José Elias Claudio Arroyo

Multi-objective Variable Neighborhood Search Algorithms for a Single Machine Scheduling Problem with Distinct due Windows

In this paper, we compare three multi-objective algorithms based on Variable Neighborhood Search (VNS) heuristic. The algorithms are applied to solve the single machine scheduling problem with sequence dependent setup times and distinct due windows. In this problem, we consider minimizing the total weighted earliness/tardiness and the total flowtime criteria. We introduce two intensification procedures to improve a multi-objective VNS (MOVNS) algorithm proposed in the literature. The performance of the algorithms is tested on a set of medium and larger instances of the problem. The computational results show that the proposed algorithms outperform the original MOVNS algorithm in terms of solution quality. A statistical analysis is conducted in order to analyze the performance of the proposed methods.

Iterative Local Search Heuristic for the Single Machine Scheduling Problem with Sequence Dependent Setup Times and Due Dates

In this paper the NP-hard problem of scheduling jobs in a single machine with sequence dependent setup times is considered with the objective of minimizing the total tardiness with respect to the due dates. An Iterative Local Search (ILS) heuristic is proposed which uses a GRASP (Greedy Randomized Adaptive Search Procedure) algorithm to generate an initial solution. The ILS heuristic is compared with the GRASP algorithm proposed by Gupta and Smith (2006) and with the Ant Colony Optimization (ACO) algorithm of Ching and Hsiao (2007). These algorithms obtained better solutions than other algorithms from the literature. Computational tests, on a set of test problems involving up to 85 jobs, show that our ILS heuristic is very efficient and competitive.

Hybrid GRASP Heuristics to Solve an Unrelated Parallel Machine Scheduling Problem with Earliness and Tardiness Penalties

This paper considers an unrelated parallel machine scheduling problem with the objective of minimizing the total earliness and tardiness penalties. Machine and job-sequence dependent setup times and idle times are considered. Since the studied problem is NP-Hard, we test the applicability of algorithms based on Greedy Randomized Adaptive Search Procedure (GRASP) metaheuristic to determine near-optimal solutions. We propose three different heuristics. The first is a simple GRASP heuristic, the second heuristic includes an intensification procedure based on Path Relinking technique, and the third uses an Iterated Local Search (ILS) heuristic in the local search phase of the GRASP algorithm. The results obtained by the heuristics are compared using a set of small, medium and large instances. Comprehensive computational and statistical analyses are carried out in order to compare the performance of the algorithms.

Hybrid metaheuristic for the single vehicle routing problem with deliveries and selective pickups

This paper presents a hybrid metaheuristic for the single vehicle routing problem with deliveries and selective pickups (SVRPDSP). A vehicle departs loaded from the depot, visit every customer delivering a certain amount of goods according to their demand, and optionally pickup items from those customers, receiving a profit for each pickup realized. The vehicle has a limited capacity, which may turn impossible to attend all pickups, or make this unprofitable if it has to come back later in the customer after unloaded enough to fit the pickup demand. The objective is to find a minimal cost feasible route, the cost being the total travel costs minus the total revenue earned with pickups. Despite the many real applications, the literature is scarce. We propose an evolutionary algorithm whose crossover and mutation operators use data mining strategies to capture good characteristics from the parents and the population. Solutions are improved by a VNS algorithm during the process, and new solutions are introduced regularly to avoid premature convergence, using good constructive algorithms. The algorithm was tested with a benchmark of 68 instances, and the results compared to other publications. The results show the robustness of the method and 7 new solutions were found, including 2 new optimal solutions.

Scheduling unrelated parallel batch processing machines with non-identical job sizes and unequal ready times

This research analyzes the problem of scheduling a set of n jobs with arbitrary job sizes and non-zero ready times on a set of m unrelated parallel batch processing machines so as to minimize the makespan. Unrelated parallel machine is a generalization of the identical parallel processing machines and is closer to real-world production systems. Each machine can accommodate and process several jobs simultaneously as a batch as long as the machine capacity is not exceeded. The batch processing time and the batch ready time are respectively equal to the largest processing time and the largest ready time among all the jobs in the batch. Motivated by the computational complexity and the practical relevance of the problem, we present several heuristics based on first-fit and best-fit earliest job ready time rules. We also present a mixed integer programming model for the problem and a lower bound to evaluate the quality of the heuristics. The small computational effort of deterministic heuristics, which is valuable in some practical applications, is also one of the reasons that motivates this study. The results show that the heuristic proposed in this paper has a superior performance compared to the heuristics based on ideas proposed in the literature. HighlightsScheduling unrelated batch processing machines with non-identical job sizes and unequal release times.The objective is to minimize makespan.Deterministic heuristics are proposed.According to computational experiments, one of the heuristics outperformed the others.

An effective iterated greedy algorithm for scheduling unrelated parallel batch machines with non-identical capacities and unequal ready times

We consider the problem of scheduling jobs on unrelated batch machines so as to minimize the makespan.We present a MIP formulation of the problem and present a lower bound on the optimal makespan.We propose an iterated greedy algorithm to solve the problem.We compare our algorithm with three meta-heuristics in the literature.Computational results show that our algorithm outperforms the other three for both small-size and large-size problems. This study addresses the problem of scheduling a set of n jobs with arbitrary job sizes and non-zero ready times on a set of m unrelated parallel batch machines with different capacities so as to minimize the makespan. Unrelated parallel machines is the most general case of parallel machine environments where each machine processes each job at a different speed. In the studied problem, each machine can process several jobs simultaneously as a batch as long as the machine capacity is not exceeded. The batch processing time and the batch ready time are respectively equal to the largest processing time and the largest ready time among all the jobs in the batch.In this paper, we first provide a lower bound for the problem and a mixed integer programming (MIP) model. To solve the problem, a meta-heuristic based on the iterated greedy (IG) algorithm is proposed. IG is a simple meta-heuristic which generates a sequence of solutions by iterating over a greedy constructive heuristic using destruction and construction operations. In the recent literature this meta-heuristic has been employed to solve a considerable number of combinatorial optimization problems. This is because IG is easy to implement and it often exhibits an excellent performance. The effectiveness of the proposed IG algorithm is evaluated and compared by computational experiments on a large benchmark of randomly generated instances. The obtained results indicate that the proposed algorithm has a superior performance compared to some meta-heuristic algorithms proposed for similar problems.

A multi-objective genetic algorithm with path relinking for the p-median problem

This paper considers the p-median problem that consists in finding p- locals from a set of m candidate locals to install facilities minimizing simultaneously two functions: the sum of the distances from each customer to its nearest facility and the sum of costs for opening facilities. Since this is a NP-Hard problem, heuristic algorithms are the most suitable for solving such a problem. To determine nondominated solutions, we propose a multi-objective genetic algorithm (MOGA) based on a nondominated sorting approach. The algorithm uses an efficient elitism strategy and an intensification operator based on the Path Relinking technique. To test the performance of the proposed MOGA, we develop a Mathematical Programming Algorithm, called eConstraint, that finds Pareto-optimal solutions by solving iteratively the mathematical model of the problem with additional constraints. The results show that the proposed approach is able to generate good approximations to the nondominated frontier of the bi-objective problem efficiently.

A combination of evolutionary algorithm, mathematical programming, and a new local search procedure for the just-in-time job-shop scheduling problem

This paper presents a combination of evolutionary algorithm and mathematical programming with an efficient local search procedure for a just-in-time job-shop scheduling problem (JITJSSP). Each job on the JITTSSP is composed by a sequence of operations, each operation having a specific machine where it must be scheduled and a due date when it should be completed. There is a tardiness cost if an operation is finished later than its due date and also an earliness cost if finished before. The objective is to find a feasible scheduling obeying precedence and machine constraints, minimizing the total earliness and tardiness costs. The experimental results with instances from the literature show the efficiency of the proposed hybrid method: it was able to improve the known upper bound for most of the instances tested, in very little computational time.

A hybrid multi-objective iterated local search heuristic for vehicle routing problem with time windows

The Vehicle Routing Problem with Time Windows (VRPTW) is a well known NP-Hard combinatorial optimization problem and it has received a lot of attention in the literature. In this problem, a fleet of identical vehicles must leave the depot, supply all costumers demands, and return to the depot, at minimum cost, without violating the capacity of the vehicles as well as the time window specified by each customer. This paper considers a VRPTW which aims to minimize two objective functions simultaneously: the total traveling distance and the imbalance in the distances traveled by the vehicles used. To obtain near Pareto-optimal solutions, we propose a hybrid heuristic based on Iterated Local Search, Variable Neighbourhood Descent with random neighbourhood ordering for solution improvement and Recombination of non-dominated solutions as used in genetic algorithms. The results obtained when solving a subset of Solomons benchmark problems show the good performance of the hybrid heuristic.

Reactive GRASP with path relinking for solving parallel machines scheduling problem with resource-assignable sequence dependent setup times

This paper addresses an unrelated parallel machine problem with machine and job sequence dependent setup times. The objective function considered is a linear combination of the total completion time and the total number of resources assigned. Due to the combinatorial complexity of this problem, we propose an algorithm based on the GRASP metaheuristic, in which the basic parameter that defines the restrictiveness of the candidate list during the construction phase is self-adjusted according to the quality of the solutions previously found (reactive GRASP). The algorithm uses an intensification strategy based on the path relinking technique which consists in exploring paths between elite solutions found by GRASP. The results obtained by the proposed algorithm are compared with the best results available in the literature.