scholarly journals An Environmental Selection and Transfer Learning Based Dynamic Multiobjective Optimization Evolutionary Algorithm

2021 ◽  
Author(s):  
Qiang He ◽  
Zheng Xiang ◽  
Peng Ren
Keyword(s):  
Multiobjective Optimization ◽  
Evolutionary Algorithm ◽  
Transfer Learning ◽  
Optimization Problems ◽  
Evolutionary Process ◽  
Pareto Optimal ◽  
Nsga Ii ◽  
Environmental Selection ◽  
Dynamic Multiobjective Optimization ◽  
Prediction Strategy

Abstract In recent years, the dynamic multiobjective optimization problems (DMOPs), whose major strategy is to track the varying PS (Pareto Optimal Solution, PS) and/or PF (Pareto Optimal Frontier), caused a great deal of attention worldwide. As a promising solution, reusing of “experiences” to establish a prediction model is proved to be very useful and widely used in practice. However, most existing methods overlook the importance of environmental selection in the evolutionary processes. In this paper, we propose a dynamic multiobjective optimal evolutionary algorithm which is based on environmental selection and transfer learning (DMOEA-ESTL). This approach makes full use of the environmental selection and transfer learning technique to generate individuals for a new environment by reusing experience to maintain the diversity of the population and speed up the evolutionary process. As experimental validation, we embed this new scheme in the NSGA-II (non-dominated sorting genetic algorithm). We test the proposed algorithm with the help of six benchmark functions as well as compare it with the other two prediction based strategies FPS (Forward-looking Prediction Strategy, FPS) and PPS (Population Prediction Strategy, PPS). The experimental results testify that the proposed strategy can deal with the DMOPs effectively.

Evaluating the ε-Domination Based Multi-Objective Evolutionary Algorithm for a Quick Computation of Pareto-Optimal Solutions

2005 ◽  
Vol 13 (4) ◽  
pp. 501-525 ◽  
Author(s):  
Kalyanmoy Deb ◽  
Manikanth Mohan ◽  
Shikhar Mishra
Keyword(s):  
Steady State ◽  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Computational Time ◽  
Test Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Nsga Ii ◽  
Multi Objective

Since the suggestion of a computing procedure of multiple Pareto-optimal solutions in multi-objective optimization problems in the early Nineties, researchers have been on the look out for a procedure which is computationally fast and simultaneously capable of finding a well-converged and well-distributed set of solutions. Most multi-objective evolutionary algorithms (MOEAs) developed in the past decade are either good for achieving a well-distributed solutions at the expense of a large computational effort or computationally fast at the expense of achieving a not-so-good distribution of solutions. For example, although the Strength Pareto Evolutionary Algorithm or SPEA (Zitzler and Thiele, 1999) produces a much better distribution compared to the elitist non-dominated sorting GA or NSGA-II (Deb et al., 2002a), the computational time needed to run SPEA is much greater. In this paper, we evaluate a recently-proposed steady-state MOEA (Deb et al., 2003) which was developed based on the ε-dominance concept introduced earlier (Laumanns et al., 2002) and using efficient parent and archive update strategies for achieving a well-distributed and well-converged set of solutions quickly. Based on an extensive comparative study with four other state-of-the-art MOEAs on a number of two, three, and four objective test problems, it is observed that the steady-state MOEA is a good compromise in terms of convergence near to the Pareto-optimal front, diversity of solutions, and computational time. Moreover, the ε-MOEA is a step closer towards making MOEAs pragmatic, particularly allowing a decision-maker to control the achievable accuracy in the obtained Pareto-optimal solutions.

Global WASF-GA: An Evolutionary Algorithm in Multiobjective Optimization to Approximate the Whole Pareto Optimal Front

2017 ◽  
Vol 25 (2) ◽  
pp. 309-349 ◽  
Author(s):  
Rubén Saborido ◽  
Ana B. Ruiz ◽  
Mariano Luque
Keyword(s):  
Multiobjective Optimization ◽  
Evolutionary Algorithm ◽  
Fitness Function ◽  
Weight Vector ◽  
Reference Points ◽  
Pareto Optimal ◽  
Computational Results ◽  
Nsga Ii ◽  
Nondominated Solutions ◽  
Pareto Optimal Front

In this article, we propose a new evolutionary algorithm for multiobjective optimization called Global WASF-GA ( global weighting achievement scalarizing function genetic algorithm), which falls within the aggregation-based evolutionary algorithms. The main purpose of Global WASF-GA is to approximate the whole Pareto optimal front. Its fitness function is defined by an achievement scalarizing function (ASF) based on the Tchebychev distance, in which two reference points are considered (both utopian and nadir objective vectors) and the weight vector used is taken from a set of weight vectors whose inverses are well-distributed. At each iteration, all individuals are classified into different fronts. Each front is formed by the solutions with the lowest values of the ASF for the different weight vectors in the set, using the utopian vector and the nadir vector as reference points simultaneously. Varying the weight vector in the ASF while considering the utopian and the nadir vectors at the same time enables the algorithm to obtain a final set of nondominated solutions that approximate the whole Pareto optimal front. We compared Global WASF-GA to MOEA/D (different versions) and NSGA-II in two-, three-, and five-objective problems. The computational results obtained permit us to conclude that Global WASF-GA gets better performance, regarding the hypervolume metric and the epsilon indicator, than the other two algorithms in many cases, especially in three- and five-objective problems.

scholarly journals A New Multiobjective Evolutionary Algorithm Based on Decomposition of the Objective Space for Multiobjective Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Cai Dai ◽  
Yuping Wang
Keyword(s):  
Multiobjective Optimization ◽  
Evolutionary Algorithm ◽  
Pareto Front ◽  
Optimization Problems ◽  
Experimental Studies ◽  
Evolutionary Process ◽  
Optimal Solution ◽  
Multiobjective Evolutionary Algorithm ◽  
Multiobjective Optimization Problems ◽  
Objective Space

In order to well maintain the diversity of obtained solutions, a new multiobjective evolutionary algorithm based on decomposition of the objective space for multiobjective optimization problems (MOPs) is designed. In order to achieve the goal, the objective space of a MOP is decomposed into a set of subobjective spaces by a set of direction vectors. In the evolutionary process, each subobjective space has a solution, even if it is not a Pareto optimal solution. In such a way, the diversity of obtained solutions can be maintained, which is critical for solving some MOPs. In addition, if a solution is dominated by other solutions, the solution can generate more new solutions than those solutions, which makes the solution of each subobjective space converge to the optimal solutions as far as possible. Experimental studies have been conducted to compare this proposed algorithm with classic MOEA/D and NSGAII. Simulation results on six multiobjective benchmark functions show that the proposed algorithm is able to obtain better diversity and more evenly distributed Pareto front than the other two algorithms.

scholarly journals The Evolutionary Algorithm to Find Robust Pareto-Optimal Solutions over Time

2015 ◽  
Vol 2015 ◽  
pp. 1-18 ◽  
Author(s):  
Meirong Chen ◽  
Yinan Guo ◽  
Haiyuan Liu ◽  
Chun Wang
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Multiobjective Optimization Problems ◽  
Dynamic Multiobjective Optimization ◽  
Pareto Fronts ◽  
Over Time

In dynamic multiobjective optimization problems, the environmental parameters change over time, which makes the true pareto fronts shifted. So far, most works of research on dynamic multiobjective optimization methods have concentrated on detecting the changed environment and triggering the population based optimization methods so as to track the moving pareto fronts over time. Yet, in many real-world applications, it is not necessary to find the optimal nondominant solutions in each dynamic environment. To solve this weakness, a novel method called robust pareto-optimal solution over time is proposed. It is in fact to replace the optimal pareto front at each time-varying moment with the series of robust pareto-optimal solutions. This means that each robust solution can fit for more than one time-varying moment. Two metrics, including the average survival time and average robust generational distance, are present to measure the robustness of the robust pareto solution set. Another contribution is to construct the algorithm framework searching for robust pareto-optimal solutions over time based on the survival time. Experimental results indicate that this definition is a more practical and time-saving method of addressing dynamic multiobjective optimization problems changing over time.

Multi-Objective Optimization Design of Complex Mechanical and Electrical Products Based on Improved Evolutionary Algorithm

2011 ◽  
Vol 311-313 ◽  
pp. 1384-1388 ◽  
Author(s):  
Wei Wei ◽  
Li Hong Qiao
Keyword(s):  
Multiobjective Optimization ◽  
Evolutionary Algorithm ◽  
Optimization Design ◽  
Design Space ◽  
Pareto Optimal ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Trade Off ◽  
Pareto Optimal Set ◽  
Optimal Set

The design of complex mechanical and electrical products has to achieve various objectives and satisfy various constraints. In many cases, there are trade-off relationships between these objectives, and thus it is difficult to optimize these objectives simultaneously. This invokes the need of the multiobjective optimization to achieve these objectives collectively. In this paper, multiple objectives for complex mechanical and electrical products are optimized, simultaneously using an improved multiobjective evolutionary algorithm: ISPEA2. The results showed that ISPEA2 could generate uniformly a pareto optimal set in the design space and has better robustness and convergence than SPEA2 and NSGA-II.

scholarly journals An Evolutionary Algorithm with Clustering-Based Assisted Selection Strategy for Multimodal Multiobjective Optimization

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Naili Luo ◽  
Wu Lin ◽  
Peizhi Huang ◽  
Jianyong Chen
Keyword(s):  
Multiobjective Optimization ◽  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Population Diversity ◽  
Selection Strategy ◽  
Pareto Optimal ◽  
Density Based Clustering ◽  
Multiobjective Optimization Problems ◽  
Objective Space ◽  
Multiple Clusters

In multimodal multiobjective optimization problems (MMOPs), multiple Pareto optimal sets, even some good local Pareto optimal sets, should be reserved, which can provide more choices for decision-makers. To solve MMOPs, this paper proposes an evolutionary algorithm with clustering-based assisted selection strategy for multimodal multiobjective optimization, in which the addition operator and deletion operator are proposed to comprehensively consider the diversity in both decision and objective spaces. Specifically, in decision space, the union population is partitioned into multiple clusters by using a density-based clustering method, aiming to assist the addition operator to strengthen the population diversity. Then, a number of weight vectors are adopted to divide population into N subregions in objective space (N is population size). Moreover, in the deletion operator, the solutions in the most crowded subregion are first collected into previous clusters, and then the worst solution in the most crowded cluster is deleted until there are N solutions left. Our algorithm is compared with other multimodal multiobjective evolutionary algorithms on the well-known benchmark MMOPs. Numerical experiments report the effectiveness and advantages of our proposed algorithm.

A multi-objective evolutionary algorithm based on niche selection in solving irregular Pareto fronts

2021 ◽  
pp. 1-21
Author(s):  
Xin Li ◽  
Xiaoli Li ◽  
Kang Wang
Keyword(s):  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Benchmark Problems ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Environmental Selection ◽  
Optimal Solution Set ◽  
Pareto Fronts

The key characteristic of multi-objective evolutionary algorithm is that it can find a good approximate multi-objective optimal solution set when solving multi-objective optimization problems(MOPs). However, most multi-objective evolutionary algorithms perform well on regular multi-objective optimization problems, but their performance on irregular fronts deteriorates. In order to remedy this issue, this paper studies the existing algorithms and proposes a multi-objective evolutionary based on niche selection to deal with irregular Pareto fronts. In this paper, the crowding degree is calculated by the niche method in the process of selecting parents when the non-dominated solutions converge to the first front, which improves the the quality of offspring solutions and which is beneficial to local search. In addition, niche selection is adopted into the process of environmental selection through considering the number and the location of the individuals in its niche radius, which improve the diversity of population. Finally, experimental results on 23 benchmark problems including MaF and IMOP show that the proposed algorithm exhibits better performance than the compared MOEAs.

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