A Swarm Intelligence Method Applied to Manufacturing Scheduling Davide Anghinolfi, Antonio Boccalatte, Alberto Grosso, Massimo Paolucci, Andrea Passadore, Christian Vecchiola, DIST – Department of Communications Computer and System Sciences, University of Genova STWTSDS problem. Regarding the latter point, note that the approach in  seems to be the only previous DPSO application to the single machine total weighted tardiness (STWT) problem. The rest of the paper is organized as follows. Section 2 introduces a formal problem definition and provides a general review of the relevant literature for it. Section 3 illustrates the basic aspects of the PSO algorithm, analysing in particular the DPSO approaches previously proposed in the literature. Section 4 then describes the proposed DPSO approach, discussing how it can be applied to the STWTSDS problem and highlighting the new features introduced. Section 5 presents the experimental campaign performed, which is mainly based on the benchmark set generated by Cicirello in  and available on the web. Finally, Section 6 draws some conclusions. II. THE STWTSDS PROBLEM The STWTSDS problem corresponds to the scheduling of n independent jobs on a single machine. All the jobs are released simultaneously, i.e., they are ready at time zero, the machine is continuously available and it can process only one job at a time. For each job j=1,..., n, the following quantities are given: a processing time pj, a due date dj and a weight wj. A sequence-dependent setup time sij must be waited before starting the processing of job j if it is immediately sequenced after job i. The tardiness of a job j is defined as Tj=max(0, Cjdj), being Cj the job j completion time. The scheduling objective is the minimization of the total weighted tardiness expressed as
Abstract—In this paper we present a multi-agent search technique to face the NP-hard single machine total weighted tardiness scheduling problem in presence of sequence-dependent setup times. The search technique is called Discrete Particle Swarm Optimization (DPSO): differently from previous approaches the proposed DPSO uses a discrete model both for particle position and velocity and a coherent sequence metric. We tested the proposed DPSO over a benchmark available online. The results obtained show the competitiveness of our DPSO, which is able to outperform the best known results for the benchmark, and the effectiveness of the DPSO swarm intelligence mechanisms. Index Terms—Particle Intelligence, Scheduling Swarm Optimization, Swarm
I. INTRODUCTION In this paper we propose a new DPSO approach to face the single machine total weighted tardiness scheduling with sequence-dependent setup times (STWTSDS) problem. Scheduling with performance criteria involving due dates, such as (weighted) total tardiness or total earliness and tardiness (E-T), and that takes into account sequencedependent setups, is a reference problem in many real industrial contexts. Meeting due dates is in fact recognized as the most important objective in surveys on manufacturing practise, e.g., in . The objective of minimizing the total weighted tardiness has been the subject of a very large amount of literature on scheduling even if sequence-dependent setups have not been so frequently considered. Setups usually correspond to preparing the production resources (e.g., the machines) for the execution of the next job, and when the duration of such operations depends on the type of last completed job, the setups are called sequence-dependent. The presence of sequence-dependent setups greatly increases the problem difficulty, since it prevents the application of dominance conditions used for simpler tardiness problems . The choice of the STWTSDS problem as reference application for the proposed DPSO approach has then two main motivations: first the fact that the solution of single machine problems is often required even in more complex environments , and second the...
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