Mono and multi-objective optimization techniques applied to a large range of industrial test cases using Metamodel assisted Evolutionary Algorithms

2010 ◽  
Author(s):  
Lionel Fourment ◽  
Richard Ducloux ◽  
Stéphane Marie ◽  
Mohsen Ejday ◽  
Dominique Monnereau ◽  
...  
Keyword(s):  
Evolutionary Algorithms ◽  
Large Range ◽  
Industrial Test ◽  
Optimization Techniques ◽  
Test Cases ◽  
Multi Objective Optimization ◽  
Multi Objective

An Information-Theoretic Entropy Metric for Assessing Multi-Objective Optimization Solution Set Quality

2003 ◽  
Vol 125 (4) ◽  
pp. 655-663 ◽  
Author(s):  
Ali Farhang-Mehr ◽  
Shapour Azarm
Keyword(s):  
Evolutionary Algorithms ◽  
Pareto Frontier ◽  
Optimization Techniques ◽  
Solution Set ◽  
Multi Objective Optimization ◽  
Information Theoretic ◽  
Multi Objective ◽  
Speed Reducer ◽  
Quantitative Basis

An entropy-based metric is presented that can be used for assessing the quality of a solution set as obtained from multi-objective optimization techniques. This metric quantifies the “goodness” of a set of solutions in terms of distribution quality over the Pareto frontier. The metric can be used to compare the performance of different multi-objective optimization techniques. In particular, the metric can be used in analysis of multi-objective evolutionary algorithms, wherein the capabilities of such techniques to produce and maintain diversity among different solution points are desired to be compared on a quantitative basis. An engineering test example, the multi-objective design optimization of a speed-reducer, is provided to demonstrate an application of the proposed entropy metric.

Multi-Objective Optimization Evolutionary Algorithms in Insurance-Linked Derivatives

2007 ◽  
pp. 885-908 ◽  
Author(s):  
M. J. Perez
Keyword(s):  
Evolutionary Algorithms ◽  
Optimization Procedure ◽  
Real Data ◽  
Optimization Techniques ◽  
Insurance Companies ◽  
Claim Amount ◽  
Loss Ratio ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Catastrophic Loss

This work addresses a real-world adjustment of economic models where the application of robust and global optimization techniques is required. The problem dealt with is the search for a set of parameters to calculate the reported claim amount. Several functions are proposed to obtain the reported claim amount, and a multi-objective optimization procedure is used to obtain parameters using real data and to decide the best function to approximate the reported claim amount. Using this function, insurance companies negotiate the underlying contract—that is, the catastrophic loss ratio defined from the total reported claim amount. They are associated with catastrophes that occurred during the loss period and declared until the development period expired. The suitability of different techniques coming from evolutionary computation (EC) to solve this problem is explored, contrasting the performance achieved with recent proposals of multi-objective evolutionary algorithms (MOEAs). Results show the advantages of MOEAs in the proposal in terms of effectiveness and completeness in searching for solutions, compared with particular solutions of classical EC approaches (using an aggregation operator) in problems with real data.

Efficient Computation of Probabilistic Dominance in Multi-objective Optimization

2021 ◽  
Vol 1 (4) ◽  
pp. 1-26
Author(s):  
Faramarz Khosravi ◽  
Alexander Rass ◽  
Jürgen Teich
Keyword(s):  
Optimization Problems ◽  
Statistical Tests ◽  
Optimization Techniques ◽  
Simultaneous Optimization ◽  
Sampled Data ◽  
Efficient Computation ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Conflicting Objectives ◽  
Comparison Operator

Real-world problems typically require the simultaneous optimization of multiple, often conflicting objectives. Many of these multi-objective optimization problems are characterized by wide ranges of uncertainties in their decision variables or objective functions. To cope with such uncertainties, stochastic and robust optimization techniques are widely studied aiming to distinguish candidate solutions with uncertain objectives specified by confidence intervals, probability distributions, sampled data, or uncertainty sets. In this scope, this article first introduces a novel empirical approach for the comparison of candidate solutions with uncertain objectives that can follow arbitrary distributions. The comparison is performed through accurate and efficient calculations of the probability that one solution dominates the other in terms of each uncertain objective. Second, such an operator can be flexibly used and combined with many existing multi-objective optimization frameworks and techniques by just substituting their standard comparison operator, thus easily enabling the Pareto front optimization of problems with multiple uncertain objectives. Third, a new benchmark for evaluating uncertainty-aware optimization techniques is introduced by incorporating different types of uncertainties into a well-known benchmark for multi-objective optimization problems. Fourth, the new comparison operator and benchmark suite are integrated into an existing multi-objective optimization framework that features a selection of multi-objective optimization problems and algorithms. Fifth, the efficiency in terms of performance and execution time of the proposed comparison operator is evaluated on the introduced uncertainty benchmark. Finally, statistical tests are applied giving evidence of the superiority of the new comparison operator in terms of \epsilon -dominance and attainment surfaces in comparison to previously proposed approaches.

scholarly journals Evolutionary Algorithms for Constrained Parameter Optimization Problems

1996 ◽  
Vol 4 (1) ◽  
pp. 1-32 ◽  
Author(s):  
Zbigniew Michalewicz ◽  
Marc Schoenauer
Keyword(s):  
Nonlinear Programming ◽  
Evolutionary Algorithms ◽  
Evolutionary Computation ◽  
Numerical Optimization ◽  
Optimization Problems ◽  
Optimization Techniques ◽  
Test Cases ◽  
Nonlinear Constraints ◽  
Nonlinear Programming Problem ◽  
General Nonlinear Programming

Evolutionary computation techniques have received a great deal of attention regarding their potential as optimization techniques for complex numerical functions. However, they have not produced a significant breakthrough in the area of nonlinear programming due to the fact that they have not addressed the issue of constraints in a systematic way. Only recently have several methods been proposed for handling nonlinear constraints by evolutionary algorithms for numerical optimization problems; however, these methods have several drawbacks, and the experimental results on many test cases have been disappointing. In this paper we (1) discuss difficulties connected with solving the general nonlinear programming problem; (2) survey several approaches that have emerged in the evolutionary computation community; and (3) provide a set of 11 interesting test cases that may serve as a handy reference for future methods.

scholarly journals The dilemma between eliminating dominance-resistant solutions and preserving boundary solutions of extremely convex Pareto fronts

2021 ◽  
Author(s):  
Zhenkun Wang ◽  
Qingyan Li ◽  
Qite Yang ◽  
Hisao Ishibuchi
Keyword(s):  
Evolutionary Algorithms ◽  
Coping Strategies ◽  
Test Problem ◽  
Pareto Front ◽  
Optimization Problems ◽  
Feasible Region ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Pareto Fronts ◽  
Boundary Solutions

AbstractIt has been acknowledged that dominance-resistant solutions (DRSs) extensively exist in the feasible region of multi-objective optimization problems. Recent studies show that DRSs can cause serious performance degradation of many multi-objective evolutionary algorithms (MOEAs). Thereafter, various strategies (e.g., the $$\epsilon $$ ϵ -dominance and the modified objective calculation) to eliminate DRSs have been proposed. However, these strategies may in turn cause algorithm inefficiency in other aspects. We argue that these coping strategies prevent the algorithm from obtaining some boundary solutions of an extremely convex Pareto front (ECPF). That is, there is a dilemma between eliminating DRSs and preserving boundary solutions of the ECPF. To illustrate such a dilemma, we propose a new multi-objective optimization test problem with the ECPF as well as DRSs. Using this test problem, we investigate the performance of six representative MOEAs in terms of boundary solutions preservation and DRS elimination. The results reveal that it is quite challenging to distinguish between DRSs and boundary solutions of the ECPF.

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