Parallel variable neighbourhood search algorithms for job shop scheduling problems

^** Email: msevkli{at}fatih.edu.tr^*** Corresponding author. Email: mehmetaydin{at}acm.org, mehmet.aydin{at}beds.ac.uk Variable neighbourhood search (VNS) is one of the most recentmetaheuristics used for solving combinatorial optimization problemsin which a systematic change of neighbourhood with a local searchis carried out. However, as happens with other metaheuristics,it takes a long time to reach some useful solutions while solvingsome sort of hard combinatorial problems such as job shop scheduling(JSS). Parallelization is one of the most considerable policiesto overcome this matter. In this paper, firstly, a number ofVNS algorithms are examined for JSS problems and then four differentparallelization policies are taken into account to determineefficient parallelization for VNS algorithms. The experimentationreveals the performance of various VNS algorithms and the efficiencyof policies to follow in parallelization. In the end, the unilateral-ringtopology, a noncentral parallelization method, is found as themost efficient policy.     

Dynamic tabu search strategies for the traveling purchaser problem

Tabu search is a metastrategy for guiding known heuristics to overcome local optimality with a large number of successful applications reported in the literature. In this paper we investigate two dynamic strategies, the reverse elimination method and the cancellation sequence method. The incorporation of strategic oscillation as well as a combination of these methods are developed. The impact of the different methods is shown with respect to the traveling purchaser problem, a generalization of the classical traveling salesman problem. The traveling purchaser problem is the problem of determining a tour of a purchaser buying several items in different shops by minimizing the total amount of travel and purchase costs. A comparison of the tabu search strategies with a simulated annealing approach is presented, too.     

Parallel asynchronous tabu search for multicommodity location-allocation with balancing requirements

We study and compare asynchronous parallelization strategies for tabu search, and evaluate the impact on performance and solution quality of some important algorithmic design parameters: 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.     

Assigning students to course sections using tabu search

In this paper we describe a new student registration system which has been developed at the University of Valencia, Spain. The system has two steps. First, the students make a computer-aided course selection from the courses available at the University. Thereafter, an assignment procedure allocates students to sections in order to respect two criteria: to provide the students with satisfactory schedules and to get balanced section enrollments. The assignment process has two phases. In Phase I, we obtain a set of the best solutions for each student. The algorithm is based on the construction of maximum cardinality independent sets. In Phase II, these solution sets are put together and a tabu search algorithm looks for a satisfactory balance between course sections without causing the solution obtained for each student to worsen significantly. The system was used at the beginning of the academic year 1996/97 in the Faculty of Mathematics and could be extended in the near future to the rest of the University. This revised version was published online in June 2006 with corrections to the Cover Date.     

A tabu search algorithm for solving economic lot scheduling problem

The economic lot scheduling problem has driven considerable amount of research. The problem is NP-hard and recent research is focused on finding heuristic solutions rather than searching for optimal solutions. This paper introduces a heuristic method using a tabu search algorithm to solve the economic lot scheduling problem. Diversification and intensification schemes are employed to improve the efficiency of the proposed Tabu search algorithm. Experimental design is conducted to determine the best operating parameters for the Tabu search. Results show that the tabu search algorithm proposed in this paper outperforms two well known benchmark algorithms.     

Lower bounding and tabu search procedures for the frequency assignment problem with polarization constraints

The problem retained for the ROADEF’2001 international challenge was a Frequency Assignment Problem with polarization constraints (FAPP). This NP-hard problem was proposed by the CELAR of the French Department of Defense, within the context of the CALMA project. Twenty seven competitors took part to this contest, and we present in this paper the contribution of our team that allowed us to be selected as one of the six finalists qualified for the final round of the competition.There is typically no solution satisfying all constraints of the FAPP. For this reason, some electromagnetic compatibility constraints can be progressively relaxed, and the objective is to find a feasible solution with the lowest possible level of relaxation. We have developed a procedure that computes a lower bound on the best possible level of relaxation, as well as two tabu search algorithms for the FAPP, one for the frequency assignment, and one for the polarization assignment.Received: July 2003, Revised: October 2004, AMS classification: 90C27, 90C35, 90C59Alain Hertz: Correspondence to     

Metastrategy simulated annealing and tabu search algorithms for the vehicle routing problem

The vehicle routing problem (VRP) under capacity and distance restrictions involves the design of a set of minimum cost delivery routes, originating and terminating at a central depot, which services a set of customers. Each customer must be supplied exactly once by one vehicle route. The total demand of any vehicle must not exceed the vehicle capacity. The total length of any route must not exceed a pre-specified bound. Approximate methods based on descent, hybrid simulated annealing/tabu search, and tabu search algorithms are developed and different search strategies are investigated. A special data structure for the tabu search algorithm is implemented which has reduced notably the computational time by more than 50%. An estimate for the tabu list size is statistically derived. Computational results are reported on a sample of seventeen bench-mark test problems from the literature and nine randomly generated problems. The new methods improve significantly both the number of vehicles used and the total distances travelled on all results reported in the literature.     

Scheduling linearly shortening jobs under precedence constraints

We consider the problem of scheduling a set of dependent jobs on a single machine with the maximum completion time criterion. The processing time of each job is variable and decreases linearly with respect to the starting time of the job. Applying a uniform approach based on the calculation of ratios of expressions that describe total processing times of chains of jobs, we show basic properties of the problem. On the basis of these properties, we prove that if precedence constraints among jobs are in the form of a set of chains, a tree, a forest or a series–parallel digraph, the problem can be solved in O(n log n) time, where n denotes the number of the jobs.     

Simulated annealing and tabu search for multi-mode project payment scheduling

This paper involves the multi-mode project payment scheduling problem where the activities can be performed with one of several discrete modes and the objective is to assign activities’ modes and progress payments so as to maximize the net present value of the contractor under the constraint of project deadline. Using the event-based method the basic model of the problem is constructed and in terms of the different payment rules it is extended as the progress based, expense based, and time based models further. For the strong NP-hardness of the problem which is proven by simplifying it to the deadline subproblem of the discrete time–cost tradeoff problem, we develop two heuristic algorithms, namely simulated annealing and tabu search, to solve the problem. The two heuristic algorithms are compared with the multi-start iterative improvement method as well as random sampling on the basis of a computational experiment performed on a data set constructed by ProGen project generator. The results show that the proposed simulated annealing heuristic algorithm seems to be the most promising algorithm for solving the defined problem especially when the instances become larger. In addition, the effects of several key parameters on the net present value of the contractor are analyzed and some conclusions are given based on the results of the computational experiment.     

A tabu search heuristic using genetic diversification for the clustered traveling salesman problem

The clustered traveling salesman problem is an extension of the classical traveling salesman problem where the set of vertices is partitioned into clusters. The objective is to find a least cost Hamiltonian cycle such that the vertices of each cluster are visited contiguously and the clusters are visited in a prespecified order. A tabu search heuristic is proposed to solve this problem. This algorithm periodically restarts its search by merging two elite solutions to form a new starting solution (in a manner reminiscent of genetic algorithms). Computational results are reported on sets of Euclidean problems with different characteristics.     

A tabu search algorithm for assigning teachers to courses

In this paper we deal with the problem of assigning teachers to courses in a secondary school. The problem appears when a timetable is to be built and the teaching assignments are not fixed. We have developed a tabu search algorithm to solve the problem. The parameters involved in the algorithm have been estimated by using multiple regression techniques. The computational results, obtained on a set of Spanish secondary schools, show that the solutions obtained by this automatic procedure can be favourably compared with the solutions proposed by the experts.     

Parallel local search

We present a survey of parallel local search algorithms in which we review the concepts that can be used to incorporate parallelism into local search. For this purpose we distinguish between single-walk and multiple-walk parallel local search and between asynchronous and synchronous parallelism. Within the class of single-walk algorithms we differentiate between multiple-step and single-step parallelism. To describe parallel local search we introduce the concepts of hyper neighborhood structures and distributed neighborhood structures. Furthermore, we present templates that capture most of the parallel local search algorithms proposed in the literature. Finally, we discuss some complexity issues related to parallel local search.     

A hybrid single and dual population search procedure for the job shop scheduling problem

This paper presents a genetic algorithm and a scatter search procedure to solve the well-known job shop scheduling problem. In contrast to the single population search performed by the genetic algorithm, the scatter search algorithm splits the population of solutions in a diverse and high-quality set to exchange information between individuals in a controlled way. The extension from a single to a dual population, by taking problem specific characteristics into account, can be seen as a stimulator to add diversity in the search process. This has a positive influence on the important balance between intensification and diversification. Computational experiments verify the benefit of this diversity on the effectiveness of the meta-heuristic search process. Various algorithmic parameters from literature are embedded in both procedures and a detailed comparison is made. A set of standard instances is used to compare the different approaches and the best obtained results are benchmarked against heuristic solutions found in literature.     

A tabu search algorithm for scheduling pharmaceutical packaging operations

This paper addresses a practical scheduling problem arising in the packaging department of a pharmaceutical industrial plant. The problem is modeled as a multi-purpose machine scheduling problem with setup and removal times, release and due dates and additional constraints related to the scarce availability of tools and human operators. The objective functions are minimization of makespan and maximum tardiness in lexicographic order. Representing a solution with a directed graph allows us to devise an effective tabu search algorithm to solve the problem. Computational experiments, carried on real and randomly generated instances, show the effectiveness of this approach.     

Cooperative Parallel Tabu Search for Capacitated Network Design

We present a cooperative parallel tabu search method for the fixed charge, capacitated, multicommodity network design problem. Several communication strategies are analyzed and compared. The resulting parallel procedure displays excellent performances in terms of solution quality and solution times. The experiments show that parallel implementations find better solutions than sequential ones. They also show that, when properly designed and implemented, cooperative search outperforms independent search strategies, at least on the class of problems of interest here.     

A comparison of local search methods for flow shop scheduling

Local search techniques are widely used to obtain approximate solutions to a variety of combinatorial optimization problems. Two important categories of local search methods are neighbourhood search and genetic algorithms. Commonly used neighbourhood search methods include descent, threshold accepting, simulated annealing and tabu search. In this paper, we present a computational study that compares these four neighbourhood search methods, a genetic algorithm, and a hybrid method in which descent is incorporated into the genetic algorithm. The performance of these six local search methods is evaluated on the problem of scheduling jobs in a permutation flow shop to minimize the total weighted completion time. Based on the results of extensive computational tests, simulated annealing is found to generate better quality solutions than the other neighborhood search methods. However, the results also indicate that the hybrid genetic descent algorithm is superior to simulated annealing.     

The continuous reactive tabu search: Blending combinatorial optimization and stochastic search for global optimization

A novel algorithm for the global optimization of functions (C-RTS) is presented, in which a combinatorial optimization method cooperates with a stochastic local minimizer. The combinatorial optimization component, based on the Reactive Tabu Search recently proposed by the authors, locates the most promising boxes, in which starting points for the local minimizer are generated. In order to cover a wide spectrum of possible applications without user intervention, the method is designed with adaptive mechanisms: the box size is adapted to the local structure of the function to be optimized, the search parameters are adapted to obtain a proper balance of diversification and intensification. The algorithm is compared with some existing algorithms, and the experimental results are presented for a variety of benchmark tasks.     

An improved monotone algorithm for scheduling related machines with precedence constraints

We answer an open question posed by Krumke et al. (2008) [6] by showing how to turn the algorithm of Chekuri and Bender for scheduling related machines with precedence constraints into an O(logm)-approximation algorithm that is monotone in expectation. This significantly improves on the previously best known monotone approximation algorithms for this problem, from Krumke et al. [6] and Thielen and Krumke (2008) [8], which have an approximation guarantee of O(m^2/3).     

Solving a chemical batch scheduling problem by local search

In this paper the following chemical batch scheduling problem is considered: a set of orders has to be processed on a set of facilities. For each order a given amount of a product must be produced by means of chemical reactions before a given deadline. The production consists of a sequence of processes whereby each process has to be performed by one facility out of a given subset of facilities allowed for this process. The processing times depend on the choice of the facility and the processing is done in batch mode with given minimum and maximum sizes. The problem is to assign the processes to the facilities, splitting them into batches, and scheduling these batches in order to produce the demands within the given deadlines. For the scheduling part of the problem we present an approach based on the following steps. First, a procedure to calculate the minimum number of batches needed to satisfy the demands is presented. Based on this, the given problem is modeled in two different ways: as a general shop scheduling problem with set-up times or as scheduling problem with positive time-lags. Finally, a two-phase tabu search method is presented which is based on the two different formulations of the problem. The method is tested on some real world data. This revised version was published online in June 2006 with corrections to the Cover Date.     

A scatter search algorithm for project scheduling under partially renewable resources

In this paper we develop a heuristic algorithm, based on Scatter Search, for project scheduling problems under partially renewable resources. This new type of resource can be viewed as a generalization of renewable and non-renewable resources, and is very helpful in modelling conditions that do no fit into classical models, but which appear in real timetabling and labor scheduling problems. The Scatter Search algorithm is tested on existing test instances and obtains the best results known so far.