Hypervolume Performance of Conical Area Evolutionary Algorithm for Bi-Objective Optimization

2014 ◽  
Vol 513-517 ◽  
pp. 2215-2219
Author(s):  
Hong Ke Zhao ◽  
Wei Qin Ying ◽  
Yu Wu ◽  
Yue Hong Xie ◽  
Li Wen
Keyword(s):  
Evolutionary Algorithm ◽  
Infinite Number ◽  
Optimization Problems ◽  
Experimental Results ◽  
Nsga Ii ◽  
Better Than

The conical area evolutionary algorithm (CAEA) can efficiently solve the bi-objective optimization problems by borrowing some ideas from decomposition and hypervolume. In this paper, the optimal hypervolume performance of the CAEA with an infinite number of sub-problems is proved through the squeeze theorem for limits. Experimental results on several bi-objective optimization problems have shown that not only CAEA performs much better than NSGA-II and MOEA/D in terms of efficiency, but also CAEA with a larger number of sub-problems has the better hypervolume performance.

Multi-Objective Evolutionary Algorithm Based on Two Reference Points Decomposition and Historical Information Prediction

2021 ◽  
Vol 01 ◽  
Author(s):  
Er-chao Li ◽  
Kang-wei Li
Keyword(s):  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Reference Points ◽  
Multi Objective Optimization ◽  
Test Function ◽  
Historical Information ◽  
Multi Objective ◽  
Nadir Point ◽  
Overall Performance ◽  
Better Than

Aims: The main purpose of this paper is to solve the issues that the poor quality of offspring solutions generated by traditional evolutionary operators, and that the inability of the evolutionary algorithm based on decomposition to better solve the multi-objective optimization problems (MOPs) with complicated Pareto fronts (PFs). Background: For some complicated multi-objective optimization problems, the effect of the multi-objective evolutionary algorithm based on decomposition (MOEA/D) is poor. For specific complicated problems, there is less research on improving the algorithm's performance by setting and adjusting the direction vector in the decomposition-based evolutionary algorithm. And considering that in the existing algorithms, the optimal solutions are selected according to the selection strategy in the selection stage, without considering if it could produce the better solutions in the stage of individual generation to achieve the optimization effect faster. As a result of these, a multi-objective evolutionary algorithm that is based on two reference points decomposition and historical information prediction is proposed. Objective: In order to verify the feasibility of the proposed strategy, the F-series test function with complicated PFs is used as the test function to simulate the proposed strategy. Method: Firstly, the evolutionary operator based on Historical Information Prediction (EHIP) is used to generate better offspring solutions to improve the convergence of the algorithm; secondly, the decomposition strategy based on ideal point and nadir point is used to select solutions to solve the MOPs with complicated PFs, and the decomposition method with augmentation term is used to improve the population diversity when selecting solutions according to the nadir point. Finally, the proposed algorithm is compared to several popular algorithms by the F-series test function, and the comparison is made according to the corresponding performance metrics. Result: The performance of the algorithm is improved obviously compared with the popular algorithms after using the EHIP. When the decomposition method with augmentation term is added, the performance of the proposed algorithm is better than the algorithm with only the EHIP on the whole. However, the overall performance is better than the popular algorithms. Conclusion and Prospect: The experimental results show that the overall performance of the proposed algorithm is superior to the popular algorithms. The EHIP can produce better quality offspring solutions, and the decomposition strategy based on two reference points can well solve the MOPs with complicated PFs. This paper mainly demonstrates the theory without testing the practical problems. The following research mainly focuses on the application of the proposed algorithm to the practical problems such as robot path planning.

A Method for Solving Multi-Objective Optimization Problems Containing an Infinite Number of Parameterized Objectives

2020 ◽  
Author(s):  
Eliot Rudnick-Cohen
Keyword(s):  
Decision Making ◽  
Infinite Number ◽  
Optimization Problems ◽  
Pareto Frontier ◽  
Brute Force ◽  
Multi Objective Optimization ◽  
New Approach ◽  
Multi Objective ◽  
Brute Force Approach ◽  
Better Than

Abstract Multi-objective decision making problems can sometimes involve an infinite number of objectives. In this paper, an approach is presented for solving multi-objective optimization problems containing an infinite number of parameterized objectives, termed “infinite objective optimization”. A formulation is given for infinite objective optimization problems and an approach for checking whether a Pareto frontier is a solution to this formulation is detailed. Using this approach, a new sampling based approach is developed for solving infinite objective optimization problems. The new approach is tested on several different example problems and is shown to be faster and perform better than a brute force approach.

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.

Composite Evolutionary Algorithm for Constrained Optimization

2012 ◽  
Vol 220-223 ◽  
pp. 2846-2851
Author(s):  
Si Lian Xie ◽  
Tie Bin Wu ◽  
Shui Ping Wu ◽  
Yun Lian Liu
Keyword(s):  
Evolutionary Algorithms ◽  
Constrained Optimization ◽  
Evolutionary Algorithm ◽  
Selection Criteria ◽  
Optimization Problems ◽  
Experimental Results ◽  
Constrained Optimization Problems ◽  
Mutation Operators ◽  
Single Operator ◽  
Algorithm Framework

Evolutionary algorithms are amongst the best known methods of solving difficult constrained optimization problems, for which traditional methods are not applicable. Due to the variability of characteristics in different constrained optimization problems, no single evolutionary with single operator performs consistently over a range of problems. We introduce an algorithm framework that uses multiple search operators in each generation. A composite evolutionary algorithm is proposed in this paper and combined feasibility rule to solve constrained optimization problems. The proposed evolutionary algorithm combines three crossover operators with two mutation operators. The selection criteria based on feasibility of individual is used to deal with the constraints. The proposed method is tested on five well-known benchmark constrained optimization problems, and the experimental results show that it is effective and robust

A Novel Objective Grouping Evolutionary Algorithm for Many-Objective Optimization Problems

2019 ◽  
Vol 34 (06) ◽  
pp. 2059018
Author(s):  
Xiaofang Guo ◽  
Xiaoli Wang
Keyword(s):  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Computational Cost ◽  
Pareto Solutions ◽  
Nsga Ii ◽  
Space Partition ◽  
Dominance Structure ◽  
Objective Reduction ◽  
Original Objective ◽  
Nondominated Sorting

The thorniest difficulties for multi-objective evolutionary algorithms (MOEAs) handling many-objective optimization problems (MaOPs) are the inefficiency of selection operators and high computational cost. To alleviate such difficulties and simplify the MaOPs, objective reduction algorithms have been proposed to remove the redundant objectives during the search process. However, those algorithms can only be applicable to specific problems with redundant objectives. Worse still, the Pareto solutions obtained by reduced objective set may not be the Pareto solutions of the original MaOPs. In this paper, we present a novel objective grouping evolutionary algorithm (OGEA) for general MaOPs. First, by dividing original objective set into several overlapping lower-dimensional subsets in terms of interdependence correlation information, we aim to separate the MaOPs into a number of sub-problems so that each of them can be able to preserve as much dominance structure in the original objective set as possible. Subsequently, we employ the nondominated sorting genetic algorithm II (NSGA-II) to generate Pareto solutions. Besides, instead of nondominated sorting on the whole population, a novel dual selection mechanism is proposed to choose individuals either having high ranks in subspaces or locating sparse region in the objective space for better proximity and diversity. Finally, we compare the proposed strategy with the other two classical space partition methods on benchmark DTLZ5 (I, M), DTLZ2 and a practical engineering problem. Numerical results show the proposed objective grouping algorithm can preserve more dominance structure in original objective set and achieve better quality of Pareto solutions.

A Dimensional Diversity Based Hybrid Multiobjective Evolutionary Algorithm for Optimization Problem

2016 ◽  
Vol 30 (07) ◽  
pp. 1659020 ◽  
Author(s):  
Peng Wang ◽  
Changsheng Zhang ◽  
Bin Zhang ◽  
Tingting Liu ◽  
Jiaxuan Wu
Keyword(s):  
Multiobjective Optimization ◽  
Evolutionary Algorithm ◽  
Optimization Problem ◽  
Optimization Problems ◽  
State Of The Art ◽  
Experimental Results ◽  
Selection Scheme ◽  
Genetic Operator ◽  
Hybrid Evolutionary Algorithm ◽  
Multiobjective Optimization Problems

Multiobjective density driven evolutionary algorithm (MODdEA) has been quite successful in solving multiobjective optimization problems (MOPs). To further improve its performance and address its deficiencies, this paper proposes a hybrid evolutionary algorithm based on dimensional diversity (DD) and firework explosion (FE). DD is defined to reflect the diversity degree of population dimension. Based on DD, a selection scheme is designed to balance diversity and convergence. A hybrid variation based on FE and genetic operator is designed to facilitate diversity of population. The proposed algorithm is tested on 14 tests problems with diverse characteristics and compared with three state-of-the-art designs. Experimental results show that the proposed design is better or at par with the chosen state-of-the-art algorithms for multiobjective optimization.

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.

scholarly journals An Improved Multiobjective Algorithm: DNSGA2-PSA

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Dan Qu ◽  
Xianfeng Ding ◽  
Hongmei Wang
Keyword(s):  
Pareto Front ◽  
Optimization Problems ◽  
High Dimensional ◽  
Nsga Ii ◽  
Equal Importance ◽  
Multiobjective Optimization Problems ◽  
Diversity Preservation ◽  
Ranking Scheme ◽  
Nondominated Sorting ◽  
Better Than

In general, the proximities to a certain diversity along the front and the Pareto front have the equal importance for solving multiobjective optimization problems (MOPs). However, most of the existing evolutionary algorithms give priority to the proximity over the diversity. To improve the diversity and decrease execution time of the nondominated sorting genetic algorithm II (NSGA-II), an improved algorithm is presented in this paper, which adopts a new vector ranking scheme to decrease the whole runtime and utilize Part and Select Algorithm (PSA) to maintain the diversity. In this algorithm, a more efficient implementation of nondominated sorting, namely, dominance degree approach for nondominated sorting (DDA-NS), is presented. Moreover, an improved diversity preservation mechanism is proposed to select a well-diversified set out of an arbitrary given set. By embedding PSA and DDA-NS into NSGA-II, denoted as DNSGA2-PSA, the whole runtime of the algorithm is decreased significantly and the exploitation of diversity is enhanced. The computational experiments show that the combination of both (DDA-NS, PSA) to NSGA-II is better than the isolated use cases, and DNSGA2-PSA still performs well in the high-dimensional cases.

Evolutionary Metaheuristics to Solve Multiobjective Assignment Problem in Telecommunication Network

2020 ◽  
Vol 11 (2) ◽  
pp. 56-76
Author(s):  
Benkanoun Yazid ◽  
Bouroubi Sadek ◽  
Chaabane Djamal
Keyword(s):  
Evolutionary Algorithm ◽  
Large Scale ◽  
Optimization Problems ◽  
Choquet Integral ◽  
Telecommunication Network ◽  
Exact Algorithms ◽  
Nsga Ii ◽  
Pareto Optimal Set ◽  
System A ◽  
Integral Measure

The authors propose a computing approach for solving a multiobjective problem in the telecommunication network field, suggested by an Algerian industrial company. The principal goal is in developing a palliative solution to overcome some generated problems existing in the current management system. A mathematical operational model has been established. The exact algorithms that solve multiobjective optimization problems are not appropriate for large scale problems. However, the application of metaheuristics approach leads perfectly to approximate the Pareto optimal set. In this paper, the authors apply a well-known multiobjective evolutionary algorithm, the Non-dominated Sorting Genetic Algorithm (NSGA-II), compare the obtained results with those generated by the Strength Pareto Evolutionary Algorithm-II (SPEA2) and propose a way to help the decision maker, who is often confronted with the choice of a final solution, to make his preferences afterward using a utility function based on a Choquet integral measure. Finally, numerical experiments are presented to validate the approach.

Hybridizing Harmony Search Algorithm with Multi-Parent Crossover to Solve Real World Optimization Problems

2013 ◽  
Vol 4 (3) ◽  
pp. 1-14 ◽  
Author(s):  
Iyad Abu Doush ◽  
Faisal Alkhateeb ◽  
Eslam Al Maghayreh ◽  
Mohammed Azmi Al-Betar ◽  
Basima Hani F. Hasan
Keyword(s):  
Evolutionary Algorithm ◽  
Real World ◽  
Numerical Optimization ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Harmony Search ◽  
Harmony Search Algorithm ◽  
Experimental Results ◽  
Test Problems ◽  
Harmony Memory

Harmony search algorithm (HSA) is a recent evolutionary algorithm used to solve several optimization problems. The algorithm mimics the improvisation behaviour of a group of musicians to find a good harmony. Several variations of HSA have been proposed to enhance its performance. In this paper, a new variation of HSA that uses multi-parent crossover is proposed (HSA-MPC). In this technique three harmonies are used to generate three new harmonies that will replace the worst three solution vectors in the harmony memory (HM). The algorithm has been applied to solve a set of eight real world numerical optimization problems (1-8) introduced for IEEE-CEC2011 evolutionary algorithm competition. The experimental results of the proposed algorithm are compared with the original HSA, and two variations of HSA: global best HSA and tournament HSA. The HSA-MPC almost always shows superiority on all test problems.

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