Optimizing Objective Functions with Non-Linearly Correlated Variables Using Evolution Strategies with Kernel-Based Dimensionality Reduction

2014 ◽  
pp. 342-353
Author(s):  
Piotr Lipinski
Keyword(s):  
Dimensionality Reduction ◽  
Evolution Strategies ◽  
Objective Functions ◽  
Correlated Variables

scholarly journals A Comparison of Ensemble and Dimensionality Reduction DEA Models Based on Entropy Criterion

Algorithms ◽  
2020 ◽  
Vol 13 (9) ◽  
pp. 232
Author(s):  
Parag C. Pendharkar
Keyword(s):  
Dimensionality Reduction ◽  
Returns To Scale ◽  
Data Envelopment ◽  
Objective Functions ◽  
High Entropy ◽  
Selection Of Variables ◽  
Dea Models ◽  
Entropy Criterion ◽  
Selection Of ◽  
Normally Distributed

Dimensionality reduction research in data envelopment analysis (DEA) has focused on subjective approaches to reduce dimensionality. Such approaches are less useful or attractive in practice because a subjective selection of variables introduces bias. A competing unbiased approach would be to use ensemble DEA scores. This paper illustrates that in addition to unbiased evaluations, the ensemble DEA scores result in unique rankings that have high entropy. Under restrictive assumptions, it is also shown that the ensemble DEA scores are normally distributed. Ensemble models do not require any new modifications to existing DEA objective functions or constraints, and when ensemble scores are normally distributed, returns-to-scale hypothesis testing can be carried out using traditional parametric statistical techniques.

scholarly journals A Visualization Technique for Accessing Solution Pool in Interactive Methods of Multiobjective Optimization

2015 ◽  
Vol 10 (4) ◽  
pp. 508 ◽  
Author(s):  
Ernestas Filatovas ◽  
Dmitry Podkopaev ◽  
Olga Kurasova
Keyword(s):  
Multiobjective Optimization ◽  
Dimensionality Reduction ◽  
Decision Maker ◽  
Optimization Problem ◽  
Interactive Methods ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Visualization Technique ◽  
Preference Information ◽  
Optimal Set

<pre>Interactive methods of <span>multiobjective</span> optimization repetitively derive <span>Pareto</span> optimal solutions based on decision maker's preference information and present the obtained solutions for his/her consideration. Some interactive methods save the obtained solutions into a solution pool and, at each iteration, allow the decision maker considering any of solutions obtained earlier. This feature contributes to the flexibility of exploring the <span>Pareto</span> optimal set and learning about the optimization problem. However, in the case of many objective functions, the accumulation of derived solutions makes accessing the solution pool cognitively difficult for the decision maker. We propose to enhance interactive methods with visualization of the set of solution outcomes using dimensionality reduction and interactive mechanisms for exploration of the solution pool. We describe a proposed visualization technique and demonstrate its usage with an example problem solved using the interactive method NIMBUS.</pre>

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.

scholarly journals Regularized Embedded Multiple Kernel Dimensionality Reduction for Mine Signal Processing

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Shuang Li ◽  
Bing Liu ◽  
Chen Zhang
Keyword(s):  
Dimensionality Reduction ◽  
Convex Relaxation ◽  
Multiple Kernel Learning ◽  
Graph Embedding ◽  
Negative Influence ◽  
Objective Functions ◽  
Optimization Scheme ◽  
Multiple Kernel ◽  
Ill Posed ◽  
Dimensionality Reduction Method

Traditional multiple kernel dimensionality reduction models are generally based on graph embedding and manifold assumption. But such assumption might be invalid for some high-dimensional or sparse data due to the curse of dimensionality, which has a negative influence on the performance of multiple kernel learning. In addition, some models might be ill-posed if the rank of matrices in their objective functions was not high enough. To address these issues, we extend the traditional graph embedding framework and propose a novel regularized embedded multiple kernel dimensionality reduction method. Different from the conventional convex relaxation technique, the proposed algorithm directly takes advantage of a binary search and an alternative optimization scheme to obtain optimal solutions efficiently. The experimental results demonstrate the effectiveness of the proposed method for supervised, unsupervised, and semisupervised scenarios.

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
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