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.

scholarly journals A comparative study of many-objective optimizers on large-scale many-objective software clustering problems

2021 ◽  
Author(s):  
Amarjeet Prajapati
Keyword(s):  
Large Scale ◽  
Optimization Problems ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Software Clustering ◽  
Multi Objective ◽  
The Past ◽  
Decision Variables ◽  
Clustering Problems ◽  
Special Case

AbstractOver the past 2 decades, several multi-objective optimizers (MOOs) have been proposed to address the different aspects of multi-objective optimization problems (MOPs). Unfortunately, it has been observed that many of MOOs experiences performance degradation when applied over MOPs having a large number of decision variables and objective functions. Specially, the performance of MOOs rapidly decreases when the number of decision variables and objective functions increases by more than a hundred and three, respectively. To address the challenges caused by such special case of MOPs, some large-scale multi-objective optimization optimizers (L-MuOOs) and large-scale many-objective optimization optimizers (L-MaOOs) have been developed in the literature. Even after vast development in the direction of L-MuOOs and L-MaOOs, the supremacy of these optimizers has not been tested on real-world optimization problems containing a large number of decision variables and objectives such as large-scale many-objective software clustering problems (L-MaSCPs). In this study, the performance of nine L-MuOOs and L-MaOOs (i.e., S3-CMA-ES, LMOSCO, LSMOF, LMEA, IDMOPSO, ADC-MaOO, NSGA-III, H-RVEA, and DREA) is evaluated and compared over five L-MaSCPs in terms of IGD, Hypervolume, and MQ metrics. The experimentation results show that the S3-CMA-ES and LMOSCO perform better compared to the LSMOF, LMEA, IDMOPSO, ADC-MaOO, NSGA-III, H-RVEA, and DREA in most of the cases. The LSMOF, LMEA, IDMOPSO, ADC-MaOO, NSGA-III, and DREA, are the average performer, and H-RVEA is the worst performer.

scholarly journals An Expensive Multi-Objective Optimization Algorithm Based on Decision Space Compression

2021 ◽  
pp. 2159039
Author(s):  
Haosen Liu ◽  
Fangqing Gu ◽  
Yiu-Ming Cheung
Keyword(s):  
Optimization Algorithm ◽  
Optimization Problems ◽  
Experimental Studies ◽  
Surrogate Models ◽  
Multi Objective Optimization ◽  
Decision Space ◽  
Multi Objective ◽  
The Past ◽  
Decision Variables ◽  
Space Compression

Numerous surrogate-assisted expensive multi-objective optimization algorithms were proposed to deal with expensive multi-objective optimization problems in the past few years. The accuracy of the surrogate models degrades as the number of decision variables increases. In this paper, we propose a surrogate-assisted expensive multi-objective optimization algorithm based on decision space compression. Several surrogate models are built in the lower dimensional compressed space. The promising points are generated and selected in the lower compressed decision space and decoded to the original decision space for evaluation. Experimental studies show that the proposed algorithm achieves a good performance in handling expensive multi-objective optimization problems with high-dimensional decision space.

scholarly journals Improved SparseEA for sparse large-scale multi-objective optimization problems

2021 ◽  
Author(s):  
Yajie Zhang ◽  
Ye Tian ◽  
Xingyi Zhang
Keyword(s):  
Real World ◽  
Large Scale ◽  
Optimization Problems ◽  
State Of The Art ◽  
Benchmark Problems ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Limited Budget ◽  
Decision Variables ◽  
Real World Applications

AbstractSparse large-scale multi-objective optimization problems (LSMOPs) widely exist in real-world applications, which have the properties of involving a large number of decision variables and sparse Pareto optimal solutions, i.e., most decision variables of these solutions are zero. In recent years, sparse LSMOPs have attracted increasing attentions in the evolutionary computation community. However, all the recently tailored algorithms for sparse LSMOPs put the sparsity detection and maintenance in the first place, where the nonzero variables can hardly be optimized sufficiently within a limited budget of function evaluations. To address this issue, this paper proposes to enhance the connection between real variables and binary variables within the two-layer encoding scheme with the assistance of variable grouping techniques. In this way, more efforts can be devoted to the real part of nonzero variables, achieving the balance between sparsity maintenance and variable optimization. According to the experimental results on eight benchmark problems and three real-world applications, the proposed algorithm is superior over existing state-of-the-art evolutionary algorithms for sparse LSMOPs.

scholarly journals Two-stage multi-tasking transform framework for large-scale many-objective optimization problems

2021 ◽  
Author(s):  
Lu Chen ◽  
Handing Wang ◽  
Wenping Ma
Keyword(s):  
Large Scale ◽  
Original Problem ◽  
Optimization Problems ◽  
Reference Points ◽  
Optimization Strategy ◽  
Two Stage ◽  
Decision Space ◽  
Second Stage ◽  
Decision Variables ◽  
Objective Space

AbstractReal-world optimization applications in complex systems always contain multiple factors to be optimized, which can be formulated as multi-objective optimization problems. These problems have been solved by many evolutionary algorithms like MOEA/D, NSGA-III, and KnEA. However, when the numbers of decision variables and objectives increase, the computation costs of those mentioned algorithms will be unaffordable. To reduce such high computation cost on large-scale many-objective optimization problems, we proposed a two-stage framework. The first stage of the proposed algorithm combines with a multi-tasking optimization strategy and a bi-directional search strategy, where the original problem is reformulated as a multi-tasking optimization problem in the decision space to enhance the convergence. To improve the diversity, in the second stage, the proposed algorithm applies multi-tasking optimization to a number of sub-problems based on reference points in the objective space. In this paper, to show the effectiveness of the proposed algorithm, we test the algorithm on the DTLZ and LSMOP problems and compare it with existing algorithms, and it outperforms other compared algorithms in most cases and shows disadvantage on both convergence and diversity.

scholarly journals A Distributed Multifactorial Particle Swarm Optimization Approach

2021 ◽  
Author(s):  
Ahlem Aboud ◽  
Nizar Rokbani ◽  
Seyedali Mirjalili ◽  
Abdulrahman M. Qahtani ◽  
Omar Almutiry ◽  
...  
Keyword(s):  
Particle Swarm Optimization ◽  
Optimization Problems ◽  
Beta Function ◽  
Particle Swarm ◽  
Search Space ◽  
Optimization Approach ◽  
Multi Objective Optimization ◽  
Swarm Optimization ◽  
Multi Objective ◽  
New System

<p>Multifactorial Optimization (MFO) and Evolutionary Transfer Optimization (ETO) are new optimization challenging paradigms for which the multi-Objective Particle Swarm Optimization system (MOPSO) may be interesting despite limitations. MOPSO has been widely used in static/dynamic multi-objective optimization problems, while its potentials for multi-task optimization are not completely unveiled. This paper proposes a new Distributed Multifactorial Particle Swarm Optimization algorithm (DMFPSO) for multi-task optimization. This new system has a distributed architecture on a set of sub-swarms that are dynamically constructed based on the number of optimization tasks affected by each particle skill factor. DMFPSO is designed to deal with the issues of handling convergence and diversity concepts separately. DMFPSO uses Beta function to provide two optimized profiles with a dynamic switching behaviour. The first profile, Beta-1, is used for the exploration which aims to explore the search space toward potential solutions, while the second Beta-2 function is used for convergence enhancement. This new system is tested on 36 benchmarks provided by the CEC’2021 Evolutionary Transfer Multi-Objective Optimization Competition. Comparatives with the state-of-the-art methods are done using the Inverted General Distance (IGD) and Mean Inverted General Distance (MIGD) metrics. Based on the MSS metric, this proposal has the best results on most tested problems.</p>

Multi-Objective Optimization of Metal Forming Processes Based on the Kalai and Smorodinsky Solution

2015 ◽  
Vol 651-653 ◽  
pp. 1387-1393 ◽  
Author(s):  
Lorenzo Iorio ◽  
Lionel Fourment ◽  
Stephane Marie ◽  
Matteo Strano
Keyword(s):  
Optimization Problems ◽  
Good Method ◽  
Wire Drawing ◽  
Bargaining Problem ◽  
Mathematical Function ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Cooperative Approach ◽  
The Game Theory

The Game Theory is a good method for finding a compromise between two players in a bargaining problem. The Kalai and Smorodinsky (K-S) method is a solution the bargaining problem where players make decisions in order to maximize their own utility, with a cooperative approach. Interesting applications of the K-S method can be found in engineering multi-objective optimization problems, where two or more functions must be minimized. The aim of this paper is to develop an optimization algorithm aimed at rapidly finding the Kalai and Smorodinsky solution, where the objective functions are considered as players in a bargaining problem, avoiding the search for the Pareto front. The approach uses geometrical consideration in the space of the objective functions, starting from the knowledge of the so-called Utopia and Nadir points. An analytical solution is proposed and initially tested with a simple minimization problem based on a known mathematical function. Then, the algorithm is tested (thanks to a user friendly routine built-in the finite element code Forge®) for FEM optimization problem of a wire drawing operation, with the objective of minimizing the pulling force and the material damage. The results of the simulations are compared to previous works done with others methodologies.

scholarly journals Multi-Objective Optimization in Axial Compressor Design Using a Linked CFD-Solver

2008 ◽  
Author(s):  
Kai Becker ◽  
Martin Lawerenz ◽  
Christian Voß ◽  
Reinhard Mo¨nig
Keyword(s):  
Guide Vane ◽  
Axial Compressor ◽  
Navier Stokes ◽  
Inlet Guide Vane ◽  
Optimization Strategy ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Flow Information ◽  
Design Variation

In combination with a multi-objective 3D optimization strategy, a linked CFD-solver is presented in this paper, combining 3D-Reynolds-averaged-Navier-Stokes and an inviscid throughflow method. It enables the adjustment of the 3D boundary conditions for any design variation and contains new options for configuring the objective functions. The link is achieved by matching the flow information between both CFD codes in an iterative procedure. Compared to an individual 3D-CFD calculation, the convergence does not take significantly longer. The potential of the linked CFD-solver is demonstrated in a multi-objective optimization for one blade row to be optimized and one operating point at a 3-stage axial compressor with inlet guide vane. Within the optimization, the objective functions are formulated, so that the performance of the axial compressor is enhanced in addition to the improved efficiency of the 3D-cascade.

Robustness Against Large Variations in Multi-Objective Optimization Problems

2013 ◽  
Author(s):  
Weijun Wang ◽  
Stéphane Caro ◽  
Fouad Bennis
Keyword(s):  
Optimization Problems ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Design Environment ◽  
Multi Objective ◽  
Uncertainty Sources ◽  
Design Variables ◽  
Robustness Index ◽  
Environment Parameters

In the presence of multiple optimal solutions in multi-modal optimization problems and in multi-objective optimization problems, the designer may be interested in the robustness of those solutions to make a decision. Here, the robustness is related to the sensitivity of the performance functions to uncertainties. The uncertainty sources include the uncertainties in the design variables, in the design environment parameters, in the model of objective functions and in the designer’s preference. There exist many robustness indices in the literature that deal with small variations in the design variables and design environment parameters, but few robustness indices consider large variations. In this paper, a new robustness index is introduced to deal with large variations in the design environment parameters. The proposed index is bounded between zero and one, and measures the probability of a solution to be optimal with respect to the values of the design environment parameters. The larger the robustness index, the more robust the solution with regard to large variations in the design environment parameters. Finally, two illustrative examples are given to highlight the contributions of this paper.

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.

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