scholarly journals Improving Vector Evaluated Particle Swarm Optimisation Using Multiple Nondominated Leaders

2014 ◽  
Vol 2014 ◽  
pp. 1-21 ◽  
Author(s):  
Kian Sheng Lim ◽  
Salinda Buyamin ◽  
Anita Ahmad ◽  
Mohd Ibrahim Shapiai ◽  
Faradila Naim ◽  
...  
Keyword(s):  
Objective Function ◽  
Pareto Front ◽  
Particle Swarm ◽  
Particle Swarm Optimisation ◽  
Optimal Solutions ◽  
Multiobjective Optimisation ◽  
Nondominated Solutions

The vector evaluated particle swarm optimisation (VEPSO) algorithm was previously improved by incorporating nondominated solutions for solving multiobjective optimisation problems. However, the obtained solutions did not converge close to the Pareto front and also did not distribute evenly over the Pareto front. Therefore, in this study, the concept of multiple nondominated leaders is incorporated to further improve the VEPSO algorithm. Hence, multiple nondominated solutions that are best at a respective objective function are used to guide particles in finding optimal solutions. The improved VEPSO is measured by the number of nondominated solutions found, generational distance, spread, and hypervolume. The results from the conducted experiments show that the proposed VEPSO significantly improved the existing VEPSO algorithms.

scholarly journals Improving Vector Evaluated Particle Swarm Optimisation by Incorporating Nondominated Solutions

2013 ◽  
Vol 2013 ◽  
pp. 1-19 ◽  
Author(s):  
Kian Sheng Lim ◽  
Zuwairie Ibrahim ◽  
Salinda Buyamin ◽  
Anita Ahmad ◽  
Faradila Naim ◽  
...  
Keyword(s):  
Objective Function ◽  
Performance Measures ◽  
Particle Swarm ◽  
Particle Swarm Optimisation ◽  
Multiobjective Optimisation ◽  
Nondominated Solutions ◽  
Optimisation Algorithm ◽  
Particle Swarm Optimisation Algorithm

The Vector Evaluated Particle Swarm Optimisation algorithm is widely used to solve multiobjective optimisation problems. This algorithm optimises one objective using a swarm of particles where their movements are guided by the best solution found by another swarm. However, the best solution of a swarm is only updated when a newly generated solution has better fitness than the best solution at the objective function optimised by that swarm, yielding poor solutions for the multiobjective optimisation problems. Thus, an improved Vector Evaluated Particle Swarm Optimisation algorithm is introduced by incorporating the nondominated solutions as the guidance for a swarm rather than using the best solution from another swarm. In this paper, the performance of improved Vector Evaluated Particle Swarm Optimisation algorithm is investigated using performance measures such as the number of nondominated solutions found, the generational distance, the spread, and the hypervolume. The results suggest that the improved Vector Evaluated Particle Swarm Optimisation algorithm has impressive performance compared with the conventional Vector Evaluated Particle Swarm Optimisation algorithm.

Constraint Handling in Particle Swarm Optimization

2010 ◽  
Vol 1 (1) ◽  
pp. 42-63 ◽  
Author(s):  
Wen Fung Leong ◽  
Gary G. Yen
Keyword(s):  
Particle Swarm Optimization ◽  
Pareto Front ◽  
Particle Swarm ◽  
Constraint Handling ◽  
Hidden Information ◽  
Swarm Optimization ◽  
Nondominated Solutions ◽  
Local Searches ◽  
Multiobjective Approach ◽  
Fine Tune

In this article, the authors propose a particle swarm optimization (PSO) for constrained optimization. The proposed PSO adopts a multiobjective approach to constraint handling. Procedures to update the feasible and infeasible personal best are designed to encourage finding feasible regions and convergence toward the Pareto front. In addition, the infeasible nondominated solutions are stored in the global best archive to exploit the hidden information for guiding the particles toward feasible regions. Furthermore, the number of feasible personal best in the personal best memory and the scalar constraint violations of personal best and global best are used to adapt the acceleration constants in the PSO flight equations. The purpose is to find more feasible particles and search for better solutions during the process. The mutation procedure is applied to encourage global and fine-tune local searches. The simulation results indicate that the proposed constrained PSO is highly competitive, achieving promising performance.

scholarly journals Adaptive Multiswarm Comprehensive Learning Particle Swarm Optimization

Information ◽  
2018 ◽  
Vol 9 (7) ◽  
pp. 173 ◽  
Author(s):  
Xiang Yu ◽  
Claudio Estevez
Keyword(s):  
Particle Swarm Optimization ◽  
Particle Velocity ◽  
Pareto Front ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Search Performance ◽  
Swarm Optimization ◽  
Nondominated Solutions ◽  
The Difference ◽  
Update Strategy

Multiswarm comprehensive learning particle swarm optimization (MSCLPSO) is a multiobjective metaheuristic recently proposed by the authors. MSCLPSO uses multiple swarms of particles and externally stores elitists that are nondominated solutions found so far. MSCLPSO can approximate the true Pareto front in one single run; however, it requires a large number of generations to converge, because each swarm only optimizes the associated objective and does not learn from any search experience outside the swarm. In this paper, we propose an adaptive particle velocity update strategy for MSCLPSO to improve the search efficiency. Based on whether the elitists are indifferent or complex on each dimension, each particle adaptively determines whether to just learn from some particle in the same swarm, or additionally from the difference of some pair of elitists for the velocity update on that dimension, trying to achieve a tradeoff between optimizing the associated objective and exploring diverse regions of the Pareto set. Experimental results on various two-objective and three-objective benchmark optimization problems with different dimensional complexity characteristics demonstrate that the adaptive particle velocity update strategy improves the search performance of MSCLPSO significantly and is able to help MSCLPSO locate the true Pareto front more quickly and obtain better distributed nondominated solutions over the entire Pareto front.

scholarly journals Parametric Study of Dual-particle Swarm Optimisation-modified Adaptive Bats Sonar Algorithm on Multi-objective Benchmark Test Functions

Mekatronika ◽  
2019 ◽  
Vol 1 (2) ◽  
pp. 72-80
Author(s):  
Nafrizuan Mat Yahya ◽  
Nur Atikah Nor’Azlan ◽  
M Osman Tokhi
Keyword(s):  
Parametric Study ◽  
Pareto Front ◽  
Particle Swarm ◽  
Particle Swarm Optimisation ◽  
Test Functions ◽  
Benchmark Test ◽  
Multi Objective ◽  
Searching Strategy ◽  
Particle Swarm Optimisation Algorithm ◽  
Benchmark Test Functions

An integrated algorithm for solving multi-objective optimisation problems using a dual- level searching approach is presented. The proposed algorithm named as dual-particle swarm optimisation-modified adaptive bats sonar algorithm (D-PSO-MABSA) where the concept of echolocation of a colony of bats to find prey in the modified adaptive bats sonar algorithm is combined with the established particle swarm optimisation algorithm. The proposed algorithm combines the advantages of both particle swarm optimisation and modified adaptive bats sonar algorithm approach to handling the complexity of multi-objective optimisation problems. These include swarm flight attitude and swarm searching strategy. The performance of the algorithm is verified through several multi- objective optimisation benchmark test functions. The acquired results show that the proposed algorithm performs well to produce a reliable Pareto front. The proposed algorithm can thus be an effective method for solving multi-objective optimisation problems.

Is Our Archiving Reliable? Multiobjective Archiving Methods on “Simple” Artificial Input Sequences

2021 ◽  
Vol 1 (3) ◽  
pp. 1-19
Author(s):  
Miqing Li
Keyword(s):  
Pareto Front ◽  
Search Process ◽  
Good Representation ◽  
Optimal Solutions ◽  
Fixed Size ◽  
Multiobjective Optimisation ◽  
Common Component ◽  
Front Shape ◽  
Internal Set ◽  
Pareto Fronts

In evolutionary multiobjective optimisation ( EMO ), archiving is a common component that maintains an (external or internal) set during the search process, typically with a fixed size, in order to provide a good representation of high-quality solutions produced. Such an archive set can be used solely to store the final results shown to the decision maker, but in many cases may participate in the process of producing solutions (e.g., as a solution pool where the parental solutions are selected). Over the last three decades, archiving stands as an important issue in EMO, leading to the emergence of various methods such as those based on Pareto, indicator, or decomposition criteria. Such methods have demonstrated their effectiveness in literature and have been believed to be good options to many problems, particularly those having a regular Pareto front shape, e.g., a simplex shape. In this article, we challenge this belief. We do this through artificially constructing several sequences with extremely simple shapes, i.e., 1D/2D simplex Pareto front. We show the struggle of predominantly used archiving methods which have been deemed to well handle such shapes. This reveals that the order of solutions entering the archive matters, and that current EMO algorithms may not be fully capable of maintaining a representative population on problems with linear Pareto fronts even in the case that all of their optimal solutions can be found.

MULTIOBJECTIVE PARTICLE SWARM OPTIMIZATION BASED ON DIMENSIONAL UPDATE

2013 ◽  
Vol 22 (03) ◽  
pp. 1350015 ◽  
Author(s):  
HEMING XU ◽  
YINGLIN WANG ◽  
XIN XU
Keyword(s):  
Particle Swarm Optimization ◽  
Pareto Front ◽  
Particle Swarm ◽  
Experimental Results ◽  
Entire Region ◽  
Swarm Optimization ◽  
Nondominated Solutions ◽  
Limited Size ◽  
Multiobjective Particle Swarm Optimization ◽  
The Impact

For multiobjective particle swarm optimization (MOPSO), two particles may be incomparable, i. e., not dominated by each other. The personal best and the global best for the particle become less optimal, thus the convergence becomes slow. Even worse, an archive of a limited size can not cover the entire region dominated by the Pareto front, the uncovered region can contain unidentifiable nondominated solutions that are not optimal, and thus the precision the algorithm achieves encounters a plateau. Therefore we propose dimensional update, i. e., evaluating the particle's fitness after updating each variable of its position. Separate consideration of the impact of each variable decreases the occurrence of incomparable relations, thus improves the performance. Experimental results validate the efficiency of our algorithm.

scholarly journals Robust multi-objective calibration strategies – chances for improving flood forecasting

2011 ◽  
Vol 8 (2) ◽  
pp. 3693-3741 ◽  
Author(s):  
T. Krauße ◽  
J. Cullmann ◽  
P. Saile ◽  
G. H. Schmitz
Keyword(s):  
Parameter Estimation ◽  
Objective Function ◽  
Particle Swarm ◽  
Model Performance ◽  
Data Depth ◽  
Particle Swarm Optimisation ◽  
Multi Objective ◽  
Optimisation Algorithm ◽  
Robust Parameter ◽  
Single Objective

Abstract. Process-oriented rainfall-runoff models are designed to approximate the complex hydrologic processes within a specific catchment and in particular to simulate the discharge at the catchment outlet. Most of these models exhibit a high degree of complexity and require the determination of various parameters by calibration. Recently automatic calibration methods became popular in order to identify parameter vectors with high corresponding model performance. The model performance is often assessed by a purpose-oriented objective function. Practical experience suggests that in many situations one single objective function cannot adequately describe the model's ability to represent any aspect of the catchment's behaviour. This is regardless whether the objective is aggregated of several criteria that measure different (possibly opposite) aspects of the system behaviour. One strategy to circumvent this problem is to define multiple objective functions and to apply a multi-objective optimisation algorithm to identify the set of Pareto optimal or non-dominated solutions. One possible approach to estimate the Pareto set effectively and efficiently is the particle swarm optimisation (PSO). It has already been successfully applied in various other fields and has been reported to show effective and efficient performance. Krauße and Cullmann (2011b) presented a method entitled ROPEPSO which merges the strengths of PSO and data depth measures in order to identify robust parameter vectors for hydrological models. In this paper we present a multi-objective parameter estimation algorithm, entitled the Multi-Objective Robust Particle Swarm Parameter Estimation (MO-ROPE). The algorithm is a further development of the previously mentioned single-objective ROPEPSO approach. It applies a newly developed multi-objective particle swarm optimisation algorithm in order to identify non-dominated robust model parameter vectors. Subsequently it samples robust parameter vectors by the application of data depth metrics. In a preliminary assessment MO-PSO-GA is compared with other multi-objective optimisation algorithms. In the frame of a real world case study MO-ROPE is applied identifying robust parameter vectors of a distributed hydrological model with focus on flood events in a small, pre-alpine, and fast responding catchment in Switzerland. The method is compared with existing robust parameter estimation methods.

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