scholarly journals Evolutionary Algorithm for Multiobjective Optimization Based on Density Estimation Ranking

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Lin Li ◽  
Hengfei Wu ◽  
Xiujian Hu ◽  
Guanglei Sheng
Keyword(s):  
Evolutionary Algorithms ◽  
Multiobjective Optimization ◽  
Density Estimation ◽  
Pareto Front ◽  
Selection Criterion ◽  
Pareto Dominance ◽  
Environmental Selection ◽  
Different Shapes ◽  
Pareto Fronts ◽  
Optimal Candidate

In the past few decades, a number of multiobjective evolutionary algorithms (MOEAs) have been proposed in the continue study. As pointed out in some recent studies, the performance of the most existing MOEAs is not promising when solving different shapes of Pareto fronts. To address this issue, this paper proposes an MOEA based on density estimation ranking. The algorithm includes density estimation ranking to shift the reference solution position, calculating the density of candidate solutions and ranking by the estimated density value, to modify the Pareto dominance relation and for handling complicated Pareto front. The result of this ranking can be used as the second selection criterion for environmental selection, and the optimal candidate individual with distribution and diversity information is selected. Experimental results show that the proposed algorithm can solve various types of Pareto fronts, outperformance several state-of-the-art evolutionary algorithms in multiobjective optimization.

Pareto-adaptive ε-dominance

2007 ◽  
Vol 15 (4) ◽  
pp. 493-517 ◽  
Author(s):  
Alfredo G. Hernández-Díaz ◽  
Luis V. Santana-Quintero ◽  
Carlos A. Coello Coello ◽  
Julián Molina
Keyword(s):  
Evolutionary Algorithms ◽  
Multiobjective Optimization ◽  
Pareto Front ◽  
Multiobjective Evolutionary Algorithms ◽  
Pareto Dominance ◽  
Nondominated Solutions ◽  
Evolutionary Multiobjective Optimization ◽  
The Way

Efficiency has become one of the main concerns in evolutionary multiobjective optimization during recent years. One of the possible alternatives to achieve a faster convergence is to use a relaxed form of Pareto dominance that allows us to regulate the granularity of the approximation of the Pareto front that we wish to achieve. One such relaxed forms of Pareto dominance that has become popular in the last few years is ε-dominance, which has been mainly used as an archiving strategy in some multiobjective evolutionary algorithms. Despite its advantages, ε-dominance has some limitations. In this paper, we propose a mechanism that can be seen as a variant of ε-dominance, which we call Pareto-adaptive ε-dominance (paε-dominance). Our proposed approach tries to overcome the main limitation of ε-dominance: the loss of several nondominated solutions from the hypergrid adopted in the archive because of the way in which solutions are selected within each box.

scholarly journals A Mating Selection Based on Modified Strengthened Dominance Relation for NSGA-III

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2837
Author(s):  
Saykat Dutta ◽  
Sri Srinivasa Raju M ◽  
Rammohan Mallipeddi ◽  
Kedar Nath Das ◽  
Dong-Gyu Lee
Keyword(s):  
Pareto Front ◽  
State Of The Art ◽  
Weight Vector ◽  
Dominance Relation ◽  
Additional Parameter ◽  
Pareto Dominance ◽  
Environmental Selection ◽  
Dominance Relationships ◽  
Test Suites ◽  
Selection Of

In multi/many-objective evolutionary algorithms (MOEAs), to alleviate the degraded convergence pressure of Pareto dominance with the increase in the number of objectives, numerous modified dominance relationships were proposed. Recently, the strengthened dominance relation (SDR) has been proposed, where the dominance area of a solution is determined by convergence degree and niche size (θ¯). Later, in controlled SDR (CSDR), θ¯ and an additional parameter (k) associated with the convergence degree are dynamically adjusted depending on the iteration count. Depending on the problem characteristics and the distribution of the current population, different situations require different values of k, rendering the linear reduction of k based on the generation count ineffective. This is because a particular value of k is expected to bias the dominance relationship towards a particular region on the Pareto front (PF). In addition, due to the same reason, using SDR or CSDR in the environmental selection cannot preserve the diversity of solutions required to cover the entire PF. Therefore, we propose an MOEA, referred to as NSGA-III*, where (1) a modified SDR (MSDR)-based mating selection with an adaptive ensemble of parameter k would prioritize parents from specific sections of the PF depending on k, and (2) the traditional weight vector and non-dominated sorting-based environmental selection of NSGA-III would protect the solutions corresponding to the entire PF. The performance of NSGA-III* is favourably compared with state-of-the-art MOEAs on DTLZ and WFG test suites with up to 10 objectives.

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.

scholarly journals What Weights Work for You? Adapting Weights for Any Pareto Front Shape in Decomposition-Based Evolutionary Multiobjective Optimisation

2020 ◽  
Vol 28 (2) ◽  
pp. 227-253 ◽  
Author(s):  
Miqing Li ◽  
Xin Yao
Keyword(s):  
Pareto Front ◽  
Evolutionary Process ◽  
Highly Nonlinear ◽  
Distributed Solutions ◽  
Front Shape ◽  
Different Shapes ◽  
Pareto Fronts ◽  
The Given ◽  
Update Frequency

The quality of solution sets generated by decomposition-based evolutionary multi-objective optimisation (EMO) algorithms depends heavily on the consistency between a given problem's Pareto front shape and the specified weights' distribution. A set of weights distributed uniformly in a simplex often leads to a set of well-distributed solutions on a Pareto front with a simplex-like shape, but may fail on other Pareto front shapes. It is an open problem on how to specify a set of appropriate weights without the information of the problem's Pareto front beforehand. In this article, we propose an approach to adapt weights during the evolutionary process (called AdaW). AdaW progressively seeks a suitable distribution of weights for the given problem by elaborating several key parts in weight adaptation—weight generation, weight addition, weight deletion, and weight update frequency. Experimental results have shown the effectiveness of the proposed approach. AdaW works well for Pareto fronts with very different shapes: 1) the simplex-like, 2) the inverted simplex-like, 3) the highly nonlinear, 4) the disconnect, 5) the degenerate, 6) the scaled, and 7) the high-dimensional.

scholarly journals Hybrid Selection Based Multi/Many-Objective Evolutionary Algorithm

2021 ◽  
Author(s):  
Saykat Dutta ◽  
Rammohan Mallipeddi ◽  
Kedar Nath Das
Keyword(s):  
Pareto Front ◽  
State Of The Art ◽  
Superior Performance ◽  
Selection Strategy ◽  
Convergence Properties ◽  
Pareto Dominance ◽  
Advantages And Disadvantages ◽  
Environmental Selection ◽  
Hybrid Selection ◽  
Test Suites

Abstract In the last decade, numerous Multi/Many-Objective Evolutionary Algorithms (MOEAs) have been proposed to handle Multi/Many-Objective Problems (MOPs) with challenges such as discontinuous Pareto Front (PF), degenerate PF, etc. MOEAs in the literature can be broadly divided into three categories based on the selection strategy employed such as dominance, decomposition, and indicator-based MOEAs. Each category of MOEAs have their advantages and disadvantages when solving MOPs with diverse characteristics. In this work, we propose a Hybrid Selection based MOEA, referred to as HS-MOEA, which is a simple yet effective hybridization of dominance, decomposition and indicator-based concepts. In other words, we propose a new environmental selection strategy where the Pareto-dominance, reference vectors and an indicator are combined to effectively balance the diversity and convergence properties of MOEA during the evolution. The superior performance of HS-MOEA compared to the state-of-the-art MOEAs is demonstrated through experimental simulations on DTLZ and WFG test suites with up to 10 objectives.

A many-objective evolutionary algorithm based on vector angle distance scaling

2021 ◽  
Vol 40 (5) ◽  
pp. 10285-10306
Author(s):  
Xin Li ◽  
Xiaoli Li ◽  
Kang Wang
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Pareto Front ◽  
Optimization Problems ◽  
Adaptive Strategy ◽  
Great Success ◽  
Multi Objective ◽  
Environmental Selection ◽  
Fitness Value ◽  
Vector Angle

In the past two decades, multi-objective evolutionary algorithms (MOEAs) have achieved great success in solving two or three multi-objective optimization problems. As pointed out in some recent studies, however, MOEAs face many difficulties when dealing with many-objective optimization problems(MaOPs) on account of the loss of the selection pressure of the non-dominant candidate solutions toward the Pareto front and the ineffective design of the diversity maintenance mechanism. This paper proposes a many-objective evolutionary algorithm based on vector guidance. In this algorithm, the value of vector angle distance scaling(VADS) is applied to balance convergence and diversity in environmental selection. In addition, tournament selection based on the aggregate fitness value of VADS is applied to generate a high quality offspring population. Besides, we adopt an adaptive strategy to adjust the reference vector dynamically according to the scales of the objective functions. Finally, the performance of the proposed algorithm is compared with five state-of-the-art many-objective evolutionary algorithms on 52 instances of 13 MaOPs with diverse characteristics. Experimental results show that the proposed algorithm performs competitively when dealing many-objective with different types of Pareto front.

An Efficient Framework Using Normalized Dominance Operator for Multi-Objective Evolutionary Algorithms

2019 ◽  
Vol 10 (1) ◽  
pp. 15-37 ◽  
Author(s):  
Muneendra Ojha ◽  
Krishna Pratap Singh ◽  
Pavan Chakraborty ◽  
Shekhar Verma
Keyword(s):  
Evolutionary Algorithms ◽  
Pareto Front ◽  
Optimization Problem ◽  
Computational Cost ◽  
Optimization Methods ◽  
Objective Test ◽  
Test Problems ◽  
Multi Objective Optimization ◽  
Pareto Dominance ◽  
Multi Objective

Multi-objective optimization algorithms using evolutionary optimization methods have shown strength in solving various problems using several techniques for producing uniformly distributed set of solutions. In this article, a framework is presented to solve the multi-objective optimization problem which implements a novel normalized dominance operator (ND) with the Pareto dominance concept. The proposed method has a lesser computational cost as compared to crowding-distance-based algorithms and better convergence. A parallel external elitist archive is used which enhances spread of solutions across the Pareto front. The proposed algorithm is applied to a number of benchmark multi-objective test problems with up to 10 objectives and compared with widely accepted aggregation-based techniques. Experiments produce a consistently good performance when applied to different recombination operators. Results have further been compared with other established methods to prove effective convergence and scalability.

scholarly journals Primal–Dual Type Evolutionary Multiobjective Optimization

2013 ◽  
Vol 38 (4) ◽  
pp. 267-275
Author(s):  
Ignacy Kaliszewski ◽  
Janusz Miroforidis
Keyword(s):  
Multiobjective Optimization ◽  
Pareto Front ◽  
Efficient Solutions ◽  
Test Problems ◽  
Evolutionary Computations ◽  
Evolutionary Multiobjective Optimization ◽  
Feasible Sets ◽  
Primal Dual ◽  
Feasible Solutions ◽  
Pareto Fronts

Abstract A new, primal-dual type approach for derivation of Pareto front approximations with evolutionary computations is proposed. At present, evolutionary multiobjective optimization algorithms derive a discrete approximation of the Pareto front (the set of objective maps of efficient solutions) by selecting feasible solutions such that their objective maps are close to the Pareto front. As, except of test problems, Pareto fronts are not known, the accuracy of such approximations is known neither. Here we propose to exploit also elements outside feasible sets with the aim to derive pairs of Pareto front approximations such that for each approximation pair the corresponding Pareto front lies, in a certain sense, in-between. Accuracies of Pareto front approximations by such pairs can be measured and controlled with respect to distance between such approximations. A rudimentary algorithm to derive pairs of Pareto front approximations is presented and the viability of the idea is verified on a limited number of test problems.

scholarly journals A Review of Surrogate Assisted Multiobjective Evolutionary Algorithms

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Alan Díaz-Manríquez ◽  
Gregorio Toscano ◽  
Jose Hugo Barron-Zambrano ◽  
Edgar Tello-Leal
Keyword(s):  
Evolutionary Algorithms ◽  
Multiobjective Optimization ◽  
Pareto Front ◽  
Optimization Problems ◽  
State Of The Art ◽  
Surrogate Models ◽  
Multiobjective Evolutionary Algorithms ◽  
Advantages And Disadvantages ◽  
Multiobjective Optimization Problems ◽  
Computationally Expensive

Multiobjective evolutionary algorithms have incorporated surrogate models in order to reduce the number of required evaluations to approximate the Pareto front of computationally expensive multiobjective optimization problems. Currently, few works have reviewed the state of the art in this topic. However, the existing reviews have focused on classifying the evolutionary multiobjective optimization algorithms with respect to the type of underlying surrogate model. In this paper, we center our focus on classifying multiobjective evolutionary algorithms with respect to their integration with surrogate models. This interaction has led us to classify similar approaches and identify advantages and disadvantages of each class.

scholarly journals Development of Multiple Behaviors in Evolving Robots

Robotics ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 1
Author(s):  
Victor Massagué Respall ◽  
Stefano Nolfi
Keyword(s):  
Evolutionary Algorithms ◽  
State Of The Art ◽  
Evolutionary Robotics ◽  
The Other ◽  
Evolutionary Strategies ◽  
Multiple Behaviors ◽  
Pareto Fronts ◽  
Expected Fitness

We investigate whether standard evolutionary robotics methods can be extended to support the evolution of multiple behaviors by forcing the retention of variations that are adaptive with respect to all required behaviors. This is realized by selecting the individuals located in the first Pareto fronts of the multidimensional fitness space in the case of a standard evolutionary algorithms and by computing and using multiple gradients of the expected fitness in the case of a modern evolutionary strategies that move the population in the direction of the gradient of the fitness. The results collected on two extended versions of state-of-the-art benchmarking problems indicate that the latter method permits to evolve robots capable of producing the required multiple behaviors in the majority of the replications and produces significantly better results than all the other methods considered.

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