Javier Alcaraz

A Robust Genetic Algorithm for Resource Allocation in Project Scheduling

Genetic algorithms have been applied to many different optimization problems and they are one of the most promising metaheuristics. However, there are few published studies concerning the design of efficient genetic algorithms for resource allocation in project scheduling. In this work we present a robust genetic algorithm for the single-mode resource constrained project scheduling problem. We propose a new representation for the solutions, based on the standard activity list representation and develop new crossover techniques with good performance in a wide sample of projects. Through an extensive computational experiment, using standard sets of project instances, we evaluate our genetic algorithm and demonstrate that our approach outperforms the best algorithms appearing in the literature.

Solving the Multi-Mode Resource-Constrained Project Scheduling Problem with genetic algorithms

In this paper we consider the Multi-Mode Resource-Constrained Project Scheduling Problem with makespan minimisation as the objective. We have developed new genetic algorithms, extending the representation and operators previously designed for the single-mode version of the problem. Moreover, we have defined a new fitness function for the individuals who are infeasible. We have tested different variants of the algorithm and chosen the best to be compared to different heuristics previously published, using standard sets of instances included in PSPLIB. Results illustrate the good performance of our algorithm.

SOLVING THE FLOWSHOP SCHEDULING PROBLEM WITH SEQUENCE DEPENDENT SETUP TIMES USING ADVANCED METAHEURISTICS

Abstract This paper deals with the permutation flowshop scheduling problem in which there are sequence dependent setup times on each machine, commonly known as the SDST flowshop. The optimisation criteria considered is the minimisation of the makespan or Cmax. Genetic algorithms have been successfully applied to regular flowshops before, and the objective of this paper is to assess their effectiveness in a more realistic and complex environment. We present two advanced genetic algorithms as well as several adaptations of existing advanced metaheuristics that have shown superior performance when applied to regular flowshops. We show a calibration of the genetic algorithms parameters and operators by means of a Design of Experiments (DOE) approach. For evaluating the proposed algorithms, we have coded several, if not all, known SDST flowshop specific algorithms. All methods are tested against an augmented benchmark based on the instances of Taillard. The results show a clear superiority of the algorithms proposed, especially for the genetic algorithms, regardless of instance type and size.

A decision support system for a real vehicle routing problem

Abstract The vehicle routing problem has been widely studied in the literature, mainly because of the real world logistics and transportation problems related to it. In the present paper, a new two-stage exact approach for solving a real problem is shown, along with decision making software. In the first stage, all the feasible routes are generated by means of an implicit enumeration algorithm; afterwards, an integer programming model is designed to select in the second stage the optimum routes from the set of feasible routes. The integer model uses a number of 0–1 variables ranging from 2000 to 15,000 and gives optimum solutions in an average time of 60 seconds (for instances up to 60 clients). An interactive decision support system was also developed. The system was tested with a set of real instances and, in a worst-case scenario (up to 60 clients), the routes obtained ranged from a 7% to 12% reduction in the distance travelled and from a 9% to 11% reduction in operational costs.

Ranking ranges in cross-efficiency evaluations

The existence of alternate optima for the DEA weights may reduce the usefulness of the cross-efficiency evaluation, since the ranking provided depends on the choice of weights that the different DMUs make. In this paper, we develop a procedure to carry out the cross-efficiency evaluation without the need to make any specific choice of DEA weights. The proposed procedure takes into consideration all the possible choices of weights that all the DMUs can make, and yields for each unit a range for its possible rankings instead of a single ranking. This range is determined by the best and the worst rankings that would result in the best and the worst scenarios of each unit across all the DEA weights of all the DMUs. This approach might identify good/bad performers, as those that rank at the top/bottom irrespective of the weights that are chosen, or units that outperform others in all the scenarios. In addition, it may be used to analyze the stability of the ranking provided by the standard cross-efficiency evaluation.

Design and analysis of hybrid metaheuristics for the Reliability p-Median Problem

In the p-Median Problem, it is assumed that, once the facilities are opened, they may not fail. In practice some of the facilities may become unavailable due to several factors. In the Reliability p-Median Problem some of the facilities may not be operative during certain periods. The objective now is to find facility locations that are both inexpensive and also reliable. We present different configurations of two hybrid metaheuristics to solve the problem, a genetic algorithm and a scatter search approach. We have carried out an extensive computational experiment to study the performance of the algorithms and compare its efficiency solving well-known benchmark instances.

A Hybrid Genetic Algorithm Based on Intelligent Encoding for Project Scheduling

In the last few years several heuristic, metaheuristic and hybrid techniques have been developed to solve the Resource-Constrained Project Scheduling Problem (RCPSP). Most of them use the standard activity list representation, given that it seems to perform best in solving the RCPSP independently of the paradigm employed (genetic algorithms, tabu search, simulated annealing, ...). However, we have designed an innovative representation, one which has not been used before and which includes a lot of problem-specific knowledge. Based on that representation we have developed a new competitive and robust hybrid genetic algorithm, which uses genetic operators and an improvement mechanism specially designed to work on that representation and exploit, in a very efficient way, the information contained in it. We have compared this algorithm with the best algorithms published so far, using the standard benchmark of PSPLIB. The results show the excellent performance of our algorithm.

On relaxing the integrality of the allocation variables of the reliability fixed-charge location problem

The aim of the reliability fixed-charge location problem is to find robust solutions to the fixed-charge location problem when some facilities might fail with probability q. In this paper we analyze for which allocation variables in the reliability fixed-charge location problem formulation the integrality constraint can be relaxed so that the optimal value matches the optimal value of the binary problem. We prove that we can relax the integrality of all the allocation variables associated to non-failable facilities or of all the allocation variables associated to failable facilities but not of both simultaneously. We also demonstrate that we can relax the integrality of all the allocation variables whenever a family of valid inequalities is added to the set of constraints or whenever the parameters of the problem satisfy certain conditions. Finally, when solving the instances in a data set we discuss which relaxation or which modification of the problem works better in terms of resolution time and we illustrate that relaxing the integrality of the allocation variables inappropriately can alter the objective value considerably.