On Benchmark Problems for Constrained Multi-Objective Optimization Problems

2016 ◽  
Vol 2016.12 (0) ◽  
pp. 2105
Author(s):  
Ryoji TANABE ◽  
Akira OYAMA
Keyword(s):  
Optimization Problems ◽  
Benchmark Problems ◽  
Multi Objective Optimization ◽  
Multi Objective

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.

A Strength Pareto Gravitational Search Algorithm for Multi-Objective Optimization Problems

2015 ◽  
Vol 29 (06) ◽  
pp. 1559010 ◽  
Author(s):  
Xiaohui Yuan ◽  
Zhihuan Chen ◽  
Yanbin Yuan ◽  
Yuehua Huang ◽  
Xiaopan Zhang
Keyword(s):  
Optimization Problems ◽  
Search Algorithm ◽  
Gravitational Search Algorithm ◽  
Population Diversity ◽  
Benchmark Problems ◽  
Multi Objective Optimization ◽  
Local Optima ◽  
Multi Objective ◽  
Fine Grained ◽  
Gravitational Search

A novel strength Pareto gravitational search algorithm (SPGSA) is proposed to solve multi-objective optimization problems. This SPGSA algorithm utilizes the strength Pareto concept to assign the fitness values for agents and uses a fine-grained elitism selection mechanism to keep the population diversity. Furthermore, the recombination operators are modeled in this approach to decrease the possibility of trapping in local optima. Experiments are conducted on a series of benchmark problems that are characterized by difficulties in local optimality, nonuniformity, and nonconvexity. The results show that the proposed SPGSA algorithm performs better in comparison with other related works. On the other hand, the effectiveness of two subtle means added to the GSA are verified, i.e. the fine-grained elitism selection and the use of SBX and PMO operators. Simulation results show that these measures not only improve the convergence ability of original GSA, but also preserve the population diversity adequately, which enables the SPGSA algorithm to have an excellent ability that keeps a desirable balance between the exploitation and exploration so as to accelerate the convergence speed to the true Pareto-optimal front.

scholarly journals A New Method for Dynamic Multi-Objective Optimization Based on Segment and Cloud Prediction

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 465 ◽  
Author(s):  
Peng Ni ◽  
Jiale Gao ◽  
Yafei Song ◽  
Wen Quan ◽  
Qinghua Xing
Keyword(s):  
Optimization Problems ◽  
Pareto Set ◽  
Benchmark Problems ◽  
Small Range ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Good Convergence ◽  
Multi Objective ◽  
The Law ◽  
Cloud Theory

In the real world, multi-objective optimization problems always change over time in most projects. Once the environment changes, the distribution of the optimal solutions would also be changed in decision space. Sometimes, such change may obey the law of symmetry, i.e., the minimum of the objective function in such environment is its maximum in another environment. In such cases, the optimal solutions keep unchanged or vibrate in a small range. However, in most cases, they do not obey the law of symmetry. In order to continue the search that maintains previous search advantages in the changed environment, some prediction strategy would be used to predict the operation position of the Pareto set. Because of this, the segment and multi-directional prediction is proposed in this paper, which consists of three mechanisms. First, by segmenting the optimal solutions set, the prediction about the changes in the distribution of the Pareto front can be ensured. Second, by introducing the cloud theory, the distance error of direction prediction can be offset effectively. Third, by using extra angle search, the angle error of prediction caused by the Pareto set nonlinear variation can also be offset effectively. Finally, eight benchmark problems were used to verify the performance of the proposed algorithm and compared algorithms. The results indicate that the algorithm proposed in this paper has good convergence and distribution, as well as a quick response ability to the changed environment.

scholarly journals Comparative Study of Knee-Based Algorithms for Many-Objective Optimization Problems

2018 ◽  
Vol 12 (1) ◽  
pp. 7-16
Author(s):  
Saad M. Alzahrani ◽  
Naruemon Wattanapongsakorn
Keyword(s):  
Optimization Problems ◽  
Benchmark Problems ◽  
Multi Objective Optimization ◽  
Trade Off ◽  
Knee Region ◽  
Multi Objective ◽  
Trade Offs ◽  
Conflicting Objectives ◽  
Small Set ◽  
Optimum Solution

Nowadays, most real-world optimization problems consist of many and often conflicting objectives to be optimized simultaneously. Although, many current Multi-Objective optimization algorithms can efficiently solve problems with 3 or less objectives, their performance deteriorates proportionally with the increasing of the objectives number. Furthermore, in many situations the decision maker (DM) is not interested in all trade-off solutions obtained but rather interested in a single optimum solution or a small set of those trade-offs. Therefore, determining an optimum solution or a small set of trade-off solutions is a difficult task. However, an interesting method for finding such solutions is identifying solutions in the Knee region. Solutions in the Knee region can be considered the best obtained solution in the obtained trade-off set especially if there is no preference or equally important objectives. In this paper, a pruning strategy was used to find solutions in the Knee region of Pareto optimal fronts for some benchmark problems obtained by NSGA-II, MOEA/D-DE and a promising new Multi-Objective optimization algorithm NSGA-III. Lastly, those knee solutions found were compared and evaluated using a generational distance performance metric, computation time and a statistical one-way ANOVA test.

scholarly journals The Pareto Tracer for General Inequality Constrained Multi-Objective Optimization Problems

2020 ◽  
Vol 25 (4) ◽  
pp. 80
Author(s):  
Fernanda Beltrán ◽  
Oliver Cuate ◽  
Oliver Schütze
Keyword(s):  
Optimization Problems ◽  
Continuation Method ◽  
Optimization Methods ◽  
New Method ◽  
Continuation Methods ◽  
Benchmark Problems ◽  
Multi Objective Optimization ◽  
Financial Applications ◽  
General Inequality ◽  
Multi Objective

Problems where several incommensurable objectives have to be optimized concurrently arise in many engineering and financial applications. Continuation methods for the treatment of such multi-objective optimization methods (MOPs) are very efficient if all objectives are continuous since in that case one can expect that the solution set forms at least locally a manifold. Recently, the Pareto Tracer (PT) has been proposed, which is such a multi-objective continuation method. While the method works reliably for MOPs with box and equality constraints, no strategy has been proposed yet to adequately treat general inequalities, which we address in this work. We formulate the extension of the PT and present numerical results on some selected benchmark problems. The results indicate that the new method can indeed handle general MOPs, which greatly enhances its applicability.

Evolutionary Large-Scale Multi-Objective Optimization: A Survey

2022 ◽  
Vol 54 (8) ◽  
pp. 1-34
Author(s):  
Ye Tian ◽  
Langchun Si ◽  
Xingyi Zhang ◽  
Ran Cheng ◽  
Cheng He ◽  
...  
Keyword(s):  
Large Scale ◽  
Optimization Problems ◽  
Benchmark Problems ◽  
Future Research ◽  
Decision Variable ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Space Reduction ◽  
Decision Variables ◽  
Comprehensive Survey

Multi-objective evolutionary algorithms (MOEAs) have shown promising performance in solving various optimization problems, but their performance may deteriorate drastically when tackling problems containing a large number of decision variables. In recent years, much effort been devoted to addressing the challenges brought by large-scale multi-objective optimization problems. This article presents a comprehensive survey of stat-of-the-art MOEAs for solving large-scale multi-objective optimization problems. We start with a categorization of these MOEAs into decision variable grouping based, decision space reduction based, and novel search strategy based MOEAs, discussing their strengths and weaknesses. Then, we review the benchmark problems for performance assessment and a few important and emerging applications of MOEAs for large-scale multi-objective optimization. Last, we discuss some remaining challenges and future research directions of evolutionary large-scale multi-objective optimization.

scholarly journals Adjusting normalization bounds to improve hypervolume based search for expensive multi-objective optimization

2021 ◽  
Author(s):  
Bing Wang ◽  
Hemant Kumar Singh ◽  
Tapabrata Ray
Keyword(s):  
Numerical Experiments ◽  
Optimization Problems ◽  
Surrogate Models ◽  
Benchmark Problems ◽  
Multi Objective Optimization ◽  
Promising Candidate ◽  
Multi Objective ◽  
Improved Performance

AbstractWhen solving expensive multi-objective optimization problems, surrogate models are often used to reduce the number of true evaluations. Based on predictions from the surrogate models, promising candidate solutions, also referred to as infill solutions, can be identified for evaluation to expedite the search towards the optimum. This infill process in turn involves optimization of certain criteria derived from the surrogate models. In this study, predicted hypervolume maximization is considered as the infill criterion for expensive multi/many-objective optimization. In particular, we examine the effect of normalization bounds on the performance of the algorithm building on our previous study on bi-objective optimization. We propose a more scalable approach based on “surrogate corner” search that shows improved performance where some of the conventional techniques face challenges. Numerical experiments on a range of benchmark problems with up to 5 objectives demonstrate the efficacy and reliability of the proposed approach.

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.

Solving Two Multi-Objective Optimization Problems Using Evolutionary Algorithm

2011 ◽  
pp. 218-233 ◽  
Author(s):  
Ruhul A. Sarker ◽  
Hussein A. Abbass ◽  
Charles S. Newton
Keyword(s):  
Evolutionary Algorithms ◽  
Optimization Problems ◽  
Benchmark Problems ◽  
Pareto Optimal ◽  
Multi Criteria Decision Making ◽  
Pareto Optimal Solutions ◽  
Assessment Methodology ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Multi Objective

Being capable of finding a set of pareto-optimal solutions in a single run is a necessary feature for multi-criteria decision making, Evolutionary algorithms (EAs) have attracted many researchers and practitioners to address the solution of Multi-objective Optimization Problems (MOPs). In a previous work, we developed a Pareto Differential Evolution (PDE) algorithm to handle multi-objective optimization problems. Despite the overwhelming number of Multi-objective Evolutionary Algorithms (MEAs) in the literature, little work has been done to identify the best MEA using an appropriate assessment methodology. In this chapter, we compare our algorithm with twelve other well-known MEAs, using a popular assessment methodology, by solving two benchmark problems. The comparison shows the superiority of our algorithm over others.

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.

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