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.

scholarly journals ABOUT FEATURES OF MUTATION APPLICATION IN A MODIFIED OPERATOR GENETIC ALGORITHM

2020 ◽  
Author(s):  
Leonid Oliinyk ◽  
Stanislav Bazhan
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Optimization Problems ◽  
Fitness Function ◽  
Stochastic Matrices ◽  
Global Extremum ◽  
Modified Genetic Algorithm ◽  
Wide Range ◽  
Search Field ◽  
The Impact

Genetic algorithm is a method of optimization based on the concepts of natural selection and genetics. Genetic algorithms are used in software development, in artificial intelligence systems, a wide range of optimization problems and in other fields of knowledge.One of the important issues in the theory of genetic algorithms and their modified versions is the search for the best balance between performance and accuracy. The most difficult in this sense are problems where the fitness function in the search field has many local extremes and one global or several global extremes that coincide.The effectiveness of the genetic algorithm depends on various factors, such as the successful creation of the primary population. Also in the theory of genetic algorithms, recombination methods play an important role to obtain a better population of offspring. The aim of this work is to study some types of mutations using a modified genetic algorithm to find the minimum function of one variable.The article presents the results of research and analysis of the impact of some mutation procedures. Namely, the effect of mutation on the speed of achieving the solution of the problem of finding the global extremum of a function of one variable. For which a modified genetic algorithm is used, where the operators of the "generalized crossover" are stochastic matrices

scholarly journals Solution of Mixed-Integer Optimization Problems in Bioinformatics with Differential Evolution Method

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3329
Author(s):  
Sergey Salihov ◽  
Dmitriy Maltsov ◽  
Maria Samsonova ◽  
Konstantin Kozlov
Keyword(s):  
Differential Evolution ◽  
Genomic Selection ◽  
Optimization Problems ◽  
Snp Markers ◽  
Selection Model ◽  
Mixed Integer ◽  
Integer Optimization ◽  
Mixed Integer Optimization ◽  
Wide Range ◽  
Genomic Selection Model

The solution of the so-called mixed-integer optimization problem is an important challenge for modern life sciences. A wide range of methods has been developed for its solution, including metaheuristics approaches. Here, a modification is proposed of the differential evolution entirely parallel (DEEP) method introduced recently that was successfully applied to mixed-integer optimization problems. The triangulation recombination rule was implemented and the recombination coefficients were included in the evolution process in order to increase the robustness of the optimization. The deduplication step included in the procedure ensures the uniqueness of individual integer-valued parameters in the solution vectors. The developed algorithms were implemented in the DEEP software package and applied to three bioinformatic problems. The application of the method to the optimization of predictors set in the genomic selection model in wheat resulted in dimensionality reduction such that the phenotype can be predicted with acceptable accuracy using a selected subset of SNP markers. The method was also successfully used to optimize the training set of samples for such a genomic selection model. According to the obtained results, the developed algorithm was capable of constructing a non-linear phenomenological regression model of gene expression in developing a Drosophila eye with almost the same average accuracy but significantly less standard deviation than the linear models obtained earlier.

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.

scholarly journals Optimizing schools’ start time and bus routes

2019 ◽  
Vol 116 (13) ◽  
pp. 5943-5948 ◽  
Author(s):  
Dimitris Bertsimas ◽  
Arthur Delarue ◽  
Sebastien Martin
Keyword(s):  
School Districts ◽  
Quadratic Assignment Problem ◽  
Transportation Costs ◽  
Mixed Integer ◽  
Quadratic Assignment ◽  
Integer Optimization ◽  
Start Time ◽  
Routing Problem ◽  
Health Crisis ◽  
The Impact

Maintaining a fleet of buses to transport students to school is a major expense for school districts. To reduce costs by reusing buses between schools, many districts spread start times across the morning. However, assigning each school a time involves estimating the impact on transportation costs and reconciling additional competing objectives. Facing this intricate optimization problem, school districts must resort to ad hoc approaches, which can be expensive, inequitable, and even detrimental to student health. For example, there is medical evidence that early high school starts are impacting the development of an entire generation of students and constitute a major public health crisis. We present an optimization model for the school time selection problem (STSP), which relies on a school bus routing algorithm that we call biobjective routing decomposition (BiRD). BiRD leverages a natural decomposition of the routing problem, computing and combining subproblem solutions via mixed integer optimization. It significantly outperforms state-of-the-art routing methods, and its implementation in Boston has led to $5 million in yearly savings, maintaining service quality for students despite a 50-bus fleet reduction. Using BiRD, we construct a tractable proxy to transportation costs, allowing the formulation of the STSP as a multiobjective generalized quadratic assignment problem. Local search methods provide high-quality solutions, allowing school districts to explore tradeoffs between competing priorities and choose times that best fulfill community needs. In December 2017, the development of this method led the Boston School Committee to unanimously approve the first school start time reform in 30 years.

Using genetic algorithms to evolve type-2 fuzzy logic systems for predicting bankruptcy

Kybernetes ◽  
2017 ◽  
Vol 46 (1) ◽  
pp. 142-156 ◽  
Author(s):  
Vasile Georgescu
Keyword(s):  
Genetic Algorithms ◽  
Fuzzy Logic ◽  
Degrees Of Freedom ◽  
Bankruptcy Prediction ◽  
Mixed Integer ◽  
Integer Optimization ◽  
Generalization Capability ◽  
Content Type ◽  
Chromosome Representation

Purpose Type-2 fuzzy sets became attractive in practice because of their footprint of uncertainty that gives them more degrees of freedom. This paper aims to use genetic algorithms (GAs) to design an interval Type-2 fuzzy logic system (IT2FLS) for the purpose of predicting bankruptcy. Design/methodology/approach The shape of type-2 membership functions, the parameters giving their spread and location in the fuzzy partitions and the set of fuzzy rules are evolved at the same time by encoding all together into the chromosome representation. The enhanced Karnik–Mendel algorithms are used for the centroid type-reduction and defuzzification stage. The performance in predicting bankruptcy is evaluated by benchmarking IT2FLSs against type-1 FLSs. The experimental setup consists of evolving 100 configurations for both the T1FLS and IT2FLS and comparing their in-sample and out-of-sample average accuracy. Findings The experiments confirm that representing and capturing uncertainty with more degrees of freedom is an important advantage. It is this extra potential of IT2FLSs that allows them to outperform T1FLS, especially in terms of generalization capability. Originality/value The strategy followed in this paper is to train an IT2FLS from scratch rather than tuning the parameters of an existing T1FLS. Because this leads to solving a mixed integer optimization problem, the GA-based approach is specifically designed and uses genetic operators that are most suited for such a case: tournament selection, extended Laplace crossover and power mutation. Finally, the trained IT2FLS is applied to bankruptcy prediction, and its generalization capability is compared with related techniques.

A Mixed-Integer Memetic Algorithm Applied to Batch Process Optimization

2013 ◽  
Vol 300-301 ◽  
pp. 645-648 ◽  
Author(s):  
Yung Chien Lin
Keyword(s):  
Memetic Algorithm ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Search Space ◽  
Memetic Algorithms ◽  
Batch Processes ◽  
Mixed Integer ◽  
Integer Optimization ◽  
Genetic Operators ◽  
Search Methods

Evolutionary algorithms (EAs) are population-based global search methods. Memetic Algorithms (MAs) are hybrid EAs that combine genetic operators with local search methods. With global exploration and local exploitation in search space, MAs are capable of obtaining more high-quality solutions. On the other hand, mixed-integer hybrid differential evolution (MIHDE), as an EA-based search algorithm, has been successfully applied to many mixed-integer optimization problems. In this paper, a mixed-integer memetic algorithm based on MIHDE is developed for solving mixed-integer constrained optimization problems. The proposed algorithm is implemented and applied to the optimal design of batch processes. Experimental results show that the proposed algorithm can find a better optimal solution compared with some other search algorithms.

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