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

Enhanced memetic search for reducing energy consumption in fuzzy flexible job shops

The flexible job shop is a well-known scheduling problem that has historically attracted much research attention both because of its computational complexity and its importance in manufacturing and engineering processes. Here we consider a variant of the problem where uncertainty in operation processing times is modeled using triangular fuzzy numbers. Our objective is to minimize the total energy consumption, which combines the energy required by resources when they are actively processing an operation and the energy consumed by these resources simply for being switched on. To solve this NP-Hard problem, we propose a memetic algorithm, a hybrid metaheuristic method that combines global search with local search. Our focus has been on obtaining an efficient method, capable of obtaining similar solutions quality-wise to the state of the art using a reduced amount of time. To assess the performance of our algorithm, we present an extensive experimental analysis that compares it with previous proposals and evaluates the effect on the search of its different components.Supported by the Spanish Government under research grants PID2019-106263RB-I00 and TED2021-131938B-I00 and by Universidad de Cantabria and the Government of Cantabria under Grant Concepción Arenal UC-20-20

Neighbourhood search for energy minimisation in flexible job shops under fuzziness

Uncertainty pervades real life and supposes a challenge for all industrial processes as it makes it difficult to predict the outcome of otherwise risk-free activities. In particular, time deviation from projected objectives is one of the main sources of economic losses in manufacturing, not only for the delay in production but also for the energy consumed by the equipment during the additional unexpected time they have to work to complete their labour. In this work we deal with uncertainty in the flexible job shop, one of the foremost scheduling problems due to its practical applications. We show the importance of a good model to avoid introducing unwanted imprecision and producing artificially pessimistic solutions. In our model, the total energy is decomposed into the energy required by resources when they are actively processing an operation and the energy consumed by these resources simply for being switched on. We propose a set of metrics and carry out an extensive experimental analysis that compares our proposal with the more straightforward alternative that directly translates the deterministic model. We also define a local search neighbourhood and prove that it can reach an optimal solution starting from any other solution. Results show the superiority of the new model and the good performance of the new neighbourhood.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. This research has been supported by the Spanish Government under research Grants PID2019-106263RB-I00 and TED2021-131938B-I00 and by Universidad de Cantabria and the Government of Cantabria under Grant Concepción Arenal UC-20-20

Fast elitist ABC for makespan optimisation in interval JSP

This paper addresses a variant of the Job Shop Scheduling Problem with makespan minimisation where uncertainty in task durations is taken into account and modelled with intervals. A novel Artificial Bee Colony algorithm is proposed where the classical layout is simplified, increasing the algorithm's speed and reducing the number of parameters to set up. We also take into account the fundamental principles of exploration around a local solution and attraction to a global solution to improve diversity in the hive. The increase on speed and diversity allows to include a Local Search phase to better exploit promising areas of the search space. A parametric analysis is conducted and the contribution of the new strategies is analysed. The results of the new approach are competitive with those obtained with previous methods in the literature, but taking less runtime. The addition of Local Search improves the results even further, outperforming the best-known ones from the literature. An additional sensitivity study is conducted to assess the advantages of considering uncertainty and how increasing it affects the solution's robustness.This research has been supported by the Spanish Government under research grant PID2019-106263RB-I00 and by the Asturian Government under research grant Severo Ochoa

Mathematical models and benchmarking for the fuzzy job shop scheduling problem

The fuzzy job shop scheduling problem with makespan minimisation has received considerable attention over the last decade. Different sets of benchmark instances have been made available, and many metaheuristic solutions and corresponding upper bounds of the optimal makespan have been given for these instances in different publications. However, unlike the deterministic case, very little work has been invested in proposing and solving mathematical models for the fuzzy problem. This has resulted both in a lack of a good characterisation of the hardness of existing benchmark instances and in the absence of reliable lower and upper bounds for the makespan. In consequence, it is difficult, if not impossible to properly assess and compare new proposals of exact or approximate solving methods, thus hindering progress in this field. In this work we intend to fill this gap by proposing and solving two mathematical models, a mixed integer linear programming model and a constraint programming model. A thorough analysis on the scalability of solving these mathematical models with commercial solvers is carried out. A state-of-the-art metaheuristic algorithm from the literature is also used as reference point for a better understanding of the results. Using solvers of different nature allows us to improve known upper and lower bounds for all existing instances, and certify optimality for many of them for the first time. It also enables us to structurally characterise the instances? hardness beyond their size.This work was supported by the Spanish Government [grant number PID2019-106263RB-I00] and [grant number TED2021-131938B-I00]

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]