Elsevier

Applied Soft Computing

Volume 62, January 2018, Pages 1-14
Applied Soft Computing

Hybrid Differential Evolution and Greedy Algorithm (DEGR) for solving Multi-Skill Resource-Constrained Project Scheduling Problem

https://doi.org/10.1016/j.asoc.2017.10.014Get rights and content

Highlights

  • A hybrid approach DEGR that links Differential Evolution and Greedy Algorithm uses non-direct schedule representation, and Greedy algorithm plays a role of Serial Schedule Generation Scheme.

  • Taguchi Method applied as Design of Experiments methods to tune DEGR.

  • DEGR uses non-calendar benchmark iMOPSE 36 instances optimization schedule duration.

  • DEGR results are compared to other references methods: DEGR gives solutions in average better than HANTCO (18%), multiStart Greedy (15.8%) and GRASP (2.64%). Full comparison results are statistically verified.

  • DEGR applied to iMOPSE dataset gives the best-known solution in 28 cases.

Abstract

Paper presents a hybrid Differential Evolution and Greedy Algorithm (DEGR) applied to solve Multi-Skill Resource-Constrained Project Scheduling Problem. The specialized indirect representation and transformation of solution space from discrete (typical for this problem), to continuous (typical for DE-approaches) are proposed and examined. Furthermore, Taguchi Design of Experiments method has been used to adjust parameters for investigated method to reduce the procedure of experiments. Finally, various initialisation, clone elimination, mutation and crossover operators have been applied there. The results have been compared with the results from other reference methods (HantCO, GRASP and multiStart Greedy) using the benchmark iMOPSE dataset. This comparison shows that DEGR effort is very robust and effective. For 28 instances of iMOPSE dataset DEGR has achieved the best-known solutions.

Introduction

Multi-Skill Resource-Constrained Project Scheduling Problem (MS-RCPSP) is one of the widest developed problems in the literature [10], [24]. It comes from its practical nature and the need that arise in real life problems of today's industry i.e. in manufacturing, chemistry, logistics and many other disciplines. Hence, researchers from all around the world struggle to improve existing approaches to solve this kind of problems.

The scheduling problem can be informally defined as a function that assigns jobs to resources to complete the project. However, in real-world applications such simplification is not useful. In the Project Scheduling Problem (PSP) a set of precedence-constrained jobs have to be scheduled so as to minimize a given objective. Furthermore, in extended problem definition, the Resource Constrained Project Scheduling Problem (RCPSP), tasks additionally compete for scarce resources. Such modifications make it possible through a better adaption to apply in manufacturing, production planning, project management, etc. Ultimately MS-RCPSP can be applied to solve many real-world problems. Although PSP is widely described in literature, there is no method that finds an optimal solution and could be applied under every condition. Moreover, as the above problems are NP-hard, there is no optimal solution that could be computed in polynomial time [6]. Hence, researchers try to build methods that find feasible solutions, which are (sub)optimal but can be reached in acceptable time. In such cases soft computing methods are used, mostly heuristics and metaheuristics [15], [24].

Within the metaheuristic group of methods, Genetic Algorithm [18], [30], Tabu Search [47], [48], GRASP [32], [9], [13] Swarm Intelligence Optimization, like Ant Colony Optimisation [29], [27], [31], Bee Colony Optimisation [58] or Particle Swarm Optimisation [57] and Simulated Annealing-based [7], [10] approaches are developed. Those methods can provide good enough solution in acceptable time. Their main drawback, however, is their lack of determinism, which means that they often provide different results for the same parameter configuration. What is more, they sometimes may require significantly more time to get a final solution. However, even those disadvantages cannot hide their clear pros: flexibility, extensibility, and ability to find satisfactory solution, which is very often good enough to be applied, because it is either impossible to get the global optimal solution or it would take implausibly long time.

In our previous research, we defined new problem MS-RCPSP and benchmark of 36 instances [33] to compare the effectiveness of examined methods. We developed hybrid HantCO [31] for solving MS-RCPSP. In [31] it is shown that HantCo outperforms heuristics (like Greedy-based). Moreover, we noticed that Greedy Algorithm (see [33], [32]), as a quite simple heuristic, gives promising results in solving MS-RCPSP. In next stages, we showed that to make Greedy more efficient it needs to be supported by other metaheuristics, e.g. GRASP [32]. It was the scientific question if cooperation of Greedy Algorithm and more advanced metaheuristic (like a Differential Evolution) can be more efficient tool for solving MS-RCPSP.

The main goal of this paper is to present the results of our last research. We examine how DE method can be effectively hybridized with Greedy Algorithm to solve MS-RCPSP in the new hybrid DEGR. The main goal of this paper to show its robustness in comparison to other investigated methods. The proposed approach uses non-direct representation of the problem, conversion from discrete solution space and specialized conversion to build final phenotype that represents a schedule. Additional objective was to compare various initalisation, and crossover operators to find the best configuration. What is more, this article also presents the application of a Taguchi design of experiments [1] to identify parameters that influence results most significantly, to avoid investigating all possible parameters’ configurations. Hence, the process of experiments can be optimized. Finally, results obtained by proposed DE-based approach are compared with results from other investigated methods, like greedy algorithm [33], Hybrid Ant Colony Optimization [31] (HantCO) or Greedy Randomized Adaptive Search Procedure (GRASP) [32]. In this paper benchmark MS-RCPSP instances are used in form without calendar factor [33].

The rest of the paper is organized as follows. Section 2 presents a short summary of existing publications (state of the art). In Section 3 the problem statement with constraints and requirements is described. The proposed DEGR approach is given in Section 4. Finally, Section 5 shows performed experiments and their results. Section 6 concludes the article and presents potential directions for future work.

Section snippets

Related work

The most used techniques for solving RCPSP are metaheuristics. Tabu Search (TS) [47], [48], Simulated Annealing (SA) [7], [10] or Genetic Algorithm (GA) [18], [30], [55] are well explored and widely applied to solve MS-RCPSP. Swarm Intelligence metaheuristics are also useful for solving (MS-) RCPSP. For example, Particle Swarm Optimsation (PSO) [57], [56], Bee Colony Optimization (BCO) [58], Artificial Immune Algorithm in [51] or the most popular Ant Colony Optimization (ACO) [29], [27] are

MS-RCPSP problem formulation

To describe the multi-skill extension for RCPSP (Section 3.1), the fundamentals of classical RCPSP should be presented. Then definition of MS-RCPSP can be introduced (Section 3.2). Some motivations to investigate RCPSP and its extensions came from the practical industry needs and will be explained in details. The definition of MS-RCPSP problem is based on practical problem described in [31], [33].

Proposed approach

In this section the proposed approach based on Differential Evolution [42] hybridizing with Greedy (DEGR) method has been presented. The DE is an iterative method, which aims to minimize the objective function. At the beginning the initial population is created and each individual is evaluated. Then every individual is sequentially processed using genetic operators like crossover and mutation. After those steps individual is evaluated again and if it is good enough, it is taken to the next

Experiments and results

The goal of the conducted experiments was to investigate the robustness and efficiency of DEGR approach in comparison to results obtained by other methods: Greedy, multiStart Greedy, GRASP and HAntCO. The obtained results (project schedules) are described by duration time ([hours]) and cost of its performance ([currency units]). Those project schedule properties have been used to compare the investigated methods and various configurations.

Conclusions and future work

In this paper, a new DEGR hybrid has been proposed and applied for solving Multi-Skill Resource-Constrained Project Scheduling Problem. We proposed a new genotype non-direct representation and domain transformation to apply DEGR to MS-RCPSP. The experiments have been conducted on the benchmark non-calendar iMOPSE dataset, where different parameter configurations have been investigated, as the method consists of many parameters. Comparisons to results of 3 other methods (GRASP, HAntCO and

Acknowledgements

The authors would like to thank the editor and the reviewers for their contribution in enhancing the technical quality of this paper.

References (58)

  • H. Zhang et al.

    Particle swarm optimization-based schemes for resource-constrained project scheduling

    Autom. Constr.

    (2005)
  • H. Zhang et al.

    Particle swarm optimization for resource-constrained project scheduling

    Int. J. Project Manag.

    (2006)
  • K. Ziarati et al.

    On the performance of bee algorithms for resource-constrained project scheduling problem

    Appl. Soft Comput.

    (2011)
  • B. Adenso-Daz et al.

    Fine-tuning of algorithms using fractional experimental designs and local search

    Oper. Res. J.

    (2006)
  • F.S. Al-Anzi et al.

    Weighted multi-skill resources project scheduling

    J. Softw. Eng. Appl.

    (2010)
  • B. Afshar-Nadjafi et al.

    Project Scheduling With Limited Resources Using an Efficient Differential Evolution Algorithm

    (2013)
  • A.C. Biju et al.

    An Improved Differential Evolution Solution for Software Project Scheduling Problem

    (2015)
  • W. Chen et al.

    Chaotic differential evolution algorithm for resource constrained project scheduling problem

    Int. J. Comput. Sci. Math.

    (2014)
  • C. Chyu et al.

    GRASP for maximizing cash availability in resource constrained project scheduling

    Proceedings of the 41st International Conference on Computers & Industrial Engineering

    (2011)
  • P.P. Das et al.

    Simulated annealing variants for solving resource constrained project scheduling problem: a comparative study

    Proceedings of 14th Int. Conf. on Computer and Information Technology

    (2011)
  • S. Das et al.

    Recent advances in differential evolution – an updated survey

    Swarm Evol. Comput.

    (2016)
  • S. Das et al.

    Differential evolution: a survey of the state-of-the-art

    IEEE Trans. Evol. Comput.

    (2011)
  • P. Festa et al.

    Hybrid GRASP heuristics

    Foundations of Computational Intelligence, Studies in Computational Intelligence Volume 3, vol. 203

    (2009)
  • F. Gonzalez et al.

    Multi-objective Optimization of the Resource Constrained Project Scheduling Problem (RCPSP) a heuristic approach based on the mathematical model

    Int. J. Comput. Sci. Appl.

    (2013)
  • T. Hegazy et al.

    Algorithm for scheduling with multiskilled constrained resources

    J. Constr. Eng. Manag.

    (2000)
  • C. Heimerl et al.

    Scheduling and staffing multiple projects with a multi-skilled workforce

    OR Spectrum

    (2010)
  • K.S. Hindi et al.

    An evolutionary algorithm for resource-constrained project scheduling

    IEEE Trans. Evol. Comput.

    (2002)
  • T.O. Ting et al.

    Hybrid metaheuristic algorithms: past, present, and future

  • M. Jaberi et al.

    A multi-objective resource-constrained project-scheduling problem using mean field annealing neural networks

    J. Math. Comput. Sci.

    (2014)
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