Heuristic local search for fuzzy open shop scheduling

Abstract

Abstract-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.

Particle Swarm Optimisation for Open Shop Problems with Fuzzy Durations

“…By doing this, the optimal solution to the crisp problem provides a lower bound for the expected makespan of the fuzzified version [5]. In [10], the authors propose a neighbourhood structure which combined with the GA from [18] provides a MA that not only obtains better solutions but is also more "reliable" in the sense that there is less variability in quality solution across different executions. In this experimental study we compare our PSO with this MA.…”

“…For the experimental study we use the test bed given in [10], where the authors follow [5] and generate a set of fuzzy problem instances from well-known benchmark problems from [3]. Given a crisp problem instance, each crisp processing time t is transformed into a symmetric fuzzy processing time p(t) such that its modal value is p 2 = t and p 1 , p 3 are random values, symmetric w.r.t.…”

“…Among these, [12] describes two heuristic methods to obtain a list of operation priorities later used in a list-scheduling algorithm; [16] proposes a tabu search algorithm; [7] introduces a genetic algorithm hybridised with local search; a genetic algorithm using heuristic seeding is given in [20], and [23] proposes a solution based on particle swarm optimisation. As mentioned in Section 1, among these only a genetic algorithm [18] and its combination with local search [10] have been applied to the case where durations are fuzzy numbers.…”

“…[11], [15], [24], [21]. However, to the best of our knowledge, the open shop problem has received little attention in the fuzzy framework: in [14] fuzzy sets are used to represent flexible job start and due dates, in [18] a genetic algorithm is proposed to solve the open shop with fuzzy durations, and in [10] this genetic algorithm is combined with a local search method.…”

Robust swarm optimisation for fuzzy open shop scheduling

“…Some heuristic methods have so far been proposed for fuzzy flow and job shop problems, where uncertain durations are modelled via fuzzy sets; among others, in the last years we find genetic algorithms in [12] and [22], a fuzzy-neural approach in [32], a memetic algorithm combining evolution and local search in [28], swarm-based neighbourhood search in [33] or differential evolution in [17]. However, to the best of our knowledge, the open shop problem has received little attention in the fuzzy framework: in [21] fuzzy sets are used to represent flexible job start and due dates, a possibilistic mixed-integer linear programming method is proposed in [25] for a multiobjective open shop with setup times, fuzzy processing times and fuzzy due dates and in [26] a genetic algorithm is proposed to solve the open shop with fuzzy durations, and in [11] this genetic algorithm is combined with a local search method.…”