Search results for "Mathematical optimization"
showing 10 items of 1300 documents
GRASP and Path Relinking for the Two-Dimensional Two-Stage Cutting-Stock Problem
2007
We develop a greedy randomized adaptive search procedure (GRASP) for the constrained two-dimensional two-stage cutting-stock problem. This is a special cutting problem in which the cut is performed in two phases. In the first phase, the stock rectangle is slit down its width into different vertical strips and in the second phase, each of these strips is processed to obtain the final pieces. We propose two different algorithms based on GRASP methodology. One is “piece-oriented” while the other is “strip-oriented.” Both procedures are fast and provide solutions of different structures to this cutting problem. We also propose a path-relinking algorithm, which operates on a set of elite soluti…
α-stable distributions for better performance of ACO in detecting damage on not well spaced frequency systems
2014
Abstract In this paper, the Ant Colony Optimization (ACO) algorithm is modified through α -stable Levy variables and applied to the identification of incipient damage in structural components. The main feature of the proposed optimization is an improved ability, which derives from the heavy tails of the stable random variable, to escape from local minima. This aspect is relevant since the objective function used for damage detection may have many local minima which render very challenging the search of the global minimum corresponding to the damage parameter. As the optimization is performed on the structural response and does not require the extraction of modal components, the method is pa…
SMAA - Stochastic multiobjective acceptability analysis
1998
Stochastic multiobjective acceptability analysis (SMAA) is a multicriteria decision support technique for multiple decision makers based on exploring the weight space. Inaccurate or uncertain input data can be represented as probability distributions. In SMAA the decision makers need not express their preferences explicitly or implicitly; instead the technique analyses what kind of valuations would make each alternative the preferred one. The method produces for each alternative an acceptability index measuring the variety of different valuations that support that alternative, a central weight vector representing the typical valuations resulting in that decision, and a confidence factor mea…
Incorporating preference information in interactive reference point methods for multiobjective optimization
2009
In this paper, we introduce new ways of utilizing preference information specified by the decision maker in interactive reference point based methods. A reference point consists of desirable values for each objective function. The idea is to take the desires of the decision maker into account more closely when projecting the reference point onto the set of nondominated solutions. In this way we can support the decision maker in finding the most satisfactory solutions faster. In practice, we adjust the weights in the achievement scalarizing function that projects the reference point. We identify different cases depending on the amount of additional information available and demonstrate the c…
Prospect theory and stochastic multicriteria acceptability analysis (SMAA)
2009
Abstract We consider problems where multiple decision makers (DMs) want to choose their most preferred alternative from a finite set based on multiple criteria. Several approaches to support DMs in such problems have been suggested. Prospect theory has appealed to researchers through its descriptive power, but rare attempts have been made to apply it to support multicriteria decision making. The basic idea of prospect theory is that alternatives are evaluated by a difference function in terms of gains and losses with respect to a reference point. The function is suggested to be concave for gains and convex for losses and steeper for losses than for gains. Stochastic multicriteria acceptabil…
Fully Polynomial Time Approximation Scheme for the Two-Parallel Capacitated Machines Scheduling Problem Under Unavailability Constraint
2010
Abstract Decision Support Systems (DSS) ensure the computer-based support for the conscientious decision-making in solving problems that require a large amount of information processing and complex scenarios. DSS for Transportation (DSST) are intelligent systems that are used at operational and organizational management levels. Operating a DSST in a public transportation web-based monitoring system is presented in this paper.
A novel Stochastic Discretized Weak Estimator operating in non-stationary environments
2012
The task of designing estimators that are able to track time-varying distributions has found promising applications in many real-life problems. A particularly interesting family of distributions are the binomial/multiomial distributions. Existing approaches resort to sliding windows that track changes by discarding old observations. In this paper, we report a novel estimator referred to as the Stochastic Discretized Weak Estimator (SDWE), that is based on the principles of Learning Automata (LA). In brief, the estimator is able to estimate the parameters of a time varying binomial distribution using finite memory. The estimator tracks changes in the distribution by operating on a controlled…
An operatorial description of desertification
2016
We propose a simple theoretical model for desertification processes based on three actors (soil, seeds, and plants) on a two-dimensional lattice. Each actor is described by a time dependent fermionic operator, and the dynamics is ruled by a self-adjoint Hamilton-like operator. We show that even taking into account only a few parameters, accounting for external actions on the ecosystem or the response to positive feedbacks, the model provides a plausible description of the desertification process, and can be adapted to different ecological landscapes. We first describe the simplified model in one cell. Then, we define the full model on a two-dimensional region, taking into account additional…
Conservative Averaging Method for Solutions of Inverse Problems for Heat Equation
2004
Inverse problems arise in various fields of science, technology and agriculture where from measurements of state of the system or process it is required to determine a certain typesetting of the causal characteristics. It is known that infrigement of the natural causal relationships can entail incorrectness of the mathematical formulation of inverse problem. Therefore the development of efficient methods for solving such problems allow us to simplify experimental research considerably and to increase the accuracy and reliability of the obtained results due to certain complication of algoritms for processing the experemental data. The problem of the determination of the coefficient of therma…
The stacker crane problem and the directed general routing problem
2015
[EN] This article deals with the polyhedral description and the resolution of the directed general routing problem (DGRP) and the stacker crane problem (SCP). The DGRP contains a large number of important arc and node routing problems as special cases, including the SCP. Large families of facet-defining inequalities for the DGRP are described and a branch-and-cut algorithm for these problems is presented. Extensive computational experiments over different sets of DGRP and SCP instances are included.