GENETIC ALGORITHMS FOR NONLINEAR MIXED DISCRETE-INTEGER OPTIMIZATION PROBLEMS VIA META-GENETIC PARAMETER OPTIMIZATION

1995 ◽  
Vol 24 (2) ◽  
pp. 137-159 ◽  
Author(s):  
SHYUE-JIAN WU ◽  
PEI-TSE CHOW
Keyword(s):  
Genetic Algorithms ◽  
Parameter Optimization ◽  
Optimization Problems ◽  
Genetic Parameter ◽  
Integer Optimization

Evolutionary Algorithms in Theory and Practice

1996 ◽  
Author(s):  
Thomas Bäck
Keyword(s):  
Genetic Algorithms ◽  
Evolutionary Algorithms ◽  
Optimization Problems ◽  
Theory And Practice ◽  
Evolution Strategies ◽  
Parallel Computer ◽  
Mixed Integer ◽  
Integer Optimization ◽  
Wide Range ◽  
The Impact

This book presents a unified view of evolutionary algorithms: the exciting new probabilistic search tools inspired by biological models that have immense potential as practical problem-solvers in a wide variety of settings, academic, commercial, and industrial. In this work, the author compares the three most prominent representatives of evolutionary algorithms: genetic algorithms, evolution strategies, and evolutionary programming. The algorithms are presented within a unified framework, thereby clarifying the similarities and differences of these methods. The author also presents new results regarding the role of mutation and selection in genetic algorithms, showing how mutation seems to be much more important for the performance of genetic algorithms than usually assumed. The interaction of selection and mutation, and the impact of the binary code are further topics of interest. Some of the theoretical results are also confirmed by performing an experiment in meta-evolution on a parallel computer. The meta-algorithm used in this experiment combines components from evolution strategies and genetic algorithms to yield a hybrid capable of handling mixed integer optimization problems. As a detailed description of the algorithms, with practical guidelines for usage and implementation, this work will interest a wide range of researchers in computer science and engineering disciplines, as well as graduate students in these fields.

Mixed Integer Evolution Strategies for Parameter Optimization

2013 ◽  
Vol 21 (1) ◽  
pp. 29-64 ◽  
Author(s):  
Rui Li ◽  
Michael T.M. Emmerich ◽  
Jeroen Eggermont ◽  
Thomas Bäck ◽  
M. Schütz ◽  
...  
Keyword(s):  
Parameter Optimization ◽  
Optimization Problems ◽  
Medical Image Analysis ◽  
Evolution Strategies ◽  
Mixed Integer ◽  
Maximal Entropy ◽  
Integer Optimization ◽  
Mutation Operators ◽  
Wide Range ◽  
Self Adaptation

Evolution strategies (ESs) are powerful probabilistic search and optimization algorithms gleaned from biological evolution theory. They have been successfully applied to a wide range of real world applications. The modern ESs are mainly designed for solving continuous parameter optimization problems. Their ability to adapt the parameters of the multivariate normal distribution used for mutation during the optimization run makes them well suited for this domain. In this article we describe and study mixed integer evolution strategies (MIES), which are natural extensions of ES for mixed integer optimization problems. MIES can deal with parameter vectors consisting not only of continuous variables but also with nominal discrete and integer variables. Following the design principles of the canonical evolution strategies, they use specialized mutation operators tailored for the aforementioned mixed parameter classes. For each type of variable, the choice of mutation operators is governed by a natural metric for this variable type, maximal entropy, and symmetry considerations. All distributions used for mutation can be controlled in their shape by means of scaling parameters, allowing self-adaptation to be implemented. After introducing and motivating the conceptual design of the MIES, we study the optimality of the self-adaptation of step sizes and mutation rates on a generalized (weighted) sphere model. Moreover, we prove global convergence of the MIES on a very general class of problems. The remainder of the article is devoted to performance studies on artificial landscapes (barrier functions and mixed integer NK landscapes), and a case study in the optimization of medical image analysis systems. In addition, we show that with proper constraint handling techniques, MIES can also be applied to classical mixed integer nonlinear programming problems.

Solving marketing optimization problems using genetic algorithms

1995 ◽  
Vol 29 (4) ◽  
pp. 39-56 ◽  
Author(s):  
S. Hurley ◽  
L. Moutinho ◽  
N.M. Stephens
Keyword(s):  
Genetic Algorithms ◽  
Optimization Problems

Implementation of Eurocode Load Cases in Optimization Problems of Steel Frames, Based on Genetic Algorithms

2013 ◽  
Vol 310 ◽  
pp. 609-613
Author(s):  
Ioana D. Balea ◽  
Radu Hulea ◽  
Georgios E. Stavroulakis
Keyword(s):  
Finite Element ◽  
Genetic Algorithms ◽  
Global Optimization ◽  
Optimal Design ◽  
Optimization Problems ◽  
Steel Frames ◽  
Global Optimization Algorithm ◽  
Planar Structures ◽  
Discrete Global Optimization ◽  
Steel Sections

This paper presents an implementation of Eurocode load cases for discrete global optimization algorithm for planar structures based on the principles of finite element methods and genetic algorithms. The final optimal design is obtained using IPE sections chosen as feasible by the algorithm, from the available steel sections from industry. The algorithm is tested on an asymmetric planar steel frame with promising results.

scholarly journals Partially distributed outer approximation

2021 ◽  
Author(s):  
Alexander Murray ◽  
Timm Faulwasser ◽  
Veit Hagenmeyer ◽  
Mario E. Villanueva ◽  
Boris Houska
Keyword(s):  
Large Scale ◽  
Optimization Problems ◽  
Outer Approximation ◽  
Mixed Integer ◽  
Global Optimality ◽  
Integer Optimization ◽  
Global Minimizers ◽  
Outer Approximation Method ◽  
Coupling Constraints ◽  
Outer Approximation Algorithm

AbstractThis paper presents a novel partially distributed outer approximation algorithm, named PaDOA, for solving a class of structured mixed integer convex programming problems to global optimality. The proposed scheme uses an iterative outer approximation method for coupled mixed integer optimization problems with separable convex objective functions, affine coupling constraints, and compact domain. PaDOA proceeds by alternating between solving large-scale structured mixed-integer linear programming problems and partially decoupled mixed-integer nonlinear programming subproblems that comprise much fewer integer variables. We establish conditions under which PaDOA converges to global minimizers after a finite number of iterations and verify these properties with an application to thermostatically controlled loads and to mixed-integer regression.

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