Algorithm for Generating the Pareto Optimal Set of Multiobjective Nonlinear Mixed-Integer Optimization Problems

2007 ◽  
Author(s):  
Kristo Mela ◽  
Juhani Koski ◽  
Risto Silvennoinen
Keyword(s):  
Optimization Problems ◽  
Mixed Integer ◽  
Pareto Optimal ◽  
Integer Optimization ◽  
Mixed Integer Optimization ◽  
Pareto Optimal Set ◽  
Optimal Set

scholarly journals About stability of mixed integer optimization problems under perturbations of input data of vector criterion

2021 ◽  
pp. 7-11
Author(s):  
Tetiana Lebedeva ◽  
Natalia Semenova ◽  
Tetiana Sergienko
Keyword(s):  
Initial Data ◽  
Input Data ◽  
Optimization Problems ◽  
Point Of View ◽  
Mixed Integer ◽  
Stability Of Solutions ◽  
Integer Optimization ◽  
Mixed Integer Optimization ◽  
Small Perturbations ◽  
Vector Criterion

The article is devoted to the study of the influence of uncertainty in initial data on the solutions of mixed integer optimization vector problems. In the optimization problems, including problems with vector criterion, small perturbations in initial data can result in solutions strongly different from the true ones. The problem of stability of the indicated tasks is studied from the point of view of direct coupled with her question in relation to stability of solutions belonging to some subsets of feasible set.

Introduction

1995 ◽  
Author(s):  
Christodoulos A. Floudas
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Optimization Problems ◽  
Batch Process ◽  
Mixed Integer ◽  
Optimization Models ◽  
Integer Optimization ◽  
Mixed Integer Optimization ◽  
Location Allocation ◽  
Primary Focus

This chapter introduces the reader to elementary concepts of modeling, generic formulations for nonlinear and mixed integer optimization models, and provides some illustrative applications. Section 1.1 presents the definition and key elements of mathematical models and discusses the characteristics of optimization models. Section 1.2 outlines the mathematical structure of nonlinear and mixed integer optimization problems which represent the primary focus in this book. Section 1.3 illustrates applications of nonlinear and mixed integer optimization that arise in chemical process design of separation systems, batch process operations, and facility location/allocation problems of operations research. Finally, section 1.4 provides an outline of the three main parts of this book. A plethora of applications in all areas of science and engineering employ mathematical models. A mathematical model of a system is a set of mathematical relationships (e.g., equalities, inequalities, logical conditions) which represent an abstraction of the real world system under consideration. Mathematical models can be developed using (i) fundamental approaches, (ii) empirical methods, and (iii) methods based on analogy. In (i), accepted theories of sciences are used to derive the equations (e.g., Newton’s Law). In (ii), input-output data are employed in tandem with statistical analysis principles so as to generate empirical or “black box” models. In (iii), analogy is employed in determining the essential features of the system of interest by studying a similar, well understood system. The variables can take different values and their specifications define different states of the system. They can be continuous, integer, or a mixed set of continuous and integer. The parameters are fixed to one or multiple specific values, and each fixation defines a different model. The constants are fixed quantities by the model statement. The mathematical model relations can be classified as equalities, inequalities, and logical conditions. The model equalities are usually composed of mass balances, energy balances, equilibrium relations, physical property calculations, and engineering design relations which describe the physical phenomena of the system. The model inequalities often consist of allowable operating regimes, specifications on qualities, feasibility of heat and mass transfer, performance requirements, and bounds on availabilities and demands. The logical conditions provide the connection between the continuous and integer variables.

A feasible rounding approach for mixed-integer optimization problems

2018 ◽  
Vol 72 (2) ◽  
pp. 309-337 ◽  
Author(s):  
Christoph Neumann ◽  
Oliver Stein ◽  
Nathan Sudermann-Merx
Keyword(s):  
Optimization Problems ◽  
Mixed Integer ◽  
Integer Optimization ◽  
Mixed Integer Optimization

An Evolutionary Lagrange Method for Mechanical Design

2010 ◽  
Vol 44-47 ◽  
pp. 1817-1822
Author(s):  
Yung Chin Lin ◽  
Yung Chien Lin ◽  
Kun Song Huang ◽  
Kuo Lan Su
Keyword(s):  
Design Problem ◽  
Optimization Problems ◽  
Mechanical Design ◽  
Inequality Constraints ◽  
Mixed Integer ◽  
Integer Optimization ◽  
Mixed Integer Optimization ◽  
Constrained Optimization Problems ◽  
Lagrange Method ◽  
Mechanical Design Problem

A novel application to mechanical optimal design is presented in this paper. Here, an evolutionary algorithm, called mixed-integer differential evolution (MIHDE), is used to solve general mixed-integer optimization problems. However, most of real-world mixed-integer optimization problems frequently consist of equality and/or inequality constraints. In order to effectively handle constraints, an evolutionary Lagrange method based on MIHDE is implemented to solve the mixed-integer constrained optimization problems. Finally, the evolutionary Lagrange method is applied to a mechanical design problem. The satisfactory results are achieved, and demonstrate that the evolutionary Lagrange method can effectively solve the optimal mechanical design problem.

scholarly journals Stability by the vector criterion of a mixed integer optimization problem with quadratic criterial fun ctions

2020 ◽  
pp. 15-21
Author(s):  
Т.Т. Lebedeva ◽  
◽  
N.V. Semenova ◽  
T.I. Sergienko ◽  
◽  
...  
Keyword(s):  
Initial Data ◽  
Optimization Problem ◽  
Sufficient Conditions ◽  
Mixed Integer ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Integer Optimization ◽  
Mixed Integer Optimization ◽  
Vector Criterion

The article is devoted to the study of qualitative characteristics of different concepts of stability of vector problems of mixed-integer optimization, namely, to identifying the conditions under which the set of Pareto-optimal solutions of the problem possesses some property of invariance defined in advance in relation to the external influences on initial data of the problem. We investigate the questions of stability with respect to data perturbations in a vector criterion of mixed-integer optimization problem. The necessary and sufficient conditions of stability of three types for a problem of finding the solutions of the Pareto set are found. Such conditions guarantee that the small variations of initial data of vector criterion: 1) do not result in new Paretooptimal solutions, 2) save all Pareto-optimal solutions of the problem and can admit new solutions, 3) do not change the set of Pareto-optimal solutions of the initial problem.

scholarly journals Determining a Robust, Pareto Optimal Geometry for a Welded Joint

2014 ◽  
Vol 1016 ◽  
pp. 39-43
Author(s):  
Simon Barrans ◽  
H.E. Radhi
Keyword(s):  
Welded Joint ◽  
Optimization Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Optimal Geometry ◽  
Pareto Optimal Set ◽  
Particular Solution ◽  
Optimal Set ◽  
Selection Of

Multi-criteria optimization problems are known to give rise to a set of Pareto optimal solutions where one solution cannot be regarded as being superior to another. It is often stated that the selection of a particular solution from this set should be based on additional criteria. In this paper a methodology has been proposed that allows a robust design to be selected from the Pareto optimal set. This methodology has been used to determine a robust geometry for a welded joint. It has been shown that the robust geometry is dependent on the variability of the geometric parameters.

Sign in / Sign up

Export Citation Format

Share Document