation heuristic is proposed as a means of generating location-allocation strategies in a reasonable amount of time, and tabu search is superimposed on the underlying algorithm, so as to decrease the possibility of being trapped by local optima. Two single-allocation schemes are adapted from the literature, and a further one is developed specifically for the minimax objective function, for use in the evaluation phase of the algorithm. A greedy local search is employed to improve the resulting allocations. A number of strategies for choosing the initial hub locations are discussed and initial strategy - allocation scheme combinations are compared in terms of solution quality and pragmatic efficiency.     

A tabu search algorithm for solving a multicriteria flexible job shop scheduling problem

The problem that we consider in this article is a flexible job shop scheduling problem issued from the printing and boarding industry. Two criteria have to be minimised, the makespan and the maximum lateness. Two tabu search algorithms are proposed for finding a set of non-dominated solutions: the first is based on the minimisation of one criterion subject to a bound on the second criterion (ε-constraint approach) and the second is based on the minimisation of a linear combination of criteria. These algorithms are tested on benchmark instances from the literature and the results are discussed. The total tardiness is considered as a third criterion for the second tabu search and results are presented and discussed.     

An implementation of the iterated tabu search algorithm for the quadratic assignment problem

In this paper, we describe an implementation of the iterated tabu search (ITS) algorithm for the quadratic assignment problem (QAP), which is one of the well-known problems in combinatorial optimization. The medium- and large-scale QAPs are not, to this date, practically solvable to optimality, therefore heuristic algorithms are widely used. In the proposed ITS approach, intensification and diversification mechanisms are combined in a proper way. The goal of intensification is to search for good solutions in the neighbourhood of a given solution, while diversification is responsible for escaping from local optima and moving towards new regions of the search space. In particular, the following enhancements were implemented: new formula for fast evaluation of the objective function and efficient data structure; extended intensification mechanisms (including randomized tabu criterion, combination of tabu search and local search, dynamic tabu list maintaining); enhanced diversification strategy using periodic tabu tenure and special mutation procedure. The ITS algorithm is tested on the different instances taken from the QAP library QAPLIB. The results from the experiments demonstrate promising efficiency of the proposed algorithm, especially for the random QAP instances.     

Designing manufacturing cells: A staged approach and a tabu search algorithm

This paper proposes a three-stage approach for the manufacturing cells design problem and a tabu search scheme for its solution. The proposed approach is based on the observation that almost all computationally complex aspects can be incorporated in a middle stage optimization model. A preliminary parts grouping stage precedes and a stage eliminating remaining intercellular traffic follows. The tabu search scheme that solves the middle stage problem integrates proper short- and long-term memory structures and an overall search strategy for their use. At the code-development phase, special care has been taken to enhance the explorative capability of the algorithm by correlating search statistics with the values of the search parameters. The resulting algorithm is robust and produces more than promising results with negligible computational effort. In the absence of known optimal solutions for larger dimensions (more than 30 machines), datasets from mathematically similar areas were used. Tests with problems of size up to 50 also give encouraging results.     

A tabu search algorithm with solution space partition and repairing procedure for cyclic robotic cell scheduling problem

This paper proposes a tabu search (TS) algorithm to solve an NP-hard cyclic robotic scheduling problem. The objective is to find a cyclic robot schedule that maximises the throughput. We first formulate the problem as a linear program, provided that the robot move sequence is given, and reduce the problem to searching for an optimal robot move sequence. We find that the solution space can be divided into some specific subspaces by the maximal number of works-in-process. Then, we propose a TS algorithm to synchronously perform local searches in each subspace. To speed up our algorithm, dominated subspaces are eliminated by lower and upper bounds of the cycle time during the iterations. In the TS, a constructive heuristic is developed to generate initial solutions for each subspace and a repairing procedure is proposed to maintain the feasibility of the solutions generated in the initialisation stage and the neighbours search process. Computational comparison both on benchmark instances and randomly generated instances indicates that our algorithm is efficient for the cyclic robotic scheduling problem.     

A hybrid genetic algorithm and tabu search for a multi-objective dynamic job shop scheduling problem

In most real manufacturing environments, schedules are usually inevitable with the presence of various unexpected disruptions. In this paper, a rescheduling method based on the hybrid genetic algorithm and tabu search is introduced to address the dynamic job shop scheduling problem with random job arrivals and machine breakdowns. Because the real-time events are difficult to express and take into account in the mathematical model, a simulator is proposed to tackle the complexity of the problem. A hybrid policy is selected to deal with the dynamic feature of the problem. Two objectives, which are the schedule efficiency and the schedule stability, are considered simultaneously to improve the robustness and the performance of the schedule system. Numerical experiments have been designed to test and evaluate the performance of the proposed method. This proposed method has been compared with some common dispatching rules and meta-heuristic algorithms that have been widely used in the literature. The experimental results illustrate that the proposed method is very effective in various shop-floor conditions.     

A combined global and local search method to deal with constrained optimization for continuous tabu search

Heuristic methods, such as tabu search, are efficient for global optimizations. Most studies, however, have focused on constraint‐free optimizations. Penalty functions are commonly used to deal with constraints for global optimization algorithms in dealing with constraints. This is sometimes inefficient, especially for equality constraints, as it is difficult to keep the global search within the feasible region by purely adding a penalty to the objective function. A combined global and local search method is proposed in this paper to deal with constrained optimizations. It is demonstrated by combining continuous tabu search (CTS) and sequential quadratic programming (SQP) methods. First, a nested inner‐ and outer‐loop method is presented to lead the search within the feasible region. SQP, a typical local search method, is used to quickly solve a non‐linear programming purely for constraints in the inner loop and provides feasible neighbors for the outer loop. CTS, in the outer loop, is used to seek for the global optimal. Finally, another local search using SQP is conducted with the results of CTS as initials to refine the global search results. Efficiency is demonstrated by a number of benchmark problems. Copyright © 2008 John Wiley & Sons, Ltd.     

A tabu search approach for buffer allocation in production lines with unreliable machines

The optimal allocation of buffers is an important research issue in designing production lines. In this study, a tabu search (TS) algorithm is proposed to find near-optimal buffer allocation plans for a serial production line with unreliable machines. The main objective is to maximize the production rate, i.e. throughput, of the line. The efficiency of the proposed method is also tested to solve buffer allocation problems with the objective of total buffer size minimization. To estimate the throughput of the line with a given specific buffer allocation, an analytical decomposition approximation method is used. The performance of the tabu search algorithm is demonstrated on existing benchmark problems. The results obtained by the TS algorithm are clearly encouraging, as the TS algorithm is much better than the other algorithms for all considered benchmark problems.     

Genetic algorithm with local search for the unrelated parallel machine scheduling problem with sequence-dependent set-up times

In this paper, a genetic algorithm (GA) with local search is proposed for the unrelated parallel machine scheduling problem with the objective of minimising the maximum completion time (makespan). We propose a simple chromosome structure consisting of random key numbers in a hybrid genetic-local search algorithm. Random key numbers are frequently used in GAs but create additional difficulties when hybrid factors are implemented in a local search. The best chromosome of each generation is improved using a local search during the algorithm, but the better job sequence (which might appear during the local search operation) must be adapted to the chromosome that will be used in each successive generation. Determining the genes (and the data in the genes) that would be exchanged is the challenge of using random numbers. We have developed an algorithm that satisfies the adaptation of local search results into the GAs with a minimum relocation operation of the genes’ random key numbers – this is the main contribution of the paper. A new hybrid approach is tested on a set of problems taken from the literature, and the computational results validate the effectiveness of the proposed algorithm.     

SIMD tabu search for the quadratic assignment problem with graphics hardware acceleration

This paper presents a single instruction multiple data tabu search (SIMD-TS) algorithm for the quadratic assignment problem (QAP) with graphics hardware acceleration. The QAP is a classical combinatorial optimisation problem that is difficult to solve optimally for even small problems with over 30 items. By using graphic hardware acceleration, the developed SIMD-TS algorithm executes 20 to 45 times faster than traditional CPU code. The computational improvement is made possible by the utilisation of the parallel computing capability of a graphics processing unit (GPU). The speed and effectiveness of this algorithm are demonstrated on QAP library problems. The main contribution of this paper is a fast and effective SIMD-TS algorithm capable of producing results for large QAPs on a desktop personal computer equivalent to the results achieved with a CPU cluster.     

A tabu search heuristic for scheduling the production processes at an oil refinery

In this paper we present a tabu search heuristic which can be used for scheduling the production at an oil refinery. The scheduling problem is to decide which production modes to use at the different processing units at each point in time. The problem is a type of lot-sizing problem where costs of changeovers, inventories and production are considered. In the suggested tabu search heuristic we explore the use of variable neighbourhood, dynamic penalty and different tabu lists. Computational results are presented for different versions of the heuristic and the results are compared to the best-known lower bound for a set of scheduling scenarios.     

Synchronous tabu search parallelization strategies for multicommodity location-allocation with balancing requirements

We study and compare synchronous parallelization strategies for tabu search. We identify the most promising parallelization approaches, and evaluate the impact on performance and solution quality of some important algorithmic design parameters: length of the synchronization steps, number of processors, handling of exchanged information, etc. Parallelization approaches are implemented and compared by using a tabu search algorithm for multicommodity location-allocation problems with balancing requirements.     

Optical flow-based motion compensation algorithm for very low-bit-rate video coding

In this article, we propose an efficient compression algorithm for very low-bit-rate video applications. The algorithm is based on (a) an optical-flow motion estimation to achieve more accurate motion prediction fields; (b) discrete cosine transformation (DCT) coding of the motion vectors from the optical-flow estimation to reduce the motion overheads; and (c) an adaptive threshold technique to match optical flow motion prediction and minimize the residual errors. Unlike the classic block-matching based DCT video coding schemes in MPEG-1/2 and H.261/3, the proposed algorithm uses optical flow for motion compensation and the DCT is applied to the optical flow field instead of predictive errors. Thresholding techniques are used to treat different regions to complement optical flow technique and to efficiently code residual data. While maintaining a comparable peak signal-to-noise ratio (PSNR) and computational complexity with that of ITU-T H.263/TMN5, the reconstructed video frames of the proposed coder are free of annoying blocking artifacts, and hence visually much more pleasant. The computer simulation are conducted to show the feasibility and effectiveness of the algorithm. Results at 11 kbps are presented which can be used for videophone applications in the existing public switched telephone network (PSTN). © 1998 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 9, 230–237, 1998     

Heuristics for the generalised assignment problem: simulated annealing and tabu search approaches

The generalised assignment problem (GAP) is the problem of finding a minimum cost assignment of a set of jobs to a set of agents. Each job is assigned to exactly one agent. The total demands of all jobs assigned to any agent can not exceed the total resources available to that agent. A review of exact and heuristic methods is presented. A-generation mechanism is introduced. Different search strategies and parameter settings are investigated for the-generation descent, hybrid simulated annealing/tabu search and tabu search heuristic methods. The developed methods incorporate a number of features that have proven useful for obtaining optimal and near optimal solutions. The effectiveness of our approaches is established by comparing their performance in terms of solution quality and computional requirement to other specialized branch-and-bound tree search, simulated annealing and set partitioning heuristics on a set of standard problems from the literature.