Search results for "Modeling and simulation"
showing 10 items of 1561 documents
Experiments with classification-based scalarizing functions in interactive multiobjective optimization
2006
In multiobjective optimization methods, the multiple conflicting objectives are typically converted into a single objective optimization problem with the help of scalarizing functions and such functions may be constructed in many ways. We compare both theoretically and numerically the performance of three classification-based scalarizing functions and pay attention to how well they obey the classification information. In particular, we devote special interest to the differences the scalarizing functions have in the computational cost of guaranteeing Pareto optimality. It turns out that scalarizing functions with or without so-called augmentation terms have significant differences in this re…
A spreadsheet modeling approach to the Holt–Winters optimal forecasting
2001
Abstract The objective of this paper is to determine the optimal forecasting for the Holt–Winters exponential smoothing model using spreadsheet modeling. This forecasting procedure is especially useful for short-term forecasts for series of sales data or levels of demand for goods. The non-linear programming problem associated with this forecasting model is formulated and a spreadsheet model is used to solve the problem of optimization efficiently. Also, a spreadsheet makes it possible to work in parallel with various objective functions (measures of forecast errors) and different procedures for calculating the initial values of the components of the model. Using a scenario analysis, the se…
Marginal analysis for the fuzzy p-median problem
2008
The solutions to the fuzzy p-median problem make it possible to leave part of the demand uncovered in order to obtain significant reductions in costs. Moreover, the fuzzy formulation provides the decision-maker with many flexible solutions that he or she may prefer to the classical crisp solution. We introduce some marginal analysis techniques to study how solutions depend on membership functions. Taking into account the internal structure of the problem, we propose a practical criterion to fix the tolerances for the uncovered demand, which happens to be the most sensitive aspect of the fuzzy p-median.
GRASP and path relinking for project scheduling under partially renewable resources
2008
[EN] Recently, in the field of project scheduling problems the concept of partially renewable resources has been introduced. Theoretically, it is a generalization of both renewable and non-renewable resources. From an applied point of view, partially renewable resources allow us to model a large variety of situations that do not fit into classical models, but can be found in real problems in timetabling and labor scheduling. In this paper, we develop some preprocessing techniques and several heuristic algorithms for the problem. Preprocessing significantly reduces the dimension of the problems, therefore improving the efficiency of solution procedures. Heuristic algorithms based on GRASP an…
Using box indices in supporting comparison in multiobjective optimization
2009
Because of the conflicting nature of criteria or objectives, solving a multiobjective optimization problem typically requires interaction with a decision maker who can specify preference information related to the objectives in the problem in question. Due to the difficulties of dealing with multiple objectives, the way information is presented plays a very important role. Questions posed to the decision maker must be simple enough and information shown must be easy to understand. For this purpose, visualization and graphical representations can be useful and constitute one of the main tools used in the literature. In this paper, we propose to use box indices to represent information relate…
NAUTILUS method: An interactive technique in multiobjective optimization based on the nadir point
2010
Most interactive methods developed for solving multiobjective optimization problems sequentially generate Pareto optimal or nondominated vectors and the decision maker must always allow impairment in at least one objective function to get a new solution. The NAUTILUS method proposed is based on the assumptions that past experiences affect decision makers’ hopes and that people do not react symmetrically to gains and losses. Therefore, some decision makers may prefer to start from the worst possible objective values and to improve every objective step by step according to their preferences. In NAUTILUS, starting from the nadir point, a solution is obtained at each iteration which dominates t…
Multi-start methods for combinatorial optimization
2013
Abstract Multi-start methods strategically sample the solution space of an optimization problem. The most successful of these methods have two phases that are alternated for a certain number of global iterations. The first phase generates a solution and the second seeks to improve the outcome. Each global iteration produces a solution that is typically a local optimum, and the best overall solution is the output of the algorithm. The interaction between the two phases creates a balance between search diversification (structural variation) and search intensification (improvement), to yield an effective means for generating high-quality solutions. This survey briefly sketches historical devel…
On the numerical treatment of linearly constrained semi-infinite optimization problems
2000
Abstract We consider the application of two primal algorithms to solve linear semi-infinite programming problems depending on a real parameter. Combining a simplex-type strategy with a feasible-direction scheme we obtain a descent algorithm which enables us to manage the degeneracy of the extreme points efficiently. The second algorithm runs a feasible-direction method first and then switches to the purification procedure. The linear programming subproblems that yield the search direction involve only a small subset of the constraints. These subsets are updated at each iteration using a multi-local optimization algorithm. Numerical test examples, taken from the literature in order to compar…
Pre-processing techniques for resource allocation in the heterogeneous case
1998
The Heterogeneous Resource Allocation Problem (HRAP) deals with the allocation of resources, whose units do not all share the same characteristics, to an established plan of activities. Each activity requires one or more units of each resource which possess particular characteristics, and the objective is to find the minimum number of resource units of each type, necessary to carry out all the activities within the plan, in such a way that two activities whose processing overlaps in time do not have the same resource unit assigned. The HRAP is an NP-Complete problem and it is possible to optimally solve medium-sized HRAP instances in a reasonable time. The objective of this work is to devel…
DEA-like Models for the Efficiency Evaluation of Hierarchically Structured Units
2004
Abstract The knowledge of the internal structure of decision making units (DMUs) gives further insights with respect to the “black box” perspective when considering data envelopment analysis models. We present one-level and two-level hierarchical structures of the DMUs under evaluation. Each unit is composed of consecutive stages of parallel subunits all with constant returns to scale. In particular, the maximization of the relative efficiency of a DMU is studied. For the two-stage situation, different degrees of coordination among the subunits of the hierarchical levels are discussed. When some form of coordination has to be guaranteed, we introduce balancing constraints and we compare two…