Search results for "Mathematical optimization"
showing 10 items of 1300 documents
Scatter tabu search for multiobjective clustering problems
2011
We propose a hybrid heuristic procedure based on scatter search and tabu search for the problem of clustering objects to optimize multiple criteria. Our goal is to search for good approximations of the efficient frontier for this class of problems and provide a means for improving decision making in multiple application areas. Our procedure can be viewed as an extension of SSPMO (a scatter search application to nonlinear multiobjective optimization) to which we add new elements and strategies specially suited for combinatorial optimization problems. Clustering problems have been the subject of numerous studies; however, most of the work has focused on single-objective problems. Clustering u…
Tabu search with strategic oscillation for the maximally diverse grouping problem
2013
We propose new heuristic procedures for the maximally diverse grouping problem (MDGP). This NP-hard problem consists of forming maximally diverse groups—of equal or different size—from a given set of elements. The most general formulation, which we address, allows for the size of each group to fall within specified limits. The MDGP has applications in academics, such as creating diverse teams of students, or in training settings where it may be desired to create groups that are as diverse as possible. Search mechanisms, based on the tabu search methodology, are developed for the MDGP, including a strategic oscillation that enables search paths to cross a feasibility boundary. We evaluate co…
On the generalized directed rural postman problem
2014
The generalized directed rural postman problem (GDRPP) is a generic type of arc routing problem. In the present paper, it is described how many types of practically relevant single-vehicle routing problems can be modelled as GDRPPs. This demonstrates the versatility of the GDRPP and its importance as a unified model for postman problems. In addition, an exact and a heuristic solution method are presented. Computational experiments using two large sets of benchmark instances are performed. The results show high solution quality and thus demonstrate the practical usefulness of the approach.
GRASP with path relinking for the orienteering problem
2014
In this paper, we address an optimization problem resulting from the combination of the well-known travelling salesman and knapsack problems. In particular, we target the orienteering problem, originated in the context of sport, which consists of maximizing the total score associated with the vertices visited in a path within the available time. The problem, also known as the selective travelling salesman problem, is NP-hard and can be formulated as an integer linear program. Since the 1980s, several solution methods for this problem have been developed and applied to a variety of fields, particularly in routing and tourism. We propose a heuristic method—based on the Greedy Randomized Adapt…
Improving demand forecasting accuracy using nonlinear programming software
2006
We address the problem of forecasting real time series with a proportion of zero values and a great variability among the nonzero values. In order to calculate forecasts for a time series, the model coefficients must be estimated. The appropriate choice of values for the smoothing parameters in exponential smoothing methods relies on the minimization of the fitting errors of historical data. We adapt the generalized Holt–Winters formulation so that it can consider the starting values of the local components of level, trend and seasonality as decision variables of the nonlinear programming problem associated with this forecasting procedure. A spreadsheet model is used to solve the problems o…
Constructing Good Solutions for the Spanish School Timetabling Problem
1996
In the school timetabling problem a set of lessons (combinations of classes, teachers, subjects and rooms) has to be scheduled within the school week. Considering classes, teachers and rooms as resources for the lessons, the problem may be viewed as the scheduling of a project subject to resource constraints. We have developed an algorithm with three phases. In Phase I an initial solution is built by using the scheme of parallel heuristic algorithm with priority rules, but imbedding at each period the construction of a maximum cardinality independent set on a resource graph. In Phase II a tabu search procedure starts from the solution of Phase I and obtains a feasible solution to the proble…
Tabu search algorithms for an industrial multi-product and multi-objective assembly line balancing problem, with reduction of the task dispersion
2002
This paper presents a real-world industrial application of the multi-product and multi-objective assembly line balancing problem, for a company involved in the production of four models of a white goods product. The problem solved is a GALBP-2, with 10 workstations and multiple objectives (to maximize the production rate in order to deal with an increase of the demand forecasted, to reach an equal cycle time of all the models and an equal workload of the different workstations, and finally, to minimize the dispersion of worker tasks on each one of the different models-the common tasks of the different models at the same workstation). The paper presents an integrated approach based on four h…
A Portfolio Problem with Uncertainty
2000
In this paper we present two models for cash flow matching with an uncertain level of payments at each due date. To solve the problem of minimising the initial investment we use the scenario method proposed by Dembo, and the robust optimisation method proposed by Mulvey et al. We unify these optimisation methods in a general co-ordinated model that guarantees a match under every scenario. This general model is also a multi-objective programming problem. We illustrate this methodology in a problem with several scenarios.
Constructing a Pareto front approximation for decision making
2011
An approach to constructing a Pareto front approximation to computationally expensive multiobjective optimization problems is developed. The approximation is constructed as a sub-complex of a Delaunay triangulation of a finite set of Pareto optimal outcomes to the problem. The approach is based on the concept of inherent nondominance. Rules for checking the inherent nondominance of complexes are developed and applying the rules is demonstrated with examples. The quality of the approximation is quantified with error estimates. Due to its properties, the Pareto front approximation works as a surrogate to the original problem for decision making with interactive methods. Qc 20120127
Interactive multiobjective optimization for anatomy-based three-dimensional HDR brachytherapy.
2010
In this paper, we present an anatomy-based three-dimensional dose optimization approach for HDR brachytherapy using interactive multiobjective optimization (IMOO). In brachytherapy, the goals are to irradiate a tumor without causing damage to healthy tissue. These goals are often conflicting, i.e. when one target is optimized the other will suffer, and the solution is a compromise between them. IMOO is capable of handling multiple and strongly conflicting objectives in a convenient way. With the IMOO approach, a treatment planner’s knowledge is used to direct the optimization process. Thus, the weaknesses of widely used optimization techniques (e.g. defining weights, computational burden an…