Joaquín A. Pacheco

Optimizing the periodic pick-up of raw materials for a manufacturer of auto parts

Abstract We describe a solution procedure for a special case of the periodic vehicle routing problem (PVRP). Operation managers at an auto parts manufacturer in the north of Spain described the optimization problem to the authors. The manufacturer must pick up parts (raw material) from geographically dispersed locations. The parts are picked up periodically at scheduled times. The problem consists of assigning a pickup schedule to each of its supplier’s locations and also establishing daily routes in order to minimize total transportation costs. The time horizon under consideration may be as long as 90 days. The resulting PVRP is such that the critical decision is the assignment of locations to schedules, because once this is done, the daily routing of vehicles is relatively straightforward. Through extensive computational experiments, we show that the metaheuristic procedure described in this paper is capable of finding high-quality solutions within a reasonable amount of computer time. Our main contribution is the development of a procedure that is more effective at handling PVRP instances with long planning horizons when compared to those proposed in the literature.

Tabu search for a multi-objective routing problem

Multi-objective optimization problems deal with the presence of different conflicting objectives. Given that it is not possible to obtain a single solution by optimizing all the objectives simultaneously, a common way to face these problems is to obtain a set of efficient solutions called the non-dominated frontier. In this paper, we address the problem of routing school buses with two objectives: minimize the number of buses, and minimize the longest time a student would have to stay in the bus. The trade-off in this problem is between service level, which is represented by the maximum route length, and operational cost, which is represented by the number of buses in the solution. We present different constructive solution methods and a tabu search procedure to obtain non-dominated solutions. The procedure is coupled with an intensification phase based on the path relinking methodology: a strategy proposed several years ago, which has been rarely used in actual implementations. Computational experiments with real data, in the context of routing school buses in a rural area, establish the effectiveness of our procedure in relation to the approach previously identified to be the best.

A variable selection method based on Tabu search for logistic regression models

A Tabu search method is proposed and analysed for selecting variables that are subsequently used in Logistic Regression Models. The aim is to find from among a set of m variables a smaller subset which enables the efficient classification of cases. Reducing dimensionality has some very well-known advantages that are summarized in literature. The specific problem consists in finding, for a small integer value of p, a subset of size p of the original set of variables that yields the greatest percentage of hits in Logistic Regression. The proposed Tabu search method performs a deep search in the solution space that alternates between a basic phase (that uses simple moves) and a diversification phase (to explore regions not previously visited). Testing shows that it obtains significantly better results than the Stepwise, Backward or Forward methods used by classic statistical packages. Some results of applying these methods are presented.

Design of hybrids for the minimum sum-of-squares clustering problem

A series of metaheuristic algorithms is proposed and analyzed for the non-hierarchical clustering problem under the criterion of minimum sum-of-squares clustering. These algorithms incorporate genetic operators and local search and tabu search procedures. The aim is to obtain quality solutions with short computation times. A series of computational experiments has been performed. The proposed algorithms obtain better results than previously reported methods, especially with a small number of clusters.

Analysis of new variable selection methods for discriminant analysis

Several methods to select variables that are subsequently used in discriminant analysis are proposed and analysed. The aim is to find from among a set of m variables a smaller subset which enables an efficient classification of cases. Reducing dimensionality has some advantages such as reducing the costs of data acquisition, better understanding of the final classification model, and an increase in the efficiency and efficacy of the model itself. The specific problem consists in finding, for a small integer value of p, the size p subset of original variables that yields the greatest percentage of hits in the discriminant analysis. To solve this problem a series of techniques based on metaheuristic strategies is proposed. After performing some test it is found that they obtain significantly better results than the stepwise, backward or forward methods used by classic statistical packages. The way these methods work is illustrated with several examples.

Bi-Objective Bus Routing: An Application to School Buses in Rural Areas

The min-max vehicle routing problem VRP is a variant of the classical VRP in which the objective is to minimize the duration of the longest route. Examination of the VRP literature indicates that the min-max VRP has received less attention than other variants have over the years. However, the problem has important practical applications, such as those related to routing school buses. In this setting, in addition to the min-max criterion imposed on the time it takes to complete the longest route, school districts are concerned with the minimization of the total distance traveled, which is the objective of the classical VRP. Hence, the problem is formulated as a bi-objective optimization model that trades off service i.e., the minimization of the longest route and operational cost i.e., the minimization of the total distance traveled. We develop a solution procedure for this problem by applying tabu search within the framework of Multiobjective Adaptive Memory Programming and compare it to an implementation of the Non-dominated Sorting Genetic Algorithm---a well-known approach to multiobjective optimization. We also assess the merit of the solution method by comparing our approximations with solution frontiers obtained with an e-constraint implementation.

A scatter search approach for the minimum sum-of-squares clustering problem

A metaheuristic procedure based on the scatter search approach is proposed for the non-hierarchical clustering problem under the criterion of minimum sum-of-squares clustering. This algorithm incorporates procedures based on different strategies, such as local search, GRASP, tabu search or path relinking. The aim is to obtain quality solutions with short computation times. A series of computational experiments has been performed. The proposed algorithm obtains better results than previously reported methods, especially with small numbers of clusters.

A tabu search approach to an urban transport problem in northern Spain

In this work we analyze an urban transport problem that the City Council of Burgos, a city in northern Spain, has posed to the authors. Given a fleet of buses and drivers, the problem consists in designing routes and assigning buses to the routes such that the service level is optimized. The optimality of the service level is measured in terms of the waiting time at the bus stops and the duration of the trip. Thus, the problem comprises two decision levels (route design and bus assignment) and differs from other urban transport models found in the literature. In order to solve the problem, we propose two algorithms: one with a local search strategy and another with a tabu search strategy. In both cases, the solutions of the two decision levels are modified in alternating steps. The proposed algorithms obtained significantly better results than the tools currently applied by the transport authorities. In addition, the solutions obtained are very robust with respect to variations on demand, as shown by the experiments.

Optimizing Vehicle Routes in a Bakery Company Allowing Flexibility in Delivery Dates

The work addressed in this paper is motivated from a real problem proposed to the authors by a bakery company in Northern Spain. The objective is to minimize the total distance travelled for the daily routes over the week. In order to reduce this total distance, some flexibility in the dates of delivery is introduced. A mixed-integer linear model for the problem is formulated. In addition, a two-phase method based in GRASP and path-relinking metaheuristic strategies is proposed. Computational experiments show that the method performs very well, obtaining high-quality solutions in short computational times. Moreover, when it is applied to real-data-based instances, the obtained solutions considerably reduce transportation costs over the planning horizon.

A multi-start tabu search method for a single-machine scheduling problem with periodic maintenance and sequence-dependent set-up times

In this paper we study a problem of sequencing jobs in a machine with programmed preventive maintenance and sequence-dependent set-up times. The problem combines two NP-hard problems, so we propose a heuristic method for solving it, which hybridizes multi-start strategies with Tabu Search. We compare our method with the only published metaheuristic algorithm for this problem on a set of 420 instances. The comparison favors the method developed in this work, showing that is able to find high quality solutions in very short computational times.