Particle swarm optimization combined with genetic operators for job shop scheduling problem with fuzzy processing time

Vela

et al. 2015

Fuzzy Sets and Systems

In this paper we tackle a variant of the flexible job shop scheduling problem with uncertain task durations modelled as fuzzy numbers. To minimise the schedule's makespan, we consider different ranking methods for fuzzy numbers. We then propose a cooperative co-evolutionary 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-theart methods. The experimental results also serve to analyse the influence in the robustness of the resulting schedules of the chosen ranking method.

“…This approximation has been widely used in the scheduling literature, among others, in [22,23,24,25,26] or [27]. Some arguments can be given to support this approximation.…”

Section: Uncertain Processing Timesmentioning

confidence: 99%

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

Vela

et al. 2015

Fuzzy Sets and Systems

“…However, this is cumbersome if not intractable in general, because it requires evaluating two sums or two maxima for every value α ∈ [0, 1]. For the sake of simplicity and tractability of numerical calculations, we follow [17] and approximate the results of these operations by a linear interpolation evaluating only the operation on the three defining points of each TFN (an approach also taken, for instance, in [19], [24]). The approximated sum coincides with the actual sum, so for any pair of TFNs M and N :…”

Section: A Uncertain Durations As Triangular Fuzzy Numbersmentioning

confidence: 99%

“…If S x and C x denote, respectively, the starting and completion times of a task x, it is easy to check that, for instance for task 6, S 6 = max{C 5 , C 9 } = (4, 5, 6) and C 6 = S 6 + p 6 = (9, 11, 13). (16,19,23) In the crisp case, a critical path in a solution graph is defined as the longest path from node 0 to node nm + 1 and a critical arc or critical activity is an arc or activity in a critical path. It is not trivial to extend these concepts and related algorithms to the problem with uncertain durations (cf.…”

Section: B the Disjunctive Graph Model Representationmentioning

confidence: 99%

“…For the job shop, we find a neural approach [13], genetic algorithms [14], [15], [16], simulated annealing [17], genetic algorithms hybridised with local search [18] or particle swarm optimisation [19], [20]. To the best of our knowledge, the open shop problem has not yet been tackled in the fuzzy scheduling framework, with the exception of [21], where fuzzy sets are used to represent flexible job start and due dates, and [22], where a genetic algorithm is proposed to solve the open shop with fuzzy durations.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Heuristic local search for fuzzy open shop scheduling

International Conference on Fuzzy Systems

Vela

et al. 2010

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.

“…Some attempts have been made to extend these heuristic methods to the case where uncertain durations are modelled via fuzzy intervals, among others: a genetic algorithm is hybridised with a local search procedure in [10] for the flow shop problem, and in [13] a particle swarm is proposed to solve the open shop problem. For the job shop with different optimisation criteria, we find a neural approach [19], genetic algorithms [17], [14], simulated annealing [5], genetic algorithms hybridised with local search [6] or particle swarm optimisation [12].…”

Section: Introductionmentioning

confidence: 99%

Hybrid Tabu Search for Fuzzy Job Shop

Puente

Natural and Artificial Models in Computation and Biology

et al. 2013

Abstract. We consider the fuzzy job shop scheduling problem, which is a variant of the well-known job shop problem, with uncertainty in task durations that we model using fuzzy numbers. We propose a tabu search algorithm for minimising the expected makespan based on reversing arcs within critical blocks. We test the algorithm and then combine it with a genetic algorithm from the literature so we can observe the synergy effect, obtaining better results with the hybrid algorithm than with its components by separate. Finally we compare our hybrid algorithm with a memetic algorithm from the literature and show that even in similar times, our method is better in terms of expected makespan.