A hybrid evolutionary algorithm to solve the job shop scheduling problem

This paper presents a Hybrid Evolutionary Algorithm (HEA) to solve the Job Shop Scheduling Problem (JSP). Incorporating a tabu search procedure into the framework of an evolutionary algorithm, the HEA embraces several distinguishing features such as a longest common sequence based recombination operator and a similarity-and-quality based replacement criterion for population updating. The HEA is able to easily generate the best-known solutions for 90 % of the tested difficult instances widely used in the literature, demonstrating its efficacy in terms of both solution quality and computational efficiency. In particular, the HEA identifies a better upper bound for two of these difficult instances.     

A hybrid genetic algorithm for the job shop scheduling problem

This paper presents a hybrid genetic algorithm for the job shop scheduling problem. The chromosome representation of the problem is based on random keys. The schedules are constructed using a priority rule in which the priorities are defined by the genetic algorithm. Schedules are constructed using a procedure that generates parameterized active schedules. After a schedule is obtained a local search heuristic is applied to improve the solution. The approach is tested on a set of standard instances taken from the literature and compared with other approaches. The computation results validate the effectiveness of the proposed algorithm.     

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 filter-and-fan approach to the job shop scheduling problem

The job shop scheduling problem (JSSP) is a notoriously difficult problem in combinatorial optimization. Extensive investigation has been devoted to developing efficient algorithms to find optimal or near-optimal solutions. This paper proposes a new heuristic algorithm for the JSSP that effectively combines the classical shifting bottleneck procedure (SBP) with a dynamic and adaptive neighborhood search procedure. Our new search method, based on a filter-and-fan (F&F) procedure, uses the SBP as a subroutine to generate a starting solution and to enhance the best schedules produced. The F&F approach is a local search procedure that generates compound moves by a strategically abbreviated form of tree search. Computational results carried out on a standard set of 43 benchmark problems show that our F&F algorithm performs more robustly and effectively than a number of leading metaheuristic algorithms and rivals the best of these algorithms.     

Depth-first heuristic search for the job shop scheduling problem

We evaluate two variants of depth-first search algorithms and consider the classic job shop scheduling problem as a test bed. The first one is the well-known branch-and-bound algorithm proposed by P. Brucker et al. which uses a single chronological backtracking strategy. The second is a variant that uses partially informed depth-first search strategy instead. Both algorithms use the same heuristic estimation; in the first case, it is only used for pruning states that cannot improve the incumbent solution, whereas in the second it is also used to sort the successors of an expanded state. We also propose and analyze a new heuristic estimation which is more informed and more time consuming than that used by Brucker’s algorithm. We conducted an experimental study over well-known instances showing that the proposed partially informed depth-first search algorithm outperforms the original Brucker’s algorithm.     

Permutation-induced acyclic networks for the job shop scheduling problem

In the literature of the combinatorial optimization problems, it is a commonplace to find more than one mathematical model for the same problem. The significance of a model may be measured in terms of the efficiency of the solution algorithms that can be built upon it. The purpose of this article is to present a new network model for the well known combinatorial optimization problem – the job shop scheduling problem. The new network model has similar structure as the disjunctive graph model except that it uses permutations of jobs as decision variables instead of the binary decision variables associated with the disjunctive arcs. To assess the significance of the new model, the performances of exact branch-and-bound algorithmic implementations that are based on both the new model and the disjunctive graph model are compared.     

A problem expanding parametric programming method for solving the job shop scheduling problem

A new zero-one integer programming model for the job shop scheduling problem with minimum makespan criterion is presented. The algorithm consists of two parts: (a) a branch and bound parametric linear programming code for solving the job shop problem with fixed completion time; (b) a problem expanding algorithm for finding the optimal completion time. Computational experience for problems having up to thirty-six operations is presented. The largest problem solved was limited by memory space, not computation time. Efforts are under way to improve the efficiency of the algorithm and to reduce its memory requirements.This report was prepared as part of the activities of the Management Sciences Research Group, Carnegie-Mellon University, under Contract No. N00014-82-K-0329 NR 047-048 with the U.S. Office of Naval Research. Reproduction in whole or in part is permitted for any purpose of the U.S. Government.     

The hybrid flow shop scheduling problem

The scheduling of flow shops with multiple parallel machines per stage, usually referred to as the hybrid flow shop (HFS), is a complex combinatorial problem encountered in many real world applications. Given its importance and complexity, the HFS problem has been intensively studied. This paper presents a literature review on exact, heuristic and metaheuristic methods that have been proposed for its solution. The paper briefly discusses and reviews several variants of the HFS problem, each in turn considering different assumptions, constraints and objective functions. Research opportunities in HFS are also discussed.     

Nested partitions for the large-scale extended job shop scheduling problem

This paper addresses the large-scale extended job shop scheduling problem while considering the bill of material and the working shifts constraints. We propose two approaches for the problem. One is based on dispatching rules (DR), and the other is an application of the Nested Partitions (NP) Framework. A sampling approach for the exact feasible subregion is developed to complete the NP method. Furthermore, to efficiently search each subregion, a weighted sampling approach is also presented. Computational experiments show that the NP method with weighted sampling can find good solutions for most large-scale extended job shop scheduling problems.     

A tabu search and a genetic algorithm for solving a bicriteria general job shop scheduling problem

This paper deals with a general job shop scheduling problem with multiple constraints, coming from printing and boarding industry. The objective is the minimization of two criteria, the makespan and the maximum lateness, and we are interested in finding an approximation of the Pareto frontier. We propose a fast and elitist genetic algorithm based on NSGA-II for solving the problem. The initial population of this algorithm is either randomly generated or partially generated by using a tabu search algorithm, that minimizes a linear combination of the two criteria. Both the genetic and the tabu search algorithms are tested on benchmark instances from flexible job shop literature and computational results show the interest of both methods to obtain an efficient and effective resolution method.     

A novel parallel quantum genetic algorithm for stochastic job shop scheduling

In this paper, a Novel Parallel Quantum Genetic Algorithm (NPQGA) is proposed for the stochastic Job Shop Scheduling Problem with the objective of minimizing the expected value of makespan, where the processing times are subjected to independent normal distributions. Based on the parallel evolutionary idea and some concepts of quantum theory, we simulate a model of parallel quantum computation. In this frame, there are some demes (sub-populations) and some universes (groups of populations), which are structured in super star-shaped topologies. A new migration scheme based on penetration theory is developed to control migration rate and direction adaptively between demes, and a novel quantum crossover strategy is devised among universes. The quantum evolution is executed in every deme by applying some improvement operators (the coding mechanism aiming at job shop, the new quantum rotation angle and the catastrophe operator). Experiment results show NPQGA's effectiveness and applicability.     

Bounding strategies for the hybrid flow shop scheduling problem

In this paper, we investigate new lower and upper bounds for the multiple-center hybrid flow shop scheduling problem. We propose a family of center-based lower bounds as well as a destructive lower bound that is based on the concept of revised energetic reasoning. Also, we describe an optimization-based heuristic that requires iteratively solving a sequence of parallel machine problems with heads and tails. We present the results of extensive computational experiments that provide evidence that the proposed bounding procedures consistently improve the best existing ones.     

A modified tabu search algorithm for cost-based job shop problem

In this paper, a cost-based job shop problem (JIT-JSP) is proposed to model the multi-order processing procedure in a just-in-time (JIT) environment. The objective of JIT-JSP is to minimize three costs: work-in-process holding cost of half-finished orders, inventory holding cost of finished orders and backorder cost of unfulfilled orders. A modified tabu search (MTS) method is developed to improve the schedule quality by searching the neighbourhood of a feasible schedule iteratively. The MTS method is comprised of three components that help to ensure a more effective searching procedure: neighbourhood structure, memory structure and filter structure. Computational results show that the MTS method significantly improves the initial schedule generated by an arbitrarily selected dispatching rule.     

A hybrid rank-based evolutionary algorithm applied to multi-mode resource-constrained project scheduling problem

We consider the multi-mode resource-constrained project scheduling problem (MRCPSP), where a task has different execution modes characterized by different resource requirements. Due to the nonrenewable resources and the multiple modes, this problem is NP-hard; therefore, we implement an evolutionary algorithm looking for a feasible solution minimizing the makespan.     

An efficient algorithm for a job shop problem

We study the problem of minimizing makespan in a two-machine job shop with unit processing time operations. An efficient algorithm with respect to a succinct encoding of the problem instances is proposed. The algorithm is an improvement of earlier algorithms proposed for the problem by Brucker [1,2], Hefetz and Adiri [7], and Timkovskiy [15]. The idea behind the algorithm has the potential of extension to job shops with parallel machines.This research is supported in part by NSERC Grants A4619, OGP0105675, OGP0104900, General Motors of Canada, and the Manufacturing Research Corporation of Ontario.     

Surgical case scheduling as a generalized job shop scheduling problem

Surgical case scheduling allocates hospital resources to individual surgical cases and decides on the time to perform the surgeries. This task plays a decisive role in utilizing hospital resources efficiently while ensuring quality of care for patients. This paper proposes a new surgical case scheduling approach which uses a novel extension of the Job Shop scheduling problem called multi-mode blocking job shop (MMBJS). It formulates the MMBJS as a mixed integer linear programming (MILP) problem and discusses the use of the MMBJS model for scheduling elective and add-on cases. The model is illustrated by a detailed example, and preliminary computational experiments with the CPLEX solver on practical-sized instances are reported.     

An iterated greedy metaheuristic for the blocking job shop scheduling problem

In this paper we consider a job shop scheduling problem with blocking (BJSS) constraints. Blocking constraints model the absence of buffers (zero buffer), whereas in the traditional job shop scheduling model buffers have infinite capacity. There are two known variants of this problem, namely the blocking job shop scheduling with swap allowed (BWS) and the one with no swap allowed (BNS). This scheduling problem is receiving an increasing interest in the recent literature, and we propose an Iterated Greedy (IG) algorithm to solve both variants of the problem. IG is a metaheuristic based on the repetition of a destruction phase, which removes part of the solution, and a construction phase, in which a new solution is obtained by applying an underlying greedy algorithm starting from the partial solution. A comparison with recent published results shows that the iterated greedy algorithm outperforms other state-of-the-art algorithms on benchmark instances. Moreover it is conceptually easy to implement and has a broad applicability to other constrained scheduling problems.     

Local search and genetic algorithm for the job shop scheduling problem with sequence dependent setup times

The Job Shop Scheduling Problem (JSP) is an example of a combinatorial optimization problem that has interested researchers for several decades. In this paper we confront an extension of this problem called JSP with Sequence Dependent Setup Times (SDST-JSP). The approach extends a genetic algorithm and a local search method that demonstrated to be efficient in solving the JSP. For local search, we have formalized neighborhood structures that generalize three well-know structures defined for the JSP. We have conducted an experimental study across conventional benchmark instances showing that the genetic algorithm exploited in combination with the local search, considering all three neighborhoods at the same time, provides the best results. Moreover, this approach outperforms the current state-of-the-art methods.     

A hybrid evolutionary algorithm for the two-dimensional packing problem

This paper presents a hybrid evolutionary algorithm for the two-dimensional non-guillotine packing problem. The problem consists of packing many rectangular pieces into a single rectangular sheet in order to maximize the total area of the pieces packed. Moreover, there is a constraint on the maximum number of times that a piece may be used in a packing pattern. The set of packing patterns is processed by an evolutionary algorithm. Three mutation operators and two types of quality functions are used in the algorithm. The best solution obtained by the evolutionary algorithm is used as the initial solution in a tree search improvement procedure. This approach is tested on a set of benchmark problems taken from the literature and compared with the results published by other authors.     

A hybrid evolutionary algorithm for the periodic location-routing problem

The well-known vehicle routing problem (VRP) has been studied in depth over the last decades. Nowadays, generalizations of VRP have been developed for tactical or strategic decision levels of companies but not both. The tactical extension or periodic VRP (PVRP) plans a set of trips over a multiperiod horizon, subject to frequency constraints. The strategic extension is motivated by interdependent depot location and routing decisions in most distribution systems. Low-quality solutions are obtained if depots are located first, regardless of the future routes. In the location-routing problem (LRP), location and routing decisions are tackled simultaneously. Here for the first time, except for some conference papers, the goal is to combine the PVRP and LRP into an even more realistic problem covering all decision levels: the periodic LRP or PLRP. A hybrid evolutionary algorithm is proposed to solve large size instances of the PLRP. First, an individual representing an assignment of customers to combinations of visit days is randomly generated. The evolution operates through an Evolutionary Local Search (ELS) on visit day assignments. The algorithm is hybridized with a heuristic based on the Randomized Extended Clarke and Wright Algorithm (RECWA) to create feasible solutions and stops when a given number of iterations is reached. The method is evaluated over three sets of instances, and solutions are compared to the literature on particular cases such as one-day horizon (LRP) or one depot (PVRP). This metaheuristic outperforms the previous methods for the PLRP.