scholarly journals New Reference-Neighbourhood Scalarization Problem for Multiobjective Integer Programming

2013 ◽  
Vol 13 (1) ◽  
pp. 104-114 ◽  
Author(s):  
Krasimira Genova ◽  
Leonid Kirilov ◽  
Vasil Guljashki
Keyword(s):  
Integer Programming ◽  
Decision Maker ◽  
Multicriteria Optimization ◽  
Efficient Solutions ◽  
Optimal Solutions ◽  
Additional Information ◽  
Multicriteria Problems ◽  
Computing Complexity

Abstract Scalarization is a frequently used approach for finding efficient solutions that satisfy the preferences of the Decision Maker (DM) in multicriteria optimization. The applicability of a scalarization problem to solve integer multicriteria problems depends on the possibilities it provides for the decrease of the computing complexity in finding optimal solutions of this class of problems. This paper presents a reference-neighbourhood scalarizing problem, possessing properties that make it particularly suitable for solving integer problems. One of the aims set in this development has also been the faster obtaining of desired criteria values, defined by the DM, requiring no additional information by him/her. An illustrative example demonstrates the features of this scalarizing problem.

A DECOMPOSITION-COORDINATION METHOD FOR COMPLEX MULTI-OBJECTIVE SYSTEMS

2009 ◽  
Vol 26 (06) ◽  
pp. 735-757 ◽  
Author(s):  
F. MIGUEL ◽  
T. GÓMEZ ◽  
M. LUQUE ◽  
F. RUIZ ◽  
R. CABALLERO
Keyword(s):  
Information Exchange ◽  
Exchange Process ◽  
Efficient Solutions ◽  
Pareto Optimal ◽  
Relative Importance ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Conflicting Objectives ◽  
Upper Level ◽  
Problem Instances

The generation of Pareto optimal solutions for complex systems with multiple conflicting objectives can be easier if the problem can be decomposed and solved as a set of smaller coordinated subproblems. In this paper, a new decomposition-coordination method is proposed, where the global problem is partitioned into subsystems on the basis of the connection structure of the mathematical model, assigning a relative importance to each of them. In order to obtain Pareto optimal solutions for the global system, the aforementioned subproblems are coordinated taking into account their relative importance. The scheme that has been developed is an iterative one, and the global efficient solutions are found through a continuous information exchange process between the coordination level (upper level) and the subsystem level (lower level). Computational experiments on several randomly generated problem instances show that the suggested algorithm produces efficient solutions within reasonable computational times.

TWO BI-OBJECTIVE OPTIMIZATION MODELS FOR COMPETITIVE LOCATION PROBLEMS

2006 ◽  
Vol 05 (03) ◽  
pp. 531-543 ◽  
Author(s):  
FENGMEI YANG ◽  
GUOWEI HUA ◽  
HIROSHI INOUE ◽  
JIANMING SHI
Keyword(s):  
Integer Programming ◽  
Programming Problem ◽  
Efficient Solutions ◽  
Integer Program ◽  
Location Problems ◽  
Optimization Models ◽  
Competitive Location ◽  
Integer Programming Problem ◽  
Single Objective ◽  
Parametric Integer Programming

This paper deals with two bi-objective models arising from competitive location problems. The first model simultaneously intends to maximize market share and to minimize cost. The second one aims to maximize both profit and the profit margin. We study some of the related properties of the models, examine relations between the models and a single objective parametric integer programming problem, and then show how both bi-objective location problems can be solved through the use of a single objective parametric integer program. Based on this, we propose two methods of obtaining a set of efficient solutions to the problems of fundamental approach. Finally, a numerical example is presented to illustrate the solution techniques.

LEXICOGRAPHIC PROBLEMS OF CONVEX OPTIMIZATION: SOLVABILITY AND OPTIMALITY CONDITIONS, CUTTING PLANE METHOD

2021 ◽  
Vol 1 ◽  
pp. 30-40
Author(s):  
Natalia V. Semenova ◽  
◽  
Maria M. Lomaga ◽  
Viktor V. Semenov ◽  
◽  
...  
Keyword(s):  
System Optimization ◽  
Cutting Plane ◽  
Recession Cone ◽  
Cutting Plane Method ◽  
Optimal Solutions ◽  
Feasible Set ◽  
Plane Method ◽  
Multicriteria Problems ◽  
Lexicographic Optimization ◽  
Feasible Solutions

The lexicographic approach for solving multicriteria problems consists in the strict ordering of criteria concerning relative importance and allows to obtain optimization of more important criterion due to any losses of all another, to the criteria of less importance. Hence, a lot of problems including the ones of com­plex system optimization, of stochastic programming under risk, of dynamic character, etc. may be presented in the form of lexicographic problems of opti­mization. We have revealed conditions of existence and optimality of solutions of multicriteria problems of lexicographic optimization with an unbounded convex set of feasible solutions on the basis of applying properties of a recession cone of a convex feasible set, the cone which puts in order lexicographically a feasible set with respect to optimization criteria and local tent built at the boundary points of the feasible set. The properties of lexicographic optimal solutions are described. Received conditions and properties may be successfully used while developing algorithms for finding optimal solutions of mentioned problems of lexicographic optimization. A method of finding lexicographic of optimal solutions of convex lexicographic problems is built and grounded on the basis of ideas of method of linearization and Kelley cutting-plane method.

Optimization Problem

2020 ◽  
pp. 276-291
Author(s):  
Albert N. Voronin
Keyword(s):  
Wide Class ◽  
Multicriteria Optimization ◽  
System Approach ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Systemic Approach ◽  
Multicriteria Decision ◽  
Multicriteria Problems ◽  
Linear Scheme ◽  
Non Linear

A systemic approach to solving multicriteria optimization problems is proposed. The system approach allowed uniting the models of individual schemes of compromises into a single integrated structure that adapts to the situation of adopting a multi-criteria solution. The advantage of the concept of non-linear scheme of compromises is the possibility of making a multicriteria decision formally, without the direct participation of a person. The apparatus of the non-linear scheme of compromises, developed as a formalized tool for the study of control systems with conflicting criteria, makes it possible to solve practically multicriteria problems of a wide class.

scholarly journals A Multiobjective Genetic Algorithm for the Localization of Optimal and Nearly Optimal Solutions Which Are Potentially Useful: nevMOGA

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-22 ◽  
Author(s):  
Alberto Pajares ◽  
Xavier Blasco ◽  
Juan M. Herrero ◽  
Gilberto Reynoso-Meza
Keyword(s):  
Genetic Algorithm ◽  
Decision Making ◽  
Decision Maker ◽  
Pareto Front ◽  
Optimization Problem ◽  
Engineering Problem ◽  
Multiobjective Optimization Problem ◽  
Optimal Solutions ◽  
Multiobjective Genetic Algorithm ◽  
Pi Controllers

Traditionally, in a multiobjective optimization problem, the aim is to find the set of optimal solutions, the Pareto front, which provides the decision-maker with a better understanding of the problem. This results in a more knowledgeable decision. However, multimodal solutions and nearly optimal solutions are ignored, although their consideration may be useful for the decision-maker. In particular, there are some of these solutions which we consider specially interesting, namely, the ones that have distinct characteristics from those which dominate them (i.e., the solutions that are not dominated in their neighborhood). We call these solutions potentially useful solutions. In this work, a new genetic algorithm called nevMOGA is presented, which provides not only the optimal solutions but also the multimodal and nearly optimal solutions nondominated in their neighborhood. This means that nevMOGA is able to supply additional and potentially useful solutions for the decision-making stage. This is its main advantage. In order to assess its performance, nevMOGA is tested on two benchmarks and compared with two other optimization algorithms (random and exhaustive searches). Finally, as an example of application, nevMOGA is used in an engineering problem to optimally adjust the parameters of two PI controllers that operate a plant.

The Optimization of Mechanized Earthwork Processes

2016 ◽  
Vol 820 ◽  
pp. 96-101 ◽  
Author(s):  
Lucia Paulovičová
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Models ◽  
Decision Maker ◽  
Multicriteria Optimization ◽  
Optimization Process ◽  
Multicriteria Method ◽  
Wise Decision ◽  
The Right ◽  
The Cost ◽  
Selection Of

Earthwork processes are the most costly and time consuming component of construction these days and they are characterized by a powerful heavy mechanization which participate on the earthwork process. Current pressure for minimize the cost and maximize the productivity highlights the need to optimize earthworks. In this paper, the optimization process in the area of earthwork processes is described. The selection of the right types of machines for earthwork and its implements has become very difficult these days because of availability of variety of machines models and therefore a multicriteria method is presented to tackle the problem. This paper describes methodology for optimizing the earthwork process according to the selected optimal criteria. The methodology is focused on the proposal phase of optimization where the decision maker has to make a decision and choose the right type of excavators. To overcome the problem of comparing the chosen machines a mathematical modeling approach leading to multicriteria optimization was adopted to make the step wise decision. The methodology gives an mathematical models by which we can solve this problem.

Sign in / Sign up

Export Citation Format

Share Document