Hyperplane-Approximation-Based Method for Many-Objective Optimization Problems with Redundant Objectives

2019 ◽  
Vol 27 (2) ◽  
pp. 313-344
Author(s):  
Yifan Li ◽  
Hai-Lin Liu ◽  
E. D. Goodman
Keyword(s):  
Pareto Front ◽  
Optimization Problems ◽  
Approximation Error ◽  
Main Idea ◽  
Benchmark Problems ◽  
Performance Metric ◽  
Dominance Structure ◽  
Objective Reduction ◽  
Pareto Fronts ◽  
Linearly Degenerate

For a many-objective optimization problem with redundant objectives, we propose two novel objective reduction algorithms for linearly and, nonlinearly degenerate Pareto fronts. They are called LHA and NLHA respectively. The main idea of the proposed algorithms is to use a hyperplane with non-negative sparse coefficients to roughly approximate the structure of the PF. This approach is quite different from the previous objective reduction algorithms that are based on correlation or dominance structure. Especially in NLHA, in order to reduce the approximation error, we transform a nonlinearly degenerate Pareto front into a nearly linearly degenerate Pareto front via a power transformation. In addition, an objective reduction framework integrating a magnitude adjustment mechanism and a performance metric [Formula: see text] are also proposed here. Finally, to demonstrate the performance of the proposed algorithms, comparative experiments are done with two correlation-based algorithms, LPCA and NLMVUPCA, and with two dominance-structure-based algorithms, PCSEA and greedy [Formula: see text]MOSS, on three benchmark problems: DTLZ5(I,M), MAOP(I,M), and WFG3(I,M). Experimental results show that the proposed algorithms are more effective.

scholarly journals MOPSO algorithm and its application in multipurpose multireservoir operations

2010 ◽  
Vol 13 (4) ◽  
pp. 794-811 ◽  
Author(s):  
E. Fallah-Mehdipour ◽  
O. Bozorg Haddad ◽  
M. A. Mariño
Keyword(s):  
Pareto Front ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Pso Algorithm ◽  
Benchmark Problems ◽  
Multi Objective Optimization ◽  
Warm Up ◽  
Multi Objective ◽  
A New Technique ◽  
Pareto Fronts

The main reason for applying evolutionary algorithms in multi-objective optimization problems is to obtain near-optimal nondominated solutions/Pareto fronts, from which decision-makers can choose a suitable solution. The efficiency of multi-objective optimization algorithms depends on the quality and quantity of Pareto fronts produced by them. To compare different Pareto fronts resulting from different algorithms, criteria are considered and applied in multi-objective problems. Each criterion denotes a characteristic of the Pareto front. Thus, ranking approaches are commonly used to evaluate different algorithms based on different criteria. This paper presents three multi-objective optimization methods based on the multi-objective particle swarm optimization (MOPSO) algorithm. To evaluate these methods, bi-objective mathematical benchmark problems are considered. Results show that all proposed methods are successful in finding near-optimal Pareto fronts. A ranking method is used to compare the capability of the proposed methods and the best method for further study is suggested. Moreover, the nominated method is applied as an optimization tool in real multi-objective optimization problems in multireservoir system operations. A new technique in multi-objective optimization, called warm-up, based on the PSO algorithm is then applied to improve the quality of the Pareto front by single-objective search. Results show that the proposed technique is successful in finding an optimal Pareto front.

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.

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.

Archive of Useful Solutions for Directed Mating in Evolutionary Constrained Multiobjective Optimization

2014 ◽  
Vol 18 (2) ◽  
pp. 221-231 ◽  
Author(s):  
Minami Miyakawa ◽  
◽  
Keiki Takadama ◽  
Hiroyuki Sato
Keyword(s):  
Pareto Front ◽  
Optimization Problems ◽  
Selection Process ◽  
Benchmark Problems ◽  
Search Performance ◽  
Next Generation ◽  
Multi Objective ◽  
Objective Space ◽  
Feasible Solutions ◽  
Constrained Multiobjective Optimization

As an evolutionary approach to solve multi-objective optimization problems involving several constraints, recently a multi-objective evolutionary algorithm (MOEA) using two-stage non-dominated sorting and directed mating (TNSDM) has been proposed. In TNSDM, directed mating utilizes infeasible solutions dominating feasible solutions in the objective space to generate offspring. In our previous studies, significant contribution of directed mating to the improvement of the search performancewas verified on several benchmark problems. However, in the conventional TNSDM, infeasible solutions utilized in directed mating are discarded in the selection process of parents (elites) population and cannot be utilized in the next generation. TNSDM has potential to further improve the search performance by archiving useful solutions for directed mating to the next generation and repeatedly utilizing them in directed mating. To further improve effects of directed mating in TNSDM, in this work, we propose an archiving strategy of useful solutions for directed mating. We verify the search performance of TNSDM using the proposed archive by varying the size of archive, and compare its search performance with the conventional CNSGA-II and RTS onmobjectiveskknapsacks problems. As results, we show that the search performance of TNSDM is improved by introducing the proposed archive in aspects of diversity of the obtained solutions in the objective space and convergence of solutions toward the optimal Pareto front.

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.

scholarly journals A Comprehensive Study on Metaheuristic Techniques Using Genetic Approach

2019 ◽  
Vol 7 (8) ◽  
pp. 23-31
Author(s):  
G. Kalyani ◽  
K. Krishna Jyothi ◽  
T. Pratyusha
Keyword(s):  
Pareto Front ◽  
Optimization Problems ◽  
Real Life ◽  
Decision Makers ◽  
Benchmark Problems ◽  
Multiple Decision Makers ◽  
Trade Offs ◽  
Solution Methods ◽  
Metaheuristic Techniques ◽  
Comprehensive Study

Most real-life optimization problems involve multiple objective functions. Finding  a  solution  that  satisfies  the  decision-maker  is  very  difficult  owing  to  conflict  between  the  objectives.  Furthermore,  the  solution  depends  on  the  decision-maker’s preference.  Metaheuristic solution methods have become common tools to solve these problems.  The  task  of  obtaining  solutions  that  take  account  of  a  decision-maker’s preference  is  at  the  forefront  of  current  research.  It  is  also  possible  to  have  multiple decision-makers with different preferences and with different  decision-making  powers. It may not be easy to express a preference using crisp numbers. In this study, the preferences of multiple decision-makers were simulated  and  a solution based on  a genetic  algorithm was  developed  to  solve  multi-objective  optimization  problems.  The  preferences  were collected  as  fuzzy  conditional  trade-offs  and  they  were  updated  while  running  the algorithm interactively with the decision-makers. The proposed method was tested using well-known benchmark problems.  The solutions were found to converge around the Pareto front of the problems.

scholarly journals Repulsive Self-Adaptive Acceleration Particle Swarm Optimization Approach

2014 ◽  
Vol 4 (3) ◽  
pp. 189-204 ◽  
Author(s):  
Simone A. Ludwig
Keyword(s):  
Particle Swarm Optimization ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Main Idea ◽  
Benchmark Problems ◽  
Optimization Approach ◽  
Swarm Optimization ◽  
Wide Range ◽  
Adaptive Pso ◽  
Self Adaptive

Abstract Adaptive Particle Swarm Optimization (PSO) variants have become popular in recent years. The main idea of these adaptive PSO variants is that they adaptively change their search behavior during the optimization process based on information gathered during the run. Adaptive PSO variants have shown to be able to solve a wide range of difficult optimization problems efficiently and effectively. In this paper we propose a Repulsive Self-adaptive Acceleration PSO (RSAPSO) variant that adaptively optimizes the velocity weights of every particle at every iteration. The velocity weights include the acceleration constants as well as the inertia weight that are responsible for the balance between exploration and exploitation. Our proposed RSAPSO variant optimizes the velocity weights that are then used to search for the optimal solution of the problem (e.g., benchmark function). We compare RSAPSO to four known adaptive PSO variants (decreasing weight PSO, time-varying acceleration coefficients PSO, guaranteed convergence PSO, and attractive and repulsive PSO) on twenty benchmark problems. The results show that RSAPSO achives better results compared to the known PSO variants on difficult optimization problems that require large numbers of function evaluations.

Adaptive Control of Dominance Area of Solutions in Evolutionary Many-Objective Optimization

2015 ◽  
Vol 11 (02) ◽  
pp. 135-150 ◽  
Author(s):  
Kouhei Tomita ◽  
Minami Miyakawa ◽  
Hiroyuki Sato
Keyword(s):  
Pareto Front ◽  
Optimization Problems ◽  
Benchmark Problems ◽  
Pareto Optimal ◽  
Search Performance ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Pareto Dominance ◽  
Nsga Ii ◽  
Convergence Of Solutions

Controlling the dominance area of solutions (CDAS) relaxes the concept of Pareto dominance with an user-defined parameter S. CDAS with S < 0.5 expands the dominance area and improves the search performance of multi-objective evolutionary algorithms (MOEAs) especially in many-objective optimization problems (MaOPs) by enhancing convergence of solutions toward the optimal Pareto front. However, there is a problem that CDAS with an expanded dominance area (S < 0.5) generally cannot approximate entire Pareto front. To overcome this problem we propose an adaptive CDAS (A-CDAS) that adaptively controls the dominance area of solutions during the solutions search. Our method improves the search performance in MaOPs by approximating the entire Pareto front while keeping high convergence. In early generations, A-CDAS tries to converge solutions toward the optimal Pareto front by using an expanded dominance area with S < 0.5. When we detect convergence of solutions, we gradually increase S and contract the dominance area of solutions to obtain Pareto optimal solutions (POS) covering the entire optimal Pareto front. We verify the effectiveness and the search performance of the proposed A-CDAS on concave and convex DTLZ3 benchmark problems with 2–8 objectives, and show that the proposed A-CDAS achieves higher search performance than conventional non-dominated sorting genetic algorithm II (NSGA-II) and CDAS with an expanded dominance area.

scholarly journals A Set Based Newton Method for the Averaged Hausdorff Distance for Multi-Objective Reference Set Problems

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1822
Author(s):  
Lourdes Uribe ◽  
Johan M Bogoya ◽  
Andrés Vargas ◽  
Adriana Lara ◽  
Günter Rudolph ◽  
...  
Keyword(s):  
Hausdorff Distance ◽  
Performance Indicators ◽  
Pareto Front ◽  
Optimization Problems ◽  
Benchmark Problems ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Reference Set ◽  
Common Task ◽  
Objective Reference

Multi-objective optimization problems (MOPs) naturally arise in many applications. Since for such problems one can expect an entire set of optimal solutions, a common task in set based multi-objective optimization is to compute N solutions along the Pareto set/front of a given MOP. In this work, we propose and discuss the set based Newton methods for the performance indicators Generational Distance (GD), Inverted Generational Distance (IGD), and the averaged Hausdorff distance Δp for reference set problems for unconstrained MOPs. The methods hence directly utilize the set based scalarization problems that are induced by these indicators and manipulate all N candidate solutions in each iteration. We demonstrate the applicability of the methods on several benchmark problems, and also show how the reference set approach can be used in a bootstrap manner to compute Pareto front approximations in certain cases.

scholarly journals Efficient algorithms for solving nonlinear fractional programming problems

Filomat ◽  
2019 ◽  
Vol 33 (7) ◽  
pp. 2149-2179
Author(s):  
Azam Dolatnezhadsomarin ◽  
Esmaile Khorram ◽  
Latif Pourkarimi
Keyword(s):  
Fractional Programming ◽  
Pareto Front ◽  
Optimization Problems ◽  
Test Problems ◽  
Nsga Ii ◽  
Uniform Approximations ◽  
Nonlinear Fractional Programming ◽  
Pareto Fronts ◽  
Metric Selection

In this paper, an efficient algorithm based on the Pascoletti-Serafini scalarization (PS) approach is proposed to obtain almost uniform approximations of the entire Pareto front of bi-objective optimization problems. Five test problems with convex, non-convex, connected, and disconnected Pareto fronts are applied to evaluate the quality of approximations obtained by the proposed algorithm. Results are compared with results of some algorithms including the normal constraint (NC), weighted constraint (WC), Benson type, differential evolution (DE) with binomial crossover, non-dominated sorting genetic algorithm-II (NSGA-II), and S metric selection evolutionary multiobjective algorithm (SMS-EMOA). The results confirm the effectiveness of the presented bi-objective algorithm in terms of the quality of approximations of the Pareto front and CPU time. In addition, two algorithms are presented for approximately solving fractional programming (FP) problems. The first algorithm is based on an objective space cut and bound method for solving convex FP problems and the second algorithm is based on the proposed bi-objective algorithm for solving nonlinear FP problems. In addition, several examples are provided to demonstrate the performance of these suggested fractional algorithms.

Sign in / Sign up

Export Citation Format

Share Document