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.     

Tabu search for the job-shop scheduling problem with multi-purpose machines

In this paper we study the following generalization of the job-shop scheduling problem. Each operation can be performed by one machine out of a set of machines given for this operation. The processing time does not depend on the machine which has been chosen for processing the operation. This problem arises in the area of flexible manufacturing. As a generalization of the jobshop problem it belongs to the hardest problems in combinatorial optimization. We show that an application of tabu search techniques to this problem yields excellent results for benchmark problems.Supported by Deutsche Forschungsgemeinschaft, Project JoP-TAG     

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.     

An adaptive scheduling algorithm for a parallel machine problem with rework processes

The development of a scheduling methodology for a parallel machine problem with rework processes is presented in this paper. The problem is to make a schedule for parallel machines with rework probabilities, due-dates, and sequence dependent setup times. Two heuristics are developed based on a dispatching algorithm and problem-space-based search method. In order to evaluate the efficacy of the proposed algorithms, six performance indicators are considered: total tardiness, maximum lateness, mean flow-time, mean lateness, the number of tardy jobs, and the number of reworks. This paper shows how these algorithms can adaptively capture the characteristics of manufacturing facilities for enhancing the performance under changing production environments. Extensive experimental results show that the proposed algorithms give very efficient performance in terms of computational time and each objective value.     

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     

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.     

Makespan minimisation for a parallel machine scheduling problem with preemption and job incompatibility

In this paper, an extension of the graph colouring problem is introduced to model a parallel machine scheduling problem with job incompatibility. To get closer to real-world applications, where the number of machines is limited and jobs have different processing times, each vertex of the graph requires multiple colours and the number of vertices with the same colour is bounded. In addition, several objectives related to scheduling are considered: makespan, number of pre-emptions and summation over the jobs’ throughput times. Different solution methods are proposed, namely, two greedy heuristics, two tabu search methods and an adaptive memory algorithm. The latter uses multiple recombination operators, each one being designed for optimising a subset of objectives. The most appropriate operator is selected dynamically at each iteration, depending on its past performance. Experiments show that the proposed algorithm is effective and robust, while providing high-quality solutions on benchmark instances for the graph multi-colouring problem, a simplification of the considered problem.     

A multi-objective scatter search for the ladle scheduling problem

We consider the ladle scheduling problem, which can be regarded as a vehicle routing problem with semi-soft time windows and adjustment times. The problem concerns allocating ladles to serve molten steel based on a given steelmaking scheduling plan, and determining the modification operations for the empty ladles after the service process. In addition, combining the controllable processing time of molten steel, the other aspect of the problem is to determine the service start times taking into consideration the technological constraints imposed in practice. We present a non-linear mathematical programming model with the conflicting objectives of minimising the occupation ratio of the ladles and maximising the degree of satisfaction with meeting the soft windows. To solve the multi-objective model, we develop a new scatter search (SS) approach by re-designing the common components of SS and incorporating a diversification generator, a combination method and a diversification criterion to conduct a wide exploration of the search space. We analyse and compare the performance of the proposed approach with a multi-objective genetic algorithm and with manual scheduling adopted in practical production using three real-life instances from a well-known iron–steel production plant in China. The computational results demonstrate the effectiveness of the proposed SS approach for solving the ladle scheduling problem.     

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.     

Optimization of truss topology using tabu search

A design procedure for integrating topological considerations in the framework of structural optimization is presented. The proposed approach is capable of considering multiple load conditions, stress, displacement and local/global buckling constraints, and multiple objective functions in the problem formulation. Further, since the proposed method permits members to be added to or deleted from an existing topology and the topology is not defined by member areas, the difficulty of not being able to reach singular optima is also avoided. These objectives are accomplished using a discrete optimization procedure which uses 0–1 topological variables to optimize alternate designs. Since the topological variables are discrete in nature and the member cross-sections are assumed to be continuous, the topological optimization problem has mixed discrete-continuous variables. This non-linear programming problem is solved using a memory-based combinatorial optimization technique known as tabu search. Numerical results obtained using tabu search for single and multiobjective topological optimization of truss structures are presented. To model the multiple objective functions in the problem formulation, a cooperative game theoretic approach is used. The results indicate that the optimum topologies obtained using tabu search compare favourably, and in some instances, outperform the results obtained using the ground–structure approach. However, this improvement occurs at the expense of a significant increase in computational burden owing to the fact that the proposed approach necessitates that the geometry of each trial topology be optimized.     

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.     

Speeding up a Rollout algorithm for complex parallel machine scheduling

Rollout methodology is a constructive metaheuristic algorithm and its main characteristics are its modularity, the adaptability to different objectives and constraints and the easiness of implementation. Multi-heuristic Rollout extends the Rollout by incorporating several constructive heuristics in the Rollout framework and it is able to easily incorporate human experience inside its research patterns to fulfil complex requirements dictated by the application at hand. However, a drawback for both Rollout and multi-heuristic Rollout is often represented by the required computation time. This paper proposes some alternatives of the full multi-heuristic Rollout algorithm aimed at improving the efficiency by reducing the computational effort while preserving the effectiveness. Namely, we propose dynamic heuristics pruning and candidates reduction strategies. As illustrative case studies, we analyse complex deterministic identical parallel machine scheduling problems showing how Rollout procedures can be used to tackle several additional constraints arising in real contexts. More specifically, we considered both standard (batch production, family set-ups, release, due dates, etc.) and non-standard (machine unavailabilities, maximum campaign size) scheduling constraints. An extensive campaign of computational experiments shows the behaviour of the multi-heuristic Rollout approach and the effectiveness of the different proposed speed-up methods.     

An improved harmony search algorithm for emergency inspection scheduling

The ability of nature-inspired search algorithms to efficiently handle combinatorial problems, and their successful implementation in many fields of engineering and applied sciences, have led to the development of new, improved algorithms. In this work, an improved harmony search (IHS) algorithm is presented, while a holistic approach for solving the problem of post-disaster infrastructure management is also proposed. The efficiency of IHS is compared with that of the algorithms of particle swarm optimization, differential evolution, basic harmony search and the pure random search procedure, when solving the districting problem that is the first part of post-disaster infrastructure management. The ant colony optimization algorithm is employed for solving the associated routing problem that constitutes the second part. The comparison is based on the quality of the results obtained, the computational demands and the sensitivity on the algorithmic parameters.     

Two-stage hybrid flow shop scheduling with preventive maintenance using multi-objective tabu search method

This paper investigates an integrated bi-objective optimisation problem with non-resumable jobs for production scheduling and preventive maintenance in a two-stage hybrid flow shop with one machine on the first stage and m identical parallel machines on the second stage. Sequence-dependent set-up times and preventive maintenance (PM) on the first stage machine are considered. The scheduling objectives are to minimise the unavailability of the first stage machine and to minimise the makespan simultaneously. To solve this integrated problem, three decisions have to be made: determine the processing sequence of jobs on the first stage machine, determine whether or not to perform PM activity just after each job, and specify the processing machine of each job on the second stage. Due to the complexity of the problem, a multi-objective tabu search (MOTS) method is adapted with the implementation details. The method generates non-dominated solutions with several parallel tabu lists and Pareto dominance concept. The performance of the method is compared with that of a well-known multi-objective genetic algorithm, in terms of standard multi-objective metrics. Computational results show that the proposed MOTS yields a better approximation.     

A hybrid VNS-HS algorithm for a supply chain scheduling problem with deteriorating jobs

This paper investigates a coordinated scheduling problem in a two stage supply chain where parallel-batching machine, deteriorating jobs and transportation coordination are considered simultaneously. During the production stage, jobs are processed by suppliers and there exists one parallel-batching machine in each supplier. The actual processing time of a job depends on its starting time and normal processing time. The normal processing time of a batch is equal to the largest normal processing time among all jobs in its batch. During the transportation stage, the jobs are then delivered to the manufacturer. Since suppliers are distributed in different locations, the transportation time between each supplier and the manufacturer is different. Based on some structural properties of the studied problem, an optimal algorithm for minimising makespan on a single supplier is presented. This supply chain scheduling problem is proved to be NP-hard, and a hybrid VNS-HS algorithm combining variable neighbourhood search (VNS) with harmony search (HS) is proposed to find a good solution in reasonable time. Finally, some computational experiments are conducted and the results demonstrate the effectiveness and efficiency of the proposed VNS-HS.     

Robustness and stability measures for scheduling: single-machine environment

This paper addresses the issue of finding robust and stable schedules with respect to random disruptions. Specifically, two surrogate measures for robustness and stability are developed. The proposed surrogate measures, which consider both busy and repair time distributions, are embedded in a tabu-search-based scheduling algorithm, which generates schedules in a single-machine environment subject to machine breakdowns. The performance of the proposed scheduling algorithm and the surrogate measures are tested under a wide range of experimental conditions. The results indicate that one of the proposed surrogate measures performs better than existing methods for the total tardiness and total flowtime criteria in a periodic scheduling environment. A comprehensive bibliography is also presented.     

A Meta-RaPS for the early/tardy single machine scheduling problem

This paper investigates a meta-heuristic solution approach to the early/tardy single machine scheduling problem with common due date and sequence-dependent setup times. The objective of this problem is to minimise the total amount of earliness and tardiness of jobs that are assigned to a single machine. The popularity of just-in-time (JIT) and lean manufacturing scheduling approaches makes the minimisation of earliness and tardiness important and relevant. In this research the early/tardy problem is solved by Meta-RaPS (meta-heuristic for randomised priority search). Meta-RaPS is an iterative meta-heuristic which is a generic, high level strategy used to modify greedy algorithms based on the insertion of a random element. In this case a greedy heuristic, the shortest adjusted processing time, is modified by Meta-RaPS and the good solutions are improved by a local search algorithm. A comparison with the existing ETP solution procedures using well-known test problems shows Meta-RaPS produces better solutions in terms of percent difference from optimal. The results provide high quality solutions in reasonable computation time, demonstrating the effectiveness of the simple and practical framework of Meta-RaPS.     

Parallel machine scheduling with step-deteriorating jobs and setup times by a hybrid discrete cuckoo search algorithm

This article considers the parallel machine scheduling problem with step-deteriorating jobs and sequence-dependent setup times. The objective is to minimize the total tardiness by determining the allocation and sequence of jobs on identical parallel machines. In this problem, the processing time of each job is a step function dependent upon its starting time. An individual extended time is penalized when the starting time of a job is later than a specific deterioration date. The possibility of deterioration of a job makes the parallel machine scheduling problem more challenging than ordinary ones. A mixed integer programming model for the optimal solution is derived. Due to its NP-hard nature, a hybrid discrete cuckoo search algorithm is proposed to solve this problem. In order to generate a good initial swarm, a modified Biskup–Hermann–Gupta (BHG) heuristic called MBHG is incorporated into the population initialization. Several discrete operators are proposed in the random walk of Lévy flights and the crossover search. Moreover, a local search procedure based on variable neighbourhood descent is integrated into the algorithm as a hybrid strategy in order to improve the quality of elite solutions. Computational experiments are executed on two sets of randomly generated test instances. The results show that the proposed hybrid algorithm can yield better solutions in comparison with the commercial solver CPLEX^® with a one hour time limit, the discrete cuckoo search algorithm and the existing variable neighbourhood search algorithm.     

A scatter search for the extended resource renting problem

In this paper, the extended Resource Renting Problem (RRP/extended) is presented. The RRP/extended is a time-constrained project scheduling problem, in which the total project cost is minimised. In the RRP/extended, this total project cost is determined by a number of extra costs, which are defined in this paper. These costs are based on the costs that are used in the traditional Resource Renting Problem and the Total Adjustment Cost Problem. Therefore, the RRP/extended represents a union of these two problems. To solve the RRP/extended, a scatter search is developed. The building blocks of this scatter search are specifically designed for the RRP/extended. We introduce two crossovers and an improvement method. The efficiency of these building blocks will be shown in the paper. Furthermore, a sensitivity analysis is presented in which the five costs have diverse values.