scholarly journals D2MOPSO: MOPSO Based on Decomposition and Dominance with Archiving Using Crowding Distance in Objective and Solution Spaces

2014 ◽  
Vol 22 (1) ◽  
pp. 47-77 ◽  
Author(s):  
N. Al Moubayed ◽  
A. Petrovski ◽  
J. McCall
Keyword(s):  
Optimization Problems ◽  
State Of The Art ◽  
Statistical Tests ◽  
Test Problems ◽  
Multi Objective Optimization ◽  
Improved Method ◽  
Particle Swarm Optimizer ◽  
Multi Objective ◽  
Wide Range ◽  
Comparison And Analysis

This paper improves a recently developed multi-objective particle swarm optimizer ([Formula: see text]) that incorporates dominance with decomposition used in the context of multi-objective optimization. Decomposition simplifies a multi-objective problem (MOP) by transforming it to a set of aggregation problems, whereas dominance plays a major role in building the leaders’ archive. [Formula: see text] introduces a new archiving technique that facilitates attaining better diversity and coverage in both objective and solution spaces. The improved method is evaluated on standard benchmarks including both constrained and unconstrained test problems, by comparing it with three state of the art multi-objective evolutionary algorithms: MOEA/D, OMOPSO, and dMOPSO. The comparison and analysis of the experimental results, supported by statistical tests, indicate that the proposed algorithm is highly competitive, efficient, and applicable to a wide range of multi-objective optimization problems.

Efficient Computation of Probabilistic Dominance in Multi-objective Optimization

2021 ◽  
Vol 1 (4) ◽  
pp. 1-26
Author(s):  
Faramarz Khosravi ◽  
Alexander Rass ◽  
Jürgen Teich
Keyword(s):  
Optimization Problems ◽  
Statistical Tests ◽  
Optimization Techniques ◽  
Simultaneous Optimization ◽  
Sampled Data ◽  
Efficient Computation ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Conflicting Objectives ◽  
Comparison Operator

Real-world problems typically require the simultaneous optimization of multiple, often conflicting objectives. Many of these multi-objective optimization problems are characterized by wide ranges of uncertainties in their decision variables or objective functions. To cope with such uncertainties, stochastic and robust optimization techniques are widely studied aiming to distinguish candidate solutions with uncertain objectives specified by confidence intervals, probability distributions, sampled data, or uncertainty sets. In this scope, this article first introduces a novel empirical approach for the comparison of candidate solutions with uncertain objectives that can follow arbitrary distributions. The comparison is performed through accurate and efficient calculations of the probability that one solution dominates the other in terms of each uncertain objective. Second, such an operator can be flexibly used and combined with many existing multi-objective optimization frameworks and techniques by just substituting their standard comparison operator, thus easily enabling the Pareto front optimization of problems with multiple uncertain objectives. Third, a new benchmark for evaluating uncertainty-aware optimization techniques is introduced by incorporating different types of uncertainties into a well-known benchmark for multi-objective optimization problems. Fourth, the new comparison operator and benchmark suite are integrated into an existing multi-objective optimization framework that features a selection of multi-objective optimization problems and algorithms. Fifth, the efficiency in terms of performance and execution time of the proposed comparison operator is evaluated on the introduced uncertainty benchmark. Finally, statistical tests are applied giving evidence of the superiority of the new comparison operator in terms of \epsilon -dominance and attainment surfaces in comparison to previously proposed approaches.

A Memetic Optimization Strategy Based on Dimension Reduction in Decision Space

2015 ◽  
Vol 23 (1) ◽  
pp. 69-100 ◽  
Author(s):  
Handing Wang ◽  
Licheng Jiao ◽  
Ronghua Shang ◽  
Shan He ◽  
Fang Liu
Keyword(s):  
Dimension Reduction ◽  
Optimization Problems ◽  
State Of The Art ◽  
Search Space ◽  
Optimization Strategy ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Decision Space ◽  
Multi Objective ◽  
Decision Variables

There can be a complicated mapping relation between decision variables and objective functions in multi-objective optimization problems (MOPs). It is uncommon that decision variables influence objective functions equally. Decision variables act differently in different objective functions. Hence, often, the mapping relation is unbalanced, which causes some redundancy during the search in a decision space. In response to this scenario, we propose a novel memetic (multi-objective) optimization strategy based on dimension reduction in decision space (DRMOS). DRMOS firstly analyzes the mapping relation between decision variables and objective functions. Then, it reduces the dimension of the search space by dividing the decision space into several subspaces according to the obtained relation. Finally, it improves the population by the memetic local search strategies in these decision subspaces separately. Further, DRMOS has good portability to other multi-objective evolutionary algorithms (MOEAs); that is, it is easily compatible with existing MOEAs. In order to evaluate its performance, we embed DRMOS in several state of the art MOEAs to facilitate our experiments. The results show that DRMOS has the advantage in terms of convergence speed, diversity maintenance, and portability when solving MOPs with an unbalanced mapping relation between decision variables and objective functions.

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 An Ensemble Framework of Evolutionary Algorithm for Constrained Multi-Objective Optimization

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 116
Author(s):  
Junhua Ku ◽  
Fei Ming ◽  
Wenyin Gong
Keyword(s):  
Evolutionary Algorithms ◽  
Real World ◽  
Optimization Problems ◽  
State Of The Art ◽  
Multi Objective Optimization ◽  
The Real ◽  
Multi Objective ◽  
The Past ◽  
Hypervolume Indicator ◽  
Real World Problems

In the real-world, symmetry or asymmetry widely exists in various problems. Some of them can be formulated as constrained multi-objective optimization problems (CMOPs). During the past few years, handling CMOPs by evolutionary algorithms has become more popular. Lots of constrained multi-objective optimization evolutionary algorithms (CMOEAs) have been proposed. Whereas different CMOEAs may be more suitable for different CMOPs, it is difficult to choose the best one for a CMOP at hand. In this paper, we propose an ensemble framework of CMOEAs that aims to achieve better versatility on handling diverse CMOPs. In the proposed framework, the hypervolume indicator is used to evaluate the performance of CMOEAs, and a decreasing mechanism is devised to delete the poorly performed CMOEAs and to gradually determine the most suitable CMOEA. A new CMOEA, namely ECMOEA, is developed based on the framework and three state-of-the-art CMOEAs. Experimental results on five benchmarks with totally 52 instances demonstrate the effectiveness of our approach. In addition, the superiority of ECMOEA is verified through comparisons to seven state-of-the-art CMOEAs. Moreover, the effectiveness of ECMOEA on the real-world problems is also evaluated for eight instances.

scholarly journals Multi-Objective Optimization Through Pareto Minimal Correction Subsets

2018 ◽  
Author(s):  
Miguel Terra-Neves ◽  
Inês Lynce ◽  
Vasco Manquinho
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
State Of The Art ◽  
Optimal Solution ◽  
Approximate Solutions ◽  
Pareto Optimal ◽  
Constrained Optimization Problems ◽  
Multi Objective ◽  
Wide Range ◽  
Constraint Set

A Minimal Correction Subset (MCS) of an unsatisfiable constraint set is a minimal subset of constraints that, if removed, makes the constraint set satisfiable. MCSs enjoy a wide range of applications, such as finding approximate solutions to constrained optimization problems. However, existing work on applying MCS enumeration to optimization problems focuses on the single-objective case. In this work, Pareto Minimal Correction Subsets (Pareto-MCSs) are proposed for approximating the Pareto-optimal solution set of multi-objective constrained optimization problems. We formalize and prove an equivalence relationship between Pareto-optimal solutions and Pareto-MCSs. Moreover, Pareto-MCSs and MCSs can be connected in such a way that existing state-of-the-art MCS enumeration algorithms can be used to enumerate Pareto-MCSs. Finally, experimental results on the multi-objective virtual machine consolidation problem show that the Pareto-MCS approach is competitive with state-of-the-art algorithms.

scholarly journals An Entropy-Based Multiobjective Evolutionary Algorithm with an Enhanced Elite Mechanism

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Yufang Qin ◽  
Junzhong Ji ◽  
Chunnian Liu
Keyword(s):  
Evolutionary Algorithm ◽  
Pareto Front ◽  
Optimization Problem ◽  
State Of The Art ◽  
Early Stage ◽  
Test Problems ◽  
Multiobjective Optimization Problem ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective

Multiobjective optimization problem (MOP) is an important and challenging topic in the fields of industrial design and scientific research. Multi-objective evolutionary algorithm (MOEA) has proved to be one of the most efficient algorithms solving the multi-objective optimization. In this paper, we propose an entropy-based multi-objective evolutionary algorithm with an enhanced elite mechanism (E-MOEA), which improves the convergence and diversity of solution set in MOPs effectively. In this algorithm, an enhanced elite mechanism is applied to guide the direction of the evolution of the population. Specifically, it accelerates the population to approach the true Pareto front at the early stage of the evolution process. A strategy based on entropy is used to maintain the diversity of population when the population is near to the Pareto front. The proposed algorithm is executed on widely used test problems, and the simulated results show that the algorithm has better or comparative performances in convergence and diversity of solutions compared with two state-of-the-art evolutionary algorithms: NSGA-II, SPEA2 and the MOSADE.

scholarly journals An integrated cuckoo search optimizer for single and multi-objective optimization problems

2021 ◽  
Vol 7 ◽  
pp. e370
Author(s):  
Xiangbo Qi ◽  
Zhonghu Yuan ◽  
Yan Song
Keyword(s):  
Optimization Problems ◽  
Cuckoo Search ◽  
Search Strategies ◽  
Comprehensive Analysis ◽  
Experimental Results ◽  
Test Problems ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Multiple Strategies ◽  
Single Objective

Integrating heterogeneous biological-inspired strategies and mechanisms into one algorithm can avoid the shortcomings of single algorithm. This article proposes an integrated cuckoo search optimizer (ICSO) for single objective optimization problems, which incorporates the multiple strategies into the cuckoo search (CS) algorithm. The paper also considers the proposal of multi-objective versions of ICSO called MOICSO. The two algorithms presented in this paper are benchmarked by a set of benchmark functions. The comprehensive analysis of the experimental results based on the considered test problems and comparisons with other recent methods illustrate the effectiveness of the proposed integrated mechanism of different search strategies and demonstrate the performance superiority of the proposed algorithm.

scholarly journals A New Chaotic-Based Approach for Multi-Objective Optimization

Algorithms ◽  
2020 ◽  
Vol 13 (9) ◽  
pp. 204
Author(s):  
Nassime Aslimani ◽  
Talbi El-ghazali ◽  
Rachid Ellaia
Keyword(s):  
Optimization Problems ◽  
State Of The Art ◽  
Multi Objective Optimization ◽  
New Approach ◽  
Chaotic Search ◽  
Multi Objective ◽  
Search Approach

Multi-objective optimization problems (MOPs) have been widely studied during the last decades. In this paper, we present a new approach based on Chaotic search to solve MOPs. Various Tchebychev scalarization strategies have been investigated. Moreover, a comparison with state of the art algorithms on different well known bound constrained benchmarks shows the efficiency and the effectiveness of the proposed Chaotic search approach.

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