An improved intelligent water drops algorithm for solving multi-objective job shop scheduling

https://doi.org/10.1016/j.engappai.2013.07.011Get rights and content

Highlights

  • Improved intelligent water drops algorithm.

  • Multi-objective optimization.

  • Job shop scheduling.

Abstract

Multi-objective job shop scheduling (MOJSS) problems can be found in various application areas. The efficient solution of MOJSS problems has received continuous attention. In this research, a new meta-heuristic algorithm, namely the Intelligent Water Drops (IWD) algorithm is customized for solving the MOJSS problem. The optimization objective of MOJSS in this research is to find the best compromising solutions (Pareto non-dominance set) considering multiple criteria, namely makespan, tardiness and mean flow time of the schedules. MOJSS-IWD, which is a modified version of the original IWD algorithm, is proposed to solve the MOJSS problem. A scoring function which gives each schedule a score based on its multiple criteria values is embedded into the MOJSS-IWD’s local search process. Experimental evaluation shows that the customized IWD algorithm can identify the Pareto non-dominance schedules efficiently.

Introduction

The job shop scheduling problem (JSSP) is an important research issue in a wide range of application domains. The purpose of JSSP is to allocate resources (such as machine tools) to a set of tasks while satisfying several constraints and objectives. In JSSP problem, a set of machines M={Mj|j=1,2,,m} and a set of jobs J={Ji|i=1,2,,n} are considered. Each job has a sequence of operations O={Ok|k=1,2,,l} and these n jobs (i.e., all the operations) have to be processed on m machines. Job splitting is not allowed, and the operations are non-preemptable, which means temporary interruption of an operation is not allowed after it has started. Each machine can only perform one operation at a time, and each operation is performed only once on one machine. Every operation must be assigned to a unique machine without interruption. Considering its optimization objectives, JSSP can be divided into single-objective JSSP and multi-objective JSSP. The commonly addressed objectives for single-objective JSSP include makespan, due date, work-in-process, lateness, etc. The most well-studied objective is makespan. However, merely considering one objective is not sufficient for the real job shop scheduling situations; multiple objectives should be taken into consideration. In real practice, in order to exploit the full potential of the machines, the decision makers would normally consider more than one objective when planning the resources. Multi-objective job shop scheduling involves generating schedules to allocate the operations to the different machines considering more than one objective. Multi-objective job shop scheduling (MOJSS) is an extension of the typical JSSP, and it is difficult to solve MOJSS problems optimally. It is proven to be NP-hard which means it is not possible to find the optimal solutions in polynomial time (Garey et al., 1976). The optimization goal for MOJSS is not to generate a single optimum, but to find a set of best compromising solutions, which are in the form of alternative trade-offs. The set of best compromising solutions related to the criteria in consideration is known as the Pareto optimal set and the corresponding objective values are called the Pareto front.

Many methodologies have been proposed to solve MOJSS problems, such as enumeration, linear programming, dispatching rules, as well as some generic optimization algorithms, which can be used for a wide range of optimization problems, such as the shifting bottleneck, Tabu search, genetic algorithm, simulated annealing, particle swarm algorithm, ant colony algorithm, etc. These methods have also been used in the single objective JSSP. The application of these algorithms for MOJSS problems is quite different from the single objective JSSP. Simultaneous consideration of several objectives in the scheduling generation process changes the employment of the optimization algorithms approaches. These algorithms have to be customized to be employed in the MOJSS problems as the schedules generated for MOJSS problem need to be evaluated using at least two objectives, and obtaining individual optimal solutions of each objective is usually different.

In this research, the MOJSS problem is to find the Pareto optimal set in the large solution space considering the three objectives, namely, Makespan (Cmax), Tardiness (Ti) and Meanflow time (F¯). The Intelligent Water Drops (IWD) algorithm is employed to solve the problem. The original IWD algorithm is successfully customized to solve the MOJSS problem and the newly proposed algorithm is called MOJSS-IWD. To the best of the authors' knowledge, it is the first research work on the application of the IWD algorithm to solve MOJSS. The quality and the efficien cy of the MOJSS-IWD algorithm are tested in the experiments.

The rest of the paper is organized as follows. A brief literature review of the MOJSS and the original IWD algorithm is presented in Section 2. The MOJSS problem formulation is presented in Section 3. The rationale behind the original IWD and the improved IWD algorithm (MOJSS-IWD) is presented in Section 4. The experimental evaluation of the proposed algorithm for the MOJSS problem is given in Section 5. The conclusion of the paper is presented in Section 6.

Section snippets

Review on the MOJSS problem

The objective of multi-objective job shop scheduling is to generate feasible schedules that attempt to optimize several objectives, and these schedules form the Pareto optimal solution set. Different objectives are studied for the MOJSS problem in the literature, and the techniques to handle the multiple objectives can be classified into two categories:

  • 1.

    Transform the multi-objective problem into a mono-objective problem by aggregating the different objectives into a weighted sum. The weighted

The problem under study

In a job shop, machines or resources are structured according to the processes they perform, where machines with the same or similar material processing capabilities are grouped together to form work-centers. The machines are usually general-purpose machines that can accommodate a large variety of part types. A part moves through different work-centers based on its process plan (Chryssolouris, 2006). In a MOJSS problem, the basic setting is the same as the JSSP problem where a set of machines M=

IWD algorithm for MOJSS problem

In this section, the original IWD algorithm is customized to meet the characteristics and requirements of MOJSS, and a Pareto schedule checking process is embedded into the customized IWD algorithm which is called MOJSS-IWD. A brief description of the disjunctive graph is first given in Section 4.1 as the IWD algorithm for scheduling is represented on the disjunctive graph in this research. An overview of the proposed MOJSS-IWD algorithm is presented in Section 4.2, and a detailed description

Experimental evaluation

The MOJSS-IWD algorithm is implemented on a PC with an Intel Core 2 Duo L7700 1.8 GHz CPU and 2 GB RAM. Experiments are conducted on the benchmark data for JSSP in the OR-Library (Beasley, 1990). In this research, 43 instances have been tested. Among these 43 instances, three instances (FT06, FT10, FT20) were designed by Fisher and Thompson and 40 instances (LA01–LA40) were designed by Lawrence (1984). The parameters (with their values) used in the experiments are listed in Table 3. The initial

Conclusions

MOJSS problem with the consideration of three objectives, namely, the makespan, tardiness and mean flow time, has been studied in this research. The research goal is to find a set of solutions in the form of alternative trade-offs in the Pareto optimal set, and a new method is proposed to generate the Pareto non-dominance set. A promising optimization algorithm named MOJSS-IWD is presented and applied to solve the multi-objective JSSP. The MOJSS-IWD algorithm is obtained by customizing and

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