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.

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.

scholarly journals A Multi-objective Particle Swarm Optimization Based on P System Theory

2018 ◽  
Vol 232 ◽  
pp. 03039
Author(s):  
Taowei Chen ◽  
Yiming Yu ◽  
Kun Zhao
Keyword(s):  
Particle Swarm Optimization ◽  
Pareto Front ◽  
Search Strategy ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Pso Algorithm ◽  
P System ◽  
Multi Objective Optimization ◽  
Swarm Optimization ◽  
Multi Objective

Particle swarm optimization(PSO) algorithm has been widely applied in solving multi-objective optimization problems(MOPs) since it was proposed. However, PSO algorithms updated the velocity of each particle using a single search strategy, which may be difficult to obtain approximate Pareto front for complex MOPs. In this paper, inspired by the theory of P system, a multi-objective particle swarm optimization (PSO) algorithm based on the framework of membrane system(PMOPSO) is proposed to solve MOPs. According to the hierarchical structure, objects and rules of P system, the PSO approach is used in elementary membranes to execute multiple search strategy. And non-dominated sorting and crowding distance is used in skin membrane for improving speed of convergence and maintaining population diversity by evolutionary rules. Compared with other multi-objective optimization algorithm including MOPSO, dMOPSO, SMPSO, MMOPSO, MOEA/D, SPEA2, PESA2, NSGAII on a benchmark series function, the experimental results indicate that the proposed algorithm is not only feasible and effective but also have a better convergence to true Pareto front.

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.

Toward the Use of Pareto Performance Solutions and Pareto Robustness Solutions for Multi-Objective Robust Optimization Problems

2012 ◽  
Author(s):  
Weijun Wang ◽  
Stéphane Caro ◽  
Fouad Bennis ◽  
Oscar Brito Augusto
Keyword(s):  
Robust Optimization ◽  
Pareto Front ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Multi Objective Optimization ◽  
Robust Solutions ◽  
Multi Objective ◽  
Robust Optimization Problem ◽  
Design Solutions ◽  
Further Development

For Multi-Objective Robust Optimization Problem (MOROP), it is important to obtain design solutions that are both optimal and robust. To find these solutions, usually, the designer need to set a threshold of the variation of Performance Functions (PFs) before optimization, or add the effects of uncertainties on the original PFs to generate a new Pareto robust front. In this paper, we divide a MOROP into two Multi-Objective Optimization Problems (MOOPs). One is the original MOOP, another one is that we take the Robustness Functions (RFs), robust counterparts of the original PFs, as optimization objectives. After solving these two MOOPs separately, two sets of solutions come out, namely the Pareto Performance Solutions (PP) and the Pareto Robustness Solutions (PR). Make a further development on these two sets, we can get two types of solutions, namely the Pareto Robustness Solutions among the Pareto Performance Solutions (PR(PP)), and the Pareto Performance Solutions among the Pareto Robustness Solutions (PP(PR)). Further more, the intersection of PR(PP) and PP(PR) can represent the intersection of PR and PP well. Then the designer can choose good solutions by comparing the results of PR(PP) and PP(PR). Thanks to this method, we can find out the optimal and robust solutions without setting the threshold of the variation of PFs nor losing the initial Pareto front. Finally, an illustrative example highlights the contributions of the paper.

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.

Optimization of Vehicle-Borne Radar Antenna Pedestal Based on Modified NSGA-II

2014 ◽  
Vol 945-949 ◽  
pp. 2241-2247
Author(s):  
De Gao Zhao ◽  
Qiang Li
Keyword(s):  
Pareto Front ◽  
Optimization Problems ◽  
Population Diversity ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective ◽  
Sorting Process ◽  
Definition Of ◽  
Radar Antenna ◽  
Modified Algorithm

This paper deals with application of Non-dominated Sorting Genetic Algorithm with elitism (NSGA-II) to solve multi-objective optimization problems of designing a vehicle-borne radar antenna pedestal. Five technical improvements are proposed due to the disadvantages of NSGA-II. They are as follow: (1) presenting a new method to calculate the fitness of individuals in population; (2) renewing the definition of crowding distance; (3) introducing a threshold for choosing elitist; (4) reducing some redundant sorting process; (5) developing a self-adaptive arithmetic cross and mutation probability. The modified algorithm can lead to better population diversity than the original NSGA-II. Simulation results prove rationality and validity of the modified NSGA-II. A uniformly distributed Pareto front can be obtained by using the modified NSGA-II. Finally, a multi-objective problem of designing a vehicle-borne radar antenna pedestal is settled with the modified algorithm.

Expected-Improvement-Based Methods for Adaptive Sampling in Multi-Objective Optimization Problems

2016 ◽  
Author(s):  
Jesper Kristensen ◽  
You Ling ◽  
Isaac Asher ◽  
Liping Wang
Keyword(s):  
Convex Hull ◽  
Design Optimization ◽  
Adaptive Sampling ◽  
Pareto Front ◽  
Performance Metrics ◽  
Sampling Methods ◽  
Optimization Problems ◽  
Expected Improvement ◽  
Multi Objective Optimization ◽  
Multi Objective

Adaptive sampling methods have been used to build accurate meta-models across large design spaces from which engineers can explore data trends, investigate optimal designs, study the sensitivity of objectives on the modeling design features, etc. For global design optimization applications, adaptive sampling methods need to be extended to sample more efficiently near the optimal domains of the design space (i.e., the Pareto front/frontier in multi-objective optimization). Expected Improvement (EI) methods have been shown to be efficient to solve design optimization problems using meta-models by incorporating prediction uncertainty. In this paper, a set of state-of-the-art methods (hypervolume EI method and centroid EI method) are presented and implemented for selecting sampling points for multi-objective optimizations. The classical hypervolume EI method uses hyperrectangles to represent the Pareto front, which shows undesirable behavior at the tails of the Pareto front. This issue is addressed utilizing the concepts from physical programming to shape the Pareto front. The modified hypervolume EI method can be extended to increase local Pareto front accuracy in any area identified by an engineer, and this method can be applied to Pareto frontiers of any shape. A novel hypervolume EI method is also developed that does not rely on the assumption of hyperrectangles, but instead assumes the Pareto frontier can be represented by a convex hull. The method exploits fast methods for convex hull construction and numerical integration, and results in a Pareto front shape that is desired in many practical applications. Various performance metrics are defined in order to quantitatively compare and discuss all methods applied to a particular 2D optimization problem from the literature. The modified hypervolume EI methods lead to dramatic resource savings while improving the predictive capabilities near the optimal objective values.

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