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