Fast local search for fuzzy job shop scheduling

In the sequel, we propose a new neighbourhood structure for local search for the fuzzy job shop scheduling problem. This is a variant of the well-known job shop problem, with uncertainty in task durations modelled using fuzzy numbers and where the goal is to minimise the expected makespan of the resulting schedule. The new neighbourhood structure is based in changing the relative order of subsequences of tasks within critical blocks. We study its theoretical properties and provide a makespan estimate which allows to select only feasible neighbours while covering a greater portion of the search space than a previous neighbourhood from the literature. Despite its larger search domain, experimental results show that this new structure notably reduces the computational load of local search with respect to the previous neighbourhood while maintaining or even improving solution quality

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.This research has been supported by the Spanish Government under research grants FEDER TIN2010-20976-C02-02 and MTM2010- 16051 and by the Principality of Asturias (Spain) under grants Severo Ochoa BP13106 and FC-13-COF13-03

Robust multiobjective optimisation for fuzzy job shop problems

Abstract In this paper we tackle a variant of the job shop scheduling problem with uncertain task durations modelled as fuzzy numbers. Our goal is to simultaneously minimise the schedule's fuzzy makespan and maximise its robustness. To this end, we consider two measures of solution robustness: a predictive one, prior to the schedule execution, and an empirical one, measured at execution. To optimise both the expected makespan and the predictive robustness of the fuzzy schedule we propose a multiobjective evolutionary algorithm combined with a novel dominance-based tabu search method. The resulting hybrid algorithm is then evaluated on existing benchmark instances, showing its good behaviour and the synergy between its components. The experimental results also serve to analyse the goodness of the predictive robustness measure, in terms of its correlation with simulations of the empirical measure.This research has been supported by the Spanish Government under Grants FEDER TIN2013-46511-C2-2-P and MTM2014-55262-P

Robust schedules for tardiness optimization in job shop with interval uncertainty

This paper addresses a variant of the job shop scheduling problem with total tardiness minimization where task durations and due dates are uncertain. This uncertainty is modelled with intervals. Different ranking methods for intervals are considered and embedded into a genetic algorithm. A new robustness measure is proposed to compare the different ranking methods and assess their capacity to predict ‘expected delays’ of jobs. Experimental results show that dealing with uncertainty during the optimization process yields more robust solutions. A sensitivity analysis also shows that the robustness of the solutions given by the solving method increases when the uncertainty grows.This research has been supported by the Spanish Government under research grants PID2019-106263RB-I00 and TIN2017-87600-P

Multi-objective enhanced memetic algorithm for green job shop scheduling with uncertain times

The quest for sustainability has arrived to the manufacturing world, with the emergence of a research field known as green scheduling. Traditional performance objectives now co-exist with energy-saving ones. In this work, we tackle a job shop scheduling problem with the double goal of minimising energy consumption during machine idle time and minimising the project’s makespan. We also consider uncertainty in processing times, modelled with fuzzy numbers. We present a multi-objective optimisation model of the problem and we propose a new enhanced memetic algorithm that combines a multiobjective evolutionary algorithm with three procedures that exploit the problem-specific available knowledge. Experimental results validate the proposed method with respect to hypervolume, -indicator and empirical attaintment functions

Genetic fuzzy schedules for charging electric vehicles

This work tackles the problem of scheduling the charging of electric vehicles in a real-world charging station subject to a set of physical constraints, with the goal of minimising the total tardiness with respect to a desired departure date given for each vehicle. We model a variant of the problem that incorporates uncertainty in the charging times using fuzzy numbers. As solving method, we propose a genetic algorithm with tailor-made operators, in particular, a new chromosome evaluation method based on generating schedules from a priority vector. Finally, an experimental study avails the proposed genetic algorithm both in terms of algorithm convergence and quality of the obtained solutions.Acknowledgements. This work was supported by the Spanish Government [Grant Nos.TIN2016-79190-R, MTM2014-55262-P]

Benchmarks for fuzzy job shop problems

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