A critical-path based iterated local search for the green permutation flowshop problem

The permutation flowshop scheduling problem is a widely studied combinatorial optimization problem with several real-world applications. In this paper we address a green variant of the problem with controllable processing times and two objective functions: one related to the service level of the factory (makespan) and another one related to the total cost or the total energy/carbon consumption. For this problem we propose a novel Critical-Path based Iterated Local Search. This metaheuristic incorporates several theoretical results to accelerate the search of solutions in the intensification phase. The proposed algorithm has been compared on an extensive benchmark with the most promising algorithms in the literature. The computational results show the excellent performance of the proposal.Ministerio de Ciencia e Innovación PID2019-108756RB-I00Junta de Andalucía US-126451

A multi objective volleyball premier league algorithm for green scheduling identical parallel machines with splitting jobs

Parallel machine scheduling is one of the most common studied problems in recent years, however, this classic optimization problem has to achieve two conflicting objectives, i.e. minimizing the total tardiness and minimizing the total wastes, if the scheduling is done in the context of plastic injection industry where jobs are splitting and molds are important constraints. This paper proposes a mathematical model for scheduling parallel machines with splitting jobs and resource constraints. Two minimization objectives - the total tardiness and the number of waste - are considered, simultaneously. The obtained model is a bi-objective integer linear programming model that is shown to be of NP-hard class optimization problems. In this paper, a novel Multi-Objective Volleyball Premier League (MOVPL) algorithm is presented for solving the aforementioned problem. This algorithm uses the crowding distance concept used in NSGA-II as an extension of the Volleyball Premier League (VPL) that we recently introduced. Furthermore, the results are compared with six multi-objective metaheuristic algorithms of MOPSO, NSGA-II, MOGWO, MOALO, MOEA/D, and SPEA2. Using five standard metrics and ten test problems, the performance of the Pareto-based algorithms was investigated. The results demonstrate that in general, the proposed algorithm has supremacy than the other four algorithms

Workforce Scheduling with Order-Picking Assignments in Distribution Facilities

Scheduling the availability of order pickers is crucial for effective operations in a distribution facility with manual order pickers. When order-picking activities can only be performed in specific time windows, it is essential to jointly solve the order picker shift scheduling problem and the order picker planning problem of assigning and sequencing individual orders to order pickers. This requires decisions regarding the number of order pickers to schedule, shift start and end times, break times, as well as the assignment and timing of order-picking activities. We call this the order picker scheduling problem and present two formulations. A branch-and-price algorithm and a metaheuristic are developed to solve the problem. Numerical experiments illustrate that the metaheuristic finds near-optimal solutions at 80% shorter computation times. A case study at the largest supermarket chain in The Netherlands shows the applicability of the solution approach in a real-life business application. In particular, different shift structures are analyzed, and it is concluded that the retailer can increase the minimum compensated duration for employed workers from six hours to seven or eight hours while reducing the average labor cost with up to 5% savings when a 15-minute flexibility is implemented in the scheduling of break times

Optimization Models and Approximate Algorithms for the Aerial Refueling Scheduling and Rescheduling Problems

The Aerial Refueling Scheduling Problem (ARSP) can be defined as determining the refueling completion times for fighter aircrafts (jobs) on multiple tankers (machines) to minimize the total weighted tardiness. ARSP can be modeled as a parallel machine scheduling with release times and due date-to-deadline window. ARSP assumes that the jobs have different release times, due dates, and due date-to-deadline windows between the refueling due date and a deadline to return without refueling. The Aerial Refueling Rescheduling Problem (ARRP), on the other hand, can be defined as updating the existing AR schedule after being disrupted by job related events including the arrival of new aircrafts, departure of an existing aircrafts, and changes in aircraft priorities. ARRP is formulated as a multiobjective optimization problem by minimizing the total weighted tardiness (schedule quality) and schedule instability. Both ARSP and ARRP are formulated as mixed integer programming models. The objective function in ARSP is a piecewise tardiness cost that takes into account due date-to-deadline windows and job priorities. Since ARSP is NP-hard, four approximate algorithms are proposed to obtain solutions in reasonable computational times, namely (1) apparent piecewise tardiness cost with release time rule (APTCR), (2) simulated annealing starting from random solution (SArandom ), (3) SA improving the initial solution constructed by APTCR (SAAPTCR), and (4) Metaheuristic for Randomized Priority Search (MetaRaPS). Additionally, five regeneration and partial repair algorithms (MetaRE, BestINSERT, SEPRE, LSHIFT, and SHUFFLE) were developed for ARRP to update instantly the current schedule at the disruption time. The proposed heuristic algorithms are tested in terms of solution quality and CPU time through computational experiments with randomly generated data to represent AR operations and disruptions. Effectiveness of the scheduling and rescheduling algorithms are compared to optimal solutions for problems with up to 12 jobs and to each other for larger problems with up to 60 jobs. The results show that, APTCR is more likely to outperform SArandom especially when the problem size increases, although it has significantly worse performance than SA in terms of deviation from optimal solution for small size problems. Moreover CPU time performance of APTCR is significantly better than SA in both cases. MetaRaPS is more likely to outperform SAAPTCR in terms of average error from optimal solutions for both small and large size problems. Results for small size problems show that MetaRaPS algorithm is more robust compared to SAAPTCR. However, CPU time performance of SA is significantly better than MetaRaPS in both cases. ARRP experiments were conducted with various values of objective weighting factor for extended analysis. In the job arrival case, MetaRE and BestINSERT have significantly performed better than SEPRE in terms of average relative error for small size problems. In the case of job priority disruption, there is no significant difference between MetaRE, BestINSERT, and SHUFFLE algorithms. MetaRE has significantly performed better than LSHIFT to repair job departure disruptions and significantly superior to the BestINSERT algorithm in terms of both relative error and computational time for large size problems

Energy-aware scheduling in heterogeneous computing systems

In the last decade, the grid computing systems emerged as useful provider of the computing power required for solving complex problems. The classic formulation of the scheduling problem in heterogeneous computing systems is NP-hard, thus approximation techniques are required for solving real-world scenarios of this problem. This thesis tackles the problem of scheduling tasks in a heterogeneous computing environment in reduced execution times, considering the schedule length and the total energy consumption as the optimization objectives. An efficient multithreading local search algorithm for solving the multi-objective scheduling problem in heterogeneous computing systems, named MEMLS, is presented. The proposed method follows a fully multi-objective approach, applying a Pareto-based dominance search that is executed in parallel by using several threads. The experimental analysis demonstrates that the new multithreading algorithm outperforms a set of fast and accurate two-phase deterministic heuristics based on the traditional MinMin. The new ME-MLS method is able to achieve significant improvements in both makespan and energy consumption objectives in reduced execution times for a large set of testbed instances, while exhibiting very good scalability. The ME-MLS was evaluated solving instances comprised of up to 2048 tasks and 64 machines. In order to scale the dimension of the problem instances even further and tackle large-sized problem instances, the Graphical Processing Unit (GPU) architecture is considered. This line of future work has been initially tackled with the gPALS: a hybrid CPU/GPU local search algorithm for efficiently tackling a single-objective heterogeneous computing scheduling problem. The gPALS shows very promising results, being able to tackle instances of up to 32768 tasks and 1024 machines in reasonable execution times.En la última década, los sistemas de computación grid se han convertido en útiles proveedores de la capacidad de cálculo necesaria para la resolución de problemas complejos. En su formulación clásica, el problema de la planificación de tareas en sistemas heterogéneos es un problema NP difícil, por lo que se requieren técnicas de resolución aproximadas para atacar instancias de tamaño realista de este problema. Esta tesis aborda el problema de la planificación de tareas en sistemas heterogéneos, considerando el largo de la planificación y el consumo energético como objetivos a optimizar. Para la resolución de este problema se propone un algoritmo de búsqueda local eficiente y multihilo. El método propuesto se trata de un enfoque plenamente multiobjetivo que consiste en la aplicación de una búsqueda basada en dominancia de Pareto que se ejecuta en paralelo mediante el uso de varios hilos de ejecución. El análisis experimental demuestra que el algoritmo multithilado propuesto supera a un conjunto de heurísticas deterministas rápidas y e caces basadas en el algoritmo MinMin tradicional. El nuevo método, ME-MLS, es capaz de lograr mejoras significativas tanto en el largo de la planificación y como en consumo energético, en tiempos de ejecución reducidos para un gran número de casos de prueba, mientras que exhibe una escalabilidad muy promisoria. El ME-MLS fue evaluado abordando instancias de hasta 2048 tareas y 64 máquinas. Con el n de aumentar la dimensión de las instancias abordadas y hacer frente a instancias de gran tamaño, se consideró la utilización de la arquitectura provista por las unidades de procesamiento gráfico (GPU). Esta línea de trabajo futuro ha sido abordada inicialmente con el algoritmo gPALS: un algoritmo híbrido CPU/GPU de búsqueda local para la planificación de tareas en en sistemas heterogéneos considerando el largo de la planificación como único objetivo. La evaluación del algoritmo gPALS ha mostrado resultados muy prometedores, siendo capaz de abordar instancias de hasta 32768 tareas y 1024 máquinas en tiempos de ejecución razonables