Juan José Palacios

Genetic tabu search for the fuzzy flexible job shop problem

This paper tackles the flexible job-shop scheduling problem with uncertain processing times. The uncertainty in processing times is represented by means of fuzzy numbers, hence the name fuzzy flexible job-shop scheduling. We propose an effective genetic algorithm hybridised with tabu search and heuristic seeding to minimise the total time needed to complete all jobs, known as makespan. To build a high-quality and diverse set of initial solutions we introduce a heuristic method which benefits from the flexible nature of the problem. This initial population will be the starting point for the genetic algorithm, which then applies tabu search to every generated chromosome. The tabu search algorithm relies on a neighbourhood structure that is proposed and analysed in this paper; in particular, some interesting properties are proved, such as feasibility and connectivity. Additionally, we incorporate a filtering mechanism to reduce the neighbourhood size and a method that allows to speed-up the evaluation of new chromosomes. To assess the performance of the resulting method and compare it with the state-of-the-art, we present an extensive computational study on a benchmark with 205 instances, considering both deterministic and fuzzy instances to enhance the significance of the study. The results of these experiments clearly show that not only does the hybrid algorithm benefit from the synergy among its components but it is also quite competitive with the state-of-the-art when solving both crisp and fuzzy instances, providing new best-known solutions for a number of these test instances.

Coevolutionary makespan optimisation through different ranking methods for the fuzzy flexible job shop

In this paper we tackle a variant of the flexible job shop scheduling problem with uncertain task durations modelled as fuzzy numbers, the fuzzy flexible job shop scheduling problem or FfJSP in short. To minimise the schedules fuzzy makespan, we consider different ranking methods for fuzzy numbers. We then propose a cooperative coevolutionary algorithm with two different populations evolving the two components of a solution: machine assignment and task relative order. Additionally, we incorporate a specific local search method for each population. The resulting hybrid algorithm is then evaluated on existing benchmark instances, comparing favourably with the state-of-the-art methods. The experimental results also serve to analyse the influence in the robustness of the resulting schedules of the chosen ranking method.

Heuristic local search for fuzzy open shop scheduling

We consider the fuzzy open shop scheduling problem, where task durations are assumed to be ill-known and modelled as triangular fuzzy numbers. We propose a neighbourhood structure for local search procedures, based on reversing critical arcs in the associated disjunctive graph. We provide a thorough theoretical study of the structure and, in particular, prove that feasibility and asymptotic convergence hold. We further illustrate its good behaviour with experimental results obtained by incorporating the local search procedure to an existing genetic algorithm from the literature and provide a new benchmark of problem instances.

Schedule generation schemes for job shop problems with fuzziness

We consider the job shop scheduling problem with fuzzy durations and expected makespan minimisation. We formally define the space of semi-active and active fuzzy schedules and propose and analyse different schedule-generation schemes (SGSs) in this fuzzy framework. In particular, we study dominance properties of the set of schedules obtained with each SGS. Finally, a computational study illustrates the great difference between the spaces of active and the semi-active fuzzy schedules, an analogous behaviour to that of the deterministic job shop.

Robust swarm optimisation for fuzzy open shop scheduling

Abstract In this paper we consider a variant of the open shop problem where task durations are allowed to be uncertain and where uncertainty is modelled using fuzzy numbers. Solutions to this problem are fuzzy schedules, which we argue should be seen as predictive schedules, thus establishing links with the concept of robustness and a measure thereof. We propose a particle swarm optimization (PSO) approach to minimise the schedule’s expected makespan, using priorities to represent particle position, as well as a decoding algorithm to generate schedules in a subset of possibly active ones. Our proposal is evaluated on a varied set of several benchmark problems. The experimental study includes a parametric analysis, results of the PSO compared with the state-of-the-art, and an empirical study of the robustness of taking into account uncertainty along the scheduling process.

A Genetic Algorithm for the Open Shop Problem with Uncertain Durations

We consider a variation of the open shop problem where task durations are allowed to be uncertain and where uncertainty is modelled using fuzzy numbers. We propose a genetic approach to minimise the expected makespan: we consider different possibilities for the genetic operators and analyse their performance, in order to obtain a competitive configuration. Finally, the performance of the proposed genetic algorithm is tested on several benchmark problems, modified so as to have fuzzy durations, compared with a greedy heuristic from the literature.

Swarm lexicographic goal programming for fuzzy open shop scheduling

In this work we consider a multiobjective open shop scheduling problem with uncertain processing times and flexible due dates, both modelled using fuzzy sets. We adopt a goal programming model based on lexicographic multiobjective optimisation of both makespan and due-date satisfaction and propose a particle swarm algorithm to solve the resulting problem. We present experimental results which show that this multiobjective approach achieves as good results as single-objective algorithms for the objective with the highest priority, while greatly improving on the second objective.

Particle swarm optimisation for open shop problems with fuzzy durations

In this paper we confront a variation of the open shop problem where task durations are allowed to be uncertain and where uncertainty is modelled using fuzzy numbers. We propose a particle swarm optimization (PSO) approach to minimise the expected makespan using priorities to represent particle position, as well as a decoding algorithm to generate schedules in a subset of possibly active ones. Finally, the performance of the PSO is tested on several benchmark problems, modified so as to have fuzzy durations, compared with a memetic algorithm from the literature.

Scatter search for minimizing weighted tardiness in a single machine scheduling with setups

Single machine scheduling problems have many real-life applications and may be hard to solve due to the particular characteristics of some production environments. In this paper, we tackle the single machine scheduling problem with sequence-dependent setup times with the objective of minimizing the weighted tardiness. To solve this problem, we propose a scatter search algorithm which uses path relinking in its core. This algorithm is enhanced with some procedures to speed-up the neighbors’ evaluation and with some diversification and intensification techniques, the latter taking some elements from iterated local search. We conducted an experimental study across a well-known set of instances to analyze the contribution of each component to the overall performance of the algorithm, as well as to compare our proposal with the state-of-the-art metaheuristics, obtaining competitive results. We also propose a new benchmark with larger and more challenging instances and provide the first results for them.

Benchmarks for fuzzy job shop problems

The fuzzy job shop scheduling problem with makespan minimization is revised.We survey existing metaheuristic methods and test beds for the problem.More challenging benchmark instances with LBs and competitive results are proposed.We publish old and new test beds to facilitate reproducibility and future research. The fuzzy job shop scheduling problem with makespan minimisation is a problem with a significant presence in the scientific literature. However, a common meaningful comparison base is missing for such problem. This work intends to fill the gap in this domain by reviewing existing benchmarks as well as proposing new benchmark problems. First, we shall survey the existing test beds for the fuzzy job shop, analysing whether they are sufficiently varied and, most importantly, whether there is room for improvement on these instances - an essential requirement if the instances are to be useful for the scientific community in order to compare and develop new solving strategies. In the light of this analysis, we shall propose a new family of more challenging benchmark problems and provide lower bounds for the expected makespan of each instance as well as reference makespan values obtained with a memetic algorithm from the literature. The resulting benchmark will be made available so as to facilitate experiment reproducibility and encourage research competition.