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.

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.

Solving Expensive Multi-Objective Optimization Problems by Kriging Model with Multi-Point Updating Strategy

2014 ◽  
Vol 685 ◽  
pp. 667-670 ◽  
Author(s):  
Ding Han ◽  
Jian Rong Zheng
Keyword(s):  
Optimization Problem ◽  
Optimization Problems ◽  
Average Distance ◽  
Kriging Model ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Good Convergence ◽  
Multi Objective

A method which utilizes Kriging model and a multi-point updating strategy is put forward for solving expensive multi-objective optimization problems. Assisted by a defined cheaper multi-objective optimization problem and a maximum average distance criterion, multiple updating points can be found. The proposed method is tested on two numerical functions and a ten-bar truss problem, the results show that the proposed method is efficient in obtaining Pareto optimal solutions with good convergence and diversity when the same computation resource is used comparing with two other methods.

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.

Multi-objective particle swarm optimization using Pareto-based set and aggregation approach

2017 ◽  
Vol 31 (19-21) ◽  
pp. 1740073 ◽  
Author(s):  
Song Huang ◽  
Yan Wang ◽  
Zhicheng Ji
Keyword(s):  
Particle Swarm Optimization ◽  
Local Search ◽  
Real World ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Pareto Set ◽  
Multi Objective Optimization ◽  
Particle Swarm Optimizer ◽  
Swarm Optimization ◽  
Multi Objective

Multi-objective optimization problems (MOPs) need to be solved in real world recently. In this paper, a multi-objective particle swarm optimization based on Pareto set and aggregation approach was proposed to deal with MOPs. Firstly, velocities and positions were updated similar to PSO. Then, global-best set was defined in particle swarm optimizer to preserve Pareto-based set obtained by the population. Specifically, a hybrid updating strategy based on Pareto set and aggregation approach was introduced to update the global-best set and local search was carried on global-best set. Thirdly, personal-best positions were updated in decomposition way, and global-best position was selected from global-best set. Finally, ZDT instances and DTLZ instances were selected to evaluate the performance of MULPSO and the results show validity of the proposed algorithm for MOPs.

scholarly journals A NEW PROBABILISTIC ALGORITHM FOR SOLVING A CLASS OF SINGLE OR MULTI-OBJECTIVE OPTIMAL PROBLEMS

2009 ◽  
Vol 12 (11) ◽  
pp. 11-26
Author(s):  
Hao Van Tran ◽  
Thong Huu Nguyen
Keyword(s):  
Numerical Optimization ◽  
Optimization Problems ◽  
Optimization Technique ◽  
Fixed Number ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Probabilistic Algorithm ◽  
Multi Objective ◽  
Single Objective

We consider a class of single-objective optimization problems which haves the character: there is a fixed number k (1≤k<n) that is independent of the size n of the problem such that if we only need to change values of k variables then it has the ability to find a better solution than the current one, let us call it Ok. In this paper, we propose a new numerical optimization technique, Search Via Probability (SVP) algorithm, for solving single objective optimization problems of the class Ok. The SVP algorithm uses probabilities to control the process of searching for optimal solutions. We calculate probabilities of the appearance of a better solution than the current one on each of iterations, and on the performance of SVP algorithm we create good conditions for its appearance. We tested this approach by implementing the SVP algorithm on some test single-objective and multi objective optimization problems, and we found good and very stable results.

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.

Robustness Against Large Variations in Multi-Objective Optimization Problems

2013 ◽  
Author(s):  
Weijun Wang ◽  
Stéphane Caro ◽  
Fouad Bennis
Keyword(s):  
Optimization Problems ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Design Environment ◽  
Multi Objective ◽  
Uncertainty Sources ◽  
Design Variables ◽  
Robustness Index ◽  
Environment Parameters

In the presence of multiple optimal solutions in multi-modal optimization problems and in multi-objective optimization problems, the designer may be interested in the robustness of those solutions to make a decision. Here, the robustness is related to the sensitivity of the performance functions to uncertainties. The uncertainty sources include the uncertainties in the design variables, in the design environment parameters, in the model of objective functions and in the designer’s preference. There exist many robustness indices in the literature that deal with small variations in the design variables and design environment parameters, but few robustness indices consider large variations. In this paper, a new robustness index is introduced to deal with large variations in the design environment parameters. The proposed index is bounded between zero and one, and measures the probability of a solution to be optimal with respect to the values of the design environment parameters. The larger the robustness index, the more robust the solution with regard to large variations in the design environment parameters. Finally, two illustrative examples are given to highlight the contributions of this paper.

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.

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