scholarly journals Performances Assessment of MOMA-Plus Method on Multiobjective Optimization Problems

2020 ◽  
Vol 13 (1) ◽  
pp. 48-68
Author(s):  
Alexandre Som ◽  
Kounhinir Some ◽  
Abdoulaye Compaore ◽  
Blaise Some
Keyword(s):  
Multiobjective Optimization ◽  
Comparative Study ◽  
Pareto Front ◽  
Optimization Problems ◽  
Test Problems ◽  
Nsga Ii ◽  
Multiobjective Problems ◽  
Multiobjective Optimization Problems ◽  
Non Linear

This work is devoted to evaluate the performances of the MOMA-plus method in solving multiobjective optimization problems. This assessment is doing on the complexity of its algorithm, the convergence and the diversity of solutions in relation to the Pareto front. All these parameters were evaluated on non-linear multiobjective test problems and obtained solutions are compared with those provided by the NSGA-II method. This comparative study made it possible tohighlight the performances of MOMA-plus method for solving non-linear multiobjective problems.

scholarly journals Performances Assessment of MOMA-Plus Method on Multiobjective Optimization Problems

2020 ◽  
Vol 13 (1) ◽  
pp. 48-68
Author(s):  
Alexandre Som ◽  
Kounhinir Some ◽  
Abdoulaye Compaore ◽  
Blaise Some
Keyword(s):  
Multiobjective Optimization ◽  
Comparative Study ◽  
Pareto Front ◽  
Optimization Problems ◽  
Test Problems ◽  
Nsga Ii ◽  
Multiobjective Problems ◽  
Multiobjective Optimization Problems ◽  
Non Linear

This work is devoted to evaluate the performances of the MOMA-plus method in solving multiobjective optimization problems. This assessment is doing on the complexity of its algorithm, the convergence and the diversity of solutions in relation to the Pareto front. All these parameters were evaluated on non-linear multiobjective test problems and obtained solutions are compared with those provided by the NSGA-II method. This comparative study made it possible tohighlight the performances of MOMA-plus method for solving non-linear multiobjective problems.

scholarly journals Difficulty Adjustable and Scalable Constrained Multiobjective Test Problem Toolkit

2020 ◽  
Vol 28 (3) ◽  
pp. 339-378 ◽  
Author(s):  
Zhun Fan ◽  
Wenji Li ◽  
Xinye Cai ◽  
Hui Li ◽  
Caimin Wei ◽  
...  
Keyword(s):  
Evolutionary Algorithms ◽  
Multiobjective Optimization ◽  
Real World ◽  
Optimization Problems ◽  
Test Problems ◽  
Nsga Ii ◽  
Multiobjective Problems ◽  
Multiobjective Optimization Problems ◽  
Dominance Principle ◽  
Constrained Multiobjective Optimization

Multiobjective evolutionary algorithms (MOEAs) have progressed significantly in recent decades, but most of them are designed to solve unconstrained multiobjective optimization problems. In fact, many real-world multiobjective problems contain a number of constraints. To promote research on constrained multiobjective optimization, we first propose a problem classification scheme with three primary types of difficulty, which reflect various types of challenges presented by real-world optimization problems, in order to characterize the constraint functions in constrained multiobjective optimization problems (CMOPs). These are feasibility-hardness, convergence-hardness, and diversity-hardness. We then develop a general toolkit to construct difficulty adjustable and scalable CMOPs (DAS-CMOPs, or DAS-CMaOPs when the number of objectives is greater than three) with three types of parameterized constraint functions developed to capture the three proposed types of difficulty. In fact, the combination of the three primary constraint functions with different parameters allows the construction of a large variety of CMOPs, with difficulty that can be defined by a triplet, with each of its parameters specifying the level of one of the types of primary difficulty. Furthermore, the number of objectives in this toolkit can be scaled beyond three. Based on this toolkit, we suggest nine difficulty adjustable and scalable CMOPs and nine CMaOPs, to be called DAS-CMOP1-9 and DAS-CMaOP1-9, respectively. To evaluate the proposed test problems, two popular CMOEAs—MOEA/D-CDP (MOEA/D with constraint dominance principle) and NSGA-II-CDP (NSGA-II with constraint dominance principle) and two popular constrained many-objective evolutionary algorithms (CMaOEAs)—C-MOEA/DD and C-NSGA-III—are used to compare performance on DAS-CMOP1-9 and DAS-CMaOP1-9 with a variety of difficulty triplets, respectively. The experimental results reveal that mechanisms in MOEA/D-CDP may be more effective in solving convergence-hard DAS-CMOPs, while mechanisms of NSGA-II-CDP may be more effective in solving DAS-CMOPs with simultaneous diversity-, feasibility-, and convergence-hardness. Mechanisms in C-NSGA-III may be more effective in solving feasibility-hard CMaOPs, while mechanisms of C-MOEA/DD may be more effective in solving CMaOPs with convergence-hardness. In addition, none of them can solve these problems efficiently, which stimulates us to continue to develop new CMOEAs and CMaOEAs to solve the suggested DAS-CMOPs and DAS-CMaOPs.

scholarly journals From a Pareto Front to Pareto Regions: A Novel Standpoint for Multiobjective Optimization

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3152
Author(s):  
Carine M. Rebello ◽  
Márcio A. F. Martins ◽  
Daniel D. Santana ◽  
Alírio E. Rodrigues ◽  
José M. Loureiro ◽  
...  
Keyword(s):  
Multiobjective Optimization ◽  
Pareto Front ◽  
Optimization Problems ◽  
The Novel ◽  
Particle Swarm Optimizer ◽  
Novel Approach ◽  
Multiobjective Optimization Problems ◽  
Pressure Swing ◽  
Novel Concept

This work presents a novel approach for multiobjective optimization problems, extending the concept of a Pareto front to a new idea of the Pareto region. This new concept provides all the points beyond the Pareto front, leading to the same optimal condition with statistical assurance. This region is built using a Fisher–Snedecor test over an augmented Lagragian function, for which deductions are proposed here. This test is meant to provide an approximated depiction of the feasible operation region while using meta-heuristic optimization results to extract this information. To do so, a Constrained Sliding Particle Swarm Optimizer (CSPSO) was applied to solve a series of four benchmarks and a case study. The proposed test analyzed the CSPSO results, and the novel Pareto regions were estimated. Over this Pareto region, a clustering strategy was also developed and applied to define sub-regions that prioritize one of the objectives and an intermediary region that provides a balance between objectives. This is a valuable tool in the context of process optimization, aiming at assertive decision-making purposes. As this is a novel concept, the only way to compare it was to draw the entire regions of the benchmark functions and compare them with the methodology result. The benchmark results demonstrated that the proposed method could efficiently portray the Pareto regions. Then, the optimization of a Pressure Swing Adsorption unit was performed using the proposed approach to provide a practical application of the methodology developed here. It was possible to build the Pareto region and its respective sub-regions, where each process performance parameter is prioritized. The results demonstrated that this methodology could be helpful in processes optimization and operation. It provides more flexibility and more profound knowledge of the system under evaluation.

Multiobjective Immune Algorithm with Nondominated Neighbor-Based Selection

2008 ◽  
Vol 16 (2) ◽  
pp. 225-255 ◽  
Author(s):  
Maoguo Gong ◽  
Licheng Jiao ◽  
Haifeng Du ◽  
Liefeng Bo
Keyword(s):  
Multiobjective Optimization ◽  
Heuristic Search ◽  
Performance Metrics ◽  
Optimization Problems ◽  
Selection Method ◽  
Immune Algorithm ◽  
Nsga Ii ◽  
Selection Technique ◽  
Multiobjective Optimization Problems ◽  
Low Dimensional

Nondominated Neighbor Immune Algorithm (NNIA) is proposed for multiobjective optimization by using a novel nondominated neighbor-based selection technique, an immune inspired operator, two heuristic search operators, and elitism. The unique selection technique of NNIA only selects minority isolated nondominated individuals in the population. The selected individuals are then cloned proportionally to their crowding-distance values before heuristic search. By using the nondominated neighbor-based selection and proportional cloning, NNIA pays more attention to the less-crowded regions of the current trade-off front. We compare NNIA with NSGA-II, SPEA2, PESA-II, and MISA in solving five DTLZ problems, five ZDT problems, and three low-dimensional problems. The statistical analysis based on three performance metrics including the coverage of two sets, the convergence metric, and the spacing, show that the unique selection method is effective, and NNIA is an effective algorithm for solving multiobjective optimization problems. The empirical study on NNIA's scalability with respect to the number of objectives shows that the new algorithm scales well along the number of objectives.

Comprehensive Survey of the Hybrid Evolutionary Algorithms

2013 ◽  
Vol 4 (2) ◽  
pp. 1-19 ◽  
Author(s):  
Wali Khan Mashwani
Keyword(s):  
Evolutionary Algorithms ◽  
Pareto Front ◽  
Optimization Problems ◽  
Mathematical Formulation ◽  
Multiobjective Evolutionary Algorithms ◽  
Nsga Ii ◽  
Pareto Optimal Set ◽  
Multiobjective Optimization Problems ◽  
Comprehensive Survey ◽  
Optimal Set

Multiobjective evolutionary algorithm based on decomposition (MOEA/D) and an improved non-dominating sorting multiobjective genetic algorithm (NSGA-II) is two well known multiobjective evolutionary algorithms (MOEAs) in the field of evolutionary computation. This paper mainly reviews their hybrid versions and some other algorithms which are developed for solving multiobjective optimization problems (MOPs. The mathematical formulation of a MOP and some basic definitions for tackling MOPs, including Pareto optimality, Pareto optimal set (PS), Pareto front (PF) are provided in Section 1. Section 2 presents a brief introduction to hybrid MOEAs. The authors present literature review in subsections. Subsection 2.1 provides memetic multiobjective evolutionary algorithms. Subsection 2.2 presents the hybrid versions of well-known Pareto dominance based MOEAs. Subsection 2.4 summarizes some enhanced Versions of MOEA/D paradigm. Subsection 2.5 reviews some multimethod search approaches dealing optimization problems.

scholarly journals Dynamic Multiobjective Optimization Algorithm Based on Average Distance Linear Prediction Model

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Zhiyong Li ◽  
Hengyong Chen ◽  
Zhaoxin Xie ◽  
Chao Chen ◽  
Ahmed Sallam
Keyword(s):  
Multiobjective Optimization ◽  
Prediction Model ◽  
Linear Prediction ◽  
Prediction Models ◽  
Optimization Problems ◽  
Average Distance ◽  
Test Problems ◽  
Multiobjective Optimization Problems ◽  
Dynamic Multiobjective Optimization ◽  
Linear Prediction Model

Many real-world optimization problems involve objectives, constraints, and parameters which constantly change with time. Optimization in a changing environment is a challenging task, especially when multiple objectives are required to be optimized simultaneously. Nowadays the common way to solve dynamic multiobjective optimization problems (DMOPs) is to utilize history information to guide future search, but there is no common successful method to solve different DMOPs. In this paper, we define a kind of dynamic multiobjectives problem with translational Paretooptimal set (DMOP-TPS) and propose a new prediction model named ADLM for solving DMOP-TPS. We have tested and compared the proposed prediction model (ADLM) with three traditional prediction models on several classic DMOP-TPS test problems. The simulation results show that our proposed prediction model outperforms other prediction models for DMOP-TPS.

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