A Multiobjective Particle Swarm Optimizer for Constrained Optimization

2013 ◽  
pp. 71-95
Author(s):  
Gary G. Yen ◽  
Wen-Fung Leong
Keyword(s):  
Optimization Problems ◽  
Particle Swarm ◽  
Optimal Solution ◽  
Constraint Handling ◽  
Benchmark Problems ◽  
Particle Swarm Optimizer ◽  
Multiobjective Optimization Problems ◽  
Feasible Solutions ◽  
Constrained Multiobjective Optimization

Constraint handling techniques are mainly designed for evolutionary algorithms to solve constrained multiobjective optimization problems (CMOPs). Most multiojective particle swarm optimization (MOPSO) designs adopt these existing constraint handling techniques to deal with CMOPs. In the proposed constrained MOPSO, information related to particles’ infeasibility and feasibility status is utilized effectively to guide the particles to search for feasible solutions and improve the quality of the optimal solution. This information is incorporated into the four main procedures of a standard MOPSO algorithm. The involved procedures include the updating of personal best archive based on the particles’ Pareto ranks and their constraint violation values; the adoption of infeasible global best archives to store infeasible nondominated solutions; the adjustment of acceleration constants that depend on the personal bests’ and selected global best’s infeasibility and feasibility status; and the integration of personal bests’ feasibility status to estimate the mutation rate in the mutation procedure. Simulation to investigate the proposed constrained MOPSO in solving the selected benchmark problems is conducted. The simulation results indicate that the proposed constrained MOPSO is highly competitive in solving most of the selected benchmark problems.

A Multiobjective Particle Swarm Optimizer for Constrained Optimization

2011 ◽  
Vol 2 (1) ◽  
pp. 1-23 ◽  
Author(s):  
Gary G. Yen ◽  
Wen-Fung Leong
Keyword(s):  
Optimization Problems ◽  
Particle Swarm ◽  
Optimal Solution ◽  
Constraint Handling ◽  
Benchmark Problems ◽  
Particle Swarm Optimizer ◽  
Multiobjective Optimization Problems ◽  
Feasible Solutions ◽  
Constrained Multiobjective Optimization

Constraint handling techniques are mainly designed for evolutionary algorithms to solve constrained multiobjective optimization problems (CMOPs). Most multiojective particle swarm optimization (MOPSO) designs adopt these existing constraint handling techniques to deal with CMOPs. In the proposed constrained MOPSO, information related to particles’ infeasibility and feasibility status is utilized effectively to guide the particles to search for feasible solutions and improve the quality of the optimal solution. This information is incorporated into the four main procedures of a standard MOPSO algorithm. The involved procedures include the updating of personal best archive based on the particles’ Pareto ranks and their constraint violation values; the adoption of infeasible global best archives to store infeasible nondominated solutions; the adjustment of acceleration constants that depend on the personal bests’ and selected global best’s infeasibility and feasibility status; and the integration of personal bests’ feasibility status to estimate the mutation rate in the mutation procedure. Simulation to investigate the proposed constrained MOPSO in solving the selected benchmark problems is conducted. The simulation results indicate that the proposed constrained MOPSO is highly competitive in solving most of the selected benchmark problems.

A Particle Swarm Optimizer for Constrained Multiobjective Optimization

2015 ◽  
pp. 1246-1276
Author(s):  
Wen Fung Leong ◽  
Yali Wu ◽  
Gary G. Yen
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Optimal Solution ◽  
Constraint Handling ◽  
Benchmark Problems ◽  
Particle Swarm Optimizer ◽  
Multiobjective Optimization Problems ◽  
Feasible Solutions ◽  
Constrained Multiobjective Optimization

Generally, constraint-handling techniques are designed for evolutionary algorithms to solve Constrained Multiobjective Optimization Problems (CMOPs). Most Multiojective Particle Swarm Optimization (MOPSO) designs adopt these existing constraint-handling techniques to deal with CMOPs. In this chapter, the authors present a constrained MOPSO in which the information related to particles' infeasibility and feasibility status is utilized effectively to guide the particles to search for feasible solutions and to improve the quality of the optimal solution found. The updating of personal best archive is based on the particles' Pareto ranks and their constraint violations. The infeasible global best archive is adopted to store infeasible nondominated solutions. The acceleration constants are adjusted depending on the personal bests' and selected global bests' infeasibility and feasibility statuses. The personal bests' feasibility statuses are integrated to estimate the mutation rate in the mutation procedure. The simulation results indicate that the proposed constrained MOPSO is highly competitive in solving selected benchmark problems.

A Particle Swarm Optimizer for Constrained Multiobjective Optimization

2015 ◽  
pp. 128-159
Author(s):  
Wen Fung Leong ◽  
Yali Wu ◽  
Gary G. Yen
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Optimal Solution ◽  
Constraint Handling ◽  
Benchmark Problems ◽  
Particle Swarm Optimizer ◽  
Multiobjective Optimization Problems ◽  
Feasible Solutions ◽  
Constrained Multiobjective Optimization

Generally, constraint-handling techniques are designed for evolutionary algorithms to solve Constrained Multiobjective Optimization Problems (CMOPs). Most Multiojective Particle Swarm Optimization (MOPSO) designs adopt these existing constraint-handling techniques to deal with CMOPs. In this chapter, the authors present a constrained MOPSO in which the information related to particles' infeasibility and feasibility status is utilized effectively to guide the particles to search for feasible solutions and to improve the quality of the optimal solution found. The updating of personal best archive is based on the particles' Pareto ranks and their constraint violations. The infeasible global best archive is adopted to store infeasible nondominated solutions. The acceleration constants are adjusted depending on the personal bests' and selected global bests' infeasibility and feasibility statuses. The personal bests' feasibility statuses are integrated to estimate the mutation rate in the mutation procedure. The simulation results indicate that the proposed constrained MOPSO is highly competitive in solving selected benchmark problems.

An improved proximal method with quasi-distance for nonconvex multiobjective optimization problem

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Fouzia Amir ◽  
Ali Farajzadeh ◽  
Jehad Alzabut
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Convergence Result ◽  
Proximal Method ◽  
Pareto Solution ◽  
Multiobjective Optimization Problems ◽  
Locally Lipschitz ◽  
The Cost ◽  
Constrained Multiobjective Optimization

Abstract Multiobjective optimization is the optimization with several conflicting objective functions. However, it is generally tough to find an optimal solution that satisfies all objectives from a mathematical frame of reference. The main objective of this article is to present an improved proximal method involving quasi-distance for constrained multiobjective optimization problems under the locally Lipschitz condition of the cost function. An instigation to study the proximal method with quasi distances is due to its widespread applications of the quasi distances in computer theory. To study the convergence result, Fritz John’s necessary optimality condition for weak Pareto solution is used. The suitable conditions to guarantee that the cluster points of the generated sequences are Pareto–Clarke critical points are provided.

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.

Short-Term Generation Scheduling Solved with a Particle Swarm Optimizer

2012 ◽  
pp. 285-307
Author(s):  
Víctor Hugo Hinojosa Mateus ◽  
Cristhoper Leyton Rojas
Keyword(s):  
Optimization Problems ◽  
Water Discharge ◽  
Particle Swarm ◽  
Short Term ◽  
Particle Swarm Optimizer ◽  
Discharge Rates ◽  
Generation Scheduling ◽  
Decision Variables ◽  
Feasible Solutions ◽  
Feasible Space

In this chapter, a particle swarm optimizer is applied to solve the problem of short-term Hydrothermal Generation Scheduling Problem – one day to one week in advance. The optimization problems have been formulated taking into account binary and real variables (water discharge rates and thermal states of the units). This proposal is based on a strategy to generate and keep the decision variables on feasible space through the correction operators, which were applied to each constraint. Such operators not only improve the quality of the final solutions, but also significantly improve the convergence of the search process due to the use of feasible solutions. The results and effectiveness of the proposed technique are compared to those previously discussed in the literature such as PSO, GA, and DP, among others.

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.

scholarly journals Accelerated Particle Swarm Optimizer for Optimizing Problems of Structural Engineering

2018 ◽  
Vol 10 (01) ◽  
pp. 47-54
Author(s):  
Meenu Sharma (Dwivedi) ◽  
Shahnwaz Alam ◽  
M. I. Khan
Keyword(s):  
Constrained Optimization ◽  
Structural Engineering ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Optimal Solution ◽  
Feasible Region ◽  
Particle Swarm Optimizer ◽  
Numerical Result ◽  
Accelerated Particle Swarm Optimization ◽  
Structural Design Optimization

The aim of the present work is to find a solution to non-linear constrained optimization problems of structure. Constrained optimization difficulties are practical shortcomings. The loopholes of traditional numerical methods are being removed by heuristic methods as no requirement of the functional derivatives is desired and approaches to the global way out. This article presents a “penalty guided Accelerated Particle Swarm Optimization (APSO) algorithm” to search the problem’s optimal solution in the feasible region of whole search domain. There is numerical result and comparison of the structural design optimization problems. The way out by the current perspective proves to be the better than other techniques and it can be said that our findings show better solutions to engineering problems than those earlier obtained using current algorithms.

Sign in / Sign up

Export Citation Format

Share Document