Evolution Strategies for Objective Functions with Locally Correlated Variables

2010 ◽  
pp. 352-359 ◽  
Author(s):  
Piotr Lipinski
Keyword(s):  
Evolution Strategies ◽  
Objective Functions ◽  
Correlated Variables

The Effect of Multi-Parent Recombination on Evolution Strategies for Noisy Objective Functions

2011 ◽  
pp. 264-280
Author(s):  
Yoshiyuki Matsumura ◽  
Kazuhiro Ohkura ◽  
Kanji Ueda
Keyword(s):  
Computer Simulations ◽  
Evolution Strategies ◽  
Test Functions ◽  
Objective Functions ◽  
The Many ◽  
Object Parameters ◽  
Strategy Parameters

In this chapter we apply (m / m, l)-ES to noisy test functions, in order to investigate the effect of multi-parent versions of both intermediate recombination and discrete recombination. Among the many formulations of ES, we test three in particular; Classical-ES (CES), i.e., Schwefel’s original ES (Schwefel, 1995, Bäck, 1996); Fast-ES (FES), i.e., Yao and Liu’s extended ES (Yao & Liu, 1997); and Robust-ES (RES), i.e., our extended ES (Ohkura, 2001). Computer simulations are used to compare the performance of multi-parent versions of intermediate recombination and discrete recombination in CES, FES and RES. We saw that the performance of the (m / m, l)-ES algorithms depended on the particular objective functions. However, the FES and RES algorithms were seen to be improved by multi-parent versions of discrete recombination applied to both object parameters and strategy parameters.

Empirical Investigation of Multiparent Recombination Operators in Evolution Strategies

1997 ◽  
Vol 5 (3) ◽  
pp. 347-365 ◽  
Author(s):  
Agoston E. Eiben ◽  
Thomas Bäck
Keyword(s):  
Coordinate System ◽  
Objective Function ◽  
Empirical Investigation ◽  
Variable Number ◽  
Evolution Strategies ◽  
Test Suite ◽  
Objective Functions ◽  
Local Optima ◽  
Irregular Arrangement ◽  
Search Bias

An extension of evolution strategies to multiparent recombination involving a variable number ϱ of parents to create an offspring individual is proposed. The extension is experimentally evaluated on a test suite of functions differing in their modality and separability and the regular/irregular arrangement of their local optima. Multiparent diagonal crossover and uniform scanning crossover and a multiparent version of intermediary recombination are considered in the experiments. The performance of the algorithm is observed to depend on the particular combination of recombination operator and objective function. In most of the cases a significant increase in performance is observed as the number of parents increases. However, there might also be no significant impact of recombination at all, and for one of the unimodal objective functions, the performance is observed to deteriorate over the course of evolution for certain choices of the recombination operator and the number of parents. Additional experiments with a skewed initialization of the population clarify that intermediary recombination does not cause a search bias toward the origin of the coordinate system in the case of domains of variables that are symmetric around zero.

On the Behaviour of Evolution Strategies Optimising Cigar Functions

2010 ◽  
Vol 18 (4) ◽  
pp. 661-682 ◽  
Author(s):  
Dirk V. Arnold ◽  
Hans-Georg Beyer
Keyword(s):  
Stationary State ◽  
Step Length ◽  
Evolution Strategies ◽  
Simplified Model ◽  
Objective Functions ◽  
Multiplicity One

This paper studies the performance of multi-recombinative evolution strategies using isotropically distributed mutations with cumulative step length adaptation when applied to optimising cigar functions. Cigar functions are convex-quadratic objective functions that are characterised by the presence of only two distinct eigenvalues of their Hessian, the smaller one of which occurs with multiplicity one. A simplified model of the strategy's behaviour is developed. Using it, expressions that approximately describe the stationary state that is attained when the mutation strength is adapted are derived. The performance achieved by cumulative step length adaptation is compared with that obtained when using optimally adapted step lengths.

Interactive Evolution Strategies for Minimizing Single-objective Functions

2017 ◽  
Vol 15 (5) ◽  
pp. 981-987 ◽  
Author(s):  
Luiz Henrique Reis Jesus ◽  
Leonardo Cunha Brito
Keyword(s):  
Evolution Strategies ◽  
Objective Functions ◽  
Single Objective

Fuzzy multi-objective decision making approach for nuclear power plant installation

2020 ◽  
Vol 39 (5) ◽  
pp. 6339-6350
Author(s):  
Esra Çakır ◽  
Ziya Ulukan
Keyword(s):  
Linear Programming ◽  
Power Plant ◽  
Nuclear Power Plant ◽  
Energy Supply ◽  
Energy Demand ◽  
Nuclear Power ◽  
Power Plants ◽  
Total Duration ◽  
Objective Functions ◽  
Multi Objective

Due to the increase in energy demand, many countries suffer from energy poverty because of insufficient and expensive energy supply. Plans to use alternative power like nuclear power for electricity generation are being revived among developing countries. Decisions for installation of power plants need to be based on careful assessment of future energy supply and demand, economic and financial implications and requirements for technology transfer. Since the problem involves many vague parameters, a fuzzy model should be an appropriate approach for dealing with this problem. This study develops a Fuzzy Multi-Objective Linear Programming (FMOLP) model for solving the nuclear power plant installation problem in fuzzy environment. FMOLP approach is recommended for cases where the objective functions are imprecise and can only be stated within a certain threshold level. The proposed model attempts to minimize total duration time, total cost and maximize the total crash time of the installation project. By using FMOLP, the weighted additive technique can also be applied in order to transform the model into Fuzzy Multiple Weighted-Objective Linear Programming (FMWOLP) to control the objective values such that all decision makers target on each criterion can be met. The optimum solution with the achievement level for both of the models (FMOLP and FMWOLP) are compared with each other. FMWOLP results in better performance as the overall degree of satisfaction depends on the weight given to the objective functions. A numerical example demonstrates the feasibility of applying the proposed models to nuclear power plant installation problem.

Multi-Objective Design Problem of Tire Wear and Visualization of Its Pareto Solutions2

2006 ◽  
Vol 34 (3) ◽  
pp. 170-194 ◽  
Author(s):  
M. Koishi ◽  
Z. Shida
Keyword(s):  
Inverse Problems ◽  
Conceptual Design ◽  
Dimensional Space ◽  
Design Stage ◽  
Objective Functions ◽  
Pareto Solutions ◽  
Design Problems ◽  
Multi Objective ◽  
Design Engineers ◽  
Design Variables

Abstract Since tires carry out many functions and many of them have tradeoffs, it is important to find the combination of design variables that satisfy well-balanced performance in conceptual design stage. To find a good design of tires is to solve the multi-objective design problems, i.e., inverse problems. However, due to the lack of suitable solution techniques, such problems are converted into a single-objective optimization problem before being solved. Therefore, it is difficult to find the Pareto solutions of multi-objective design problems of tires. Recently, multi-objective evolutionary algorithms have become popular in many fields to find the Pareto solutions. In this paper, we propose a design procedure to solve multi-objective design problems as the comprehensive solver of inverse problems. At first, a multi-objective genetic algorithm (MOGA) is employed to find the Pareto solutions of tire performance, which are in multi-dimensional space of objective functions. Response surface method is also used to evaluate objective functions in the optimization process and can reduce CPU time dramatically. In addition, a self-organizing map (SOM) proposed by Kohonen is used to map Pareto solutions from high-dimensional objective space onto two-dimensional space. Using SOM, design engineers see easily the Pareto solutions of tire performance and can find suitable design plans. The SOM can be considered as an inverse function that defines the relation between Pareto solutions and design variables. To demonstrate the procedure, tire tread design is conducted. The objective of design is to improve uneven wear and wear life for both the front tire and the rear tire of a passenger car. Wear performance is evaluated by finite element analysis (FEA). Response surface is obtained by the design of experiments and FEA. Using both MOGA and SOM, we obtain a map of Pareto solutions. We can find suitable design plans that satisfy well-balanced performance on the map called “multi-performance map.” It helps tire design engineers to make their decision in conceptual design stage.

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