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

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.

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A Memetic Optimization Strategy Based on Dimension Reduction in Decision Space

Evolutionary Computation ◽

10.1162/evco_a_00122 ◽

2015 ◽

Vol 23 (1) ◽

pp. 69-100 ◽

Cited By ~ 13

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.

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Comparative Analysis of Selection Hyper-Heuristics for Real-World Multi-Objective Optimization Problems

Applied Sciences ◽

10.3390/app11199153 ◽

2021 ◽

Vol 11 (19) ◽

pp. 9153

Author(s):

Vinicius Renan de Carvalho ◽

Ender Özcan ◽

Jaime Simão Sichman

Keyword(s):

Real World ◽

Optimization Problem ◽

Optimization Problems ◽

Exact Algorithms ◽

Mathematical Function ◽

Multi Objective Optimization ◽

Algorithm Selection ◽

Multi Objective ◽

Cross Domain ◽

Domain Performance

As exact algorithms are unfeasible to solve real optimization problems, due to their computational complexity, meta-heuristics are usually used to solve them. However, choosing a meta-heuristic to solve a particular optimization problem is a non-trivial task, and often requires a time-consuming trial and error process. Hyper-heuristics, which are heuristics to choose heuristics, have been proposed as a means to both simplify and improve algorithm selection or configuration for optimization problems. This paper novel presents a novel cross-domain evaluation for multi-objective optimization: we investigate how four state-of-the-art online hyper-heuristics with different characteristics perform in order to find solutions for eighteen real-world multi-objective optimization problems. These hyper-heuristics were designed in previous studies and tackle the algorithm selection problem from different perspectives: Election-Based, based on Reinforcement Learning and based on a mathematical function. All studied hyper-heuristics control a set of five Multi-Objective Evolutionary Algorithms (MOEAs) as Low-Level (meta-)Heuristics (LLHs) while finding solutions for the optimization problem. To our knowledge, this work is the first to deal conjointly with the following issues: (i) selection of meta-heuristics instead of simple operators (ii) focus on multi-objective optimization problems, (iii) experiments on real world problems and not just function benchmarks. In our experiments, we computed, for each algorithm execution, Hypervolume and IGD+ and compared the results considering the Kruskal–Wallis statistical test. Furthermore, we ranked all the tested algorithms considering three different Friedman Rankings to summarize the cross-domain analysis. Our results showed that hyper-heuristics have a better cross-domain performance than single meta-heuristics, which makes them excellent candidates for solving new multi-objective optimization problems.

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Robustness Against Large Variations in Multi-Objective Optimization Problems

Volume 3B: 39th Design Automation Conference ◽

10.1115/detc2013-12337 ◽

2013 ◽

Cited By ~ 1

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.

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Multi-Objective Optimization with Estimation of Distribution Algorithm in a Noisy Environment

Evolutionary Computation ◽

10.1162/evco_a_00066 ◽

2013 ◽

Vol 21 (1) ◽

pp. 149-177 ◽

Cited By ~ 27

Author(s):

Vui Ann Shim ◽

Kay Chen Tan ◽

Jun Yong Chia ◽

Abdullah Al Mamun

Keyword(s):

Optimization Problems ◽

Estimation Of Distribution Algorithm ◽

Computational Time ◽

Decision Variable ◽

Objective Functions ◽

Multi Objective Optimization ◽

Noisy Environment ◽

Multi Objective ◽

Noisy Information ◽

Estimation Of Distribution

Many real-world optimization problems are subjected to uncertainties that may be characterized by the presence of noise in the objective functions. The estimation of distribution algorithm (EDA), which models the global distribution of the population for searching tasks, is one of the evolutionary computation techniques that deals with noisy information. This paper studies the potential of EDAs; particularly an EDA based on restricted Boltzmann machines that handles multi-objective optimization problems in a noisy environment. Noise is introduced to the objective functions in the form of a Gaussian distribution. In order to reduce the detrimental effect of noise, a likelihood correction feature is proposed to tune the marginal probability distribution of each decision variable. The EDA is subsequently hybridized with a particle swarm optimization algorithm in a discrete domain to improve its search ability. The effectiveness of the proposed algorithm is examined via eight benchmark instances with different characteristics and shapes of the Pareto optimal front. The scalability, hybridization, and computational time are rigorously studied. Comparative studies show that the proposed approach outperforms other state of the art algorithms.

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

Complex & Intelligent Systems ◽

10.1007/s40747-021-00270-8 ◽

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.

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An Efficient Framework for Multi-Objective Risk-Informed Decision Support Systems for Drainage Rehabilitation

Mathematical and Computational Applications ◽

10.3390/mca25040073 ◽

2020 ◽

Vol 25 (4) ◽

pp. 73

Author(s):

Xiatong Cai ◽

Abdolmajid Mohammadian ◽

Hamidreza Shirkhani

Keyword(s):

Optimization Problems ◽

Drainage System ◽

Mixed Integer ◽

Engineering Optimization ◽

Continuous Variables ◽

Objective Functions ◽

Multi Objective Optimization ◽

Integer Optimization ◽

Framework Structure ◽

Multi Objective

Combining multiple modules into one framework is a key step in modelling a complex system. In this study, rather than focusing on modifying a specific model, we studied the performance of different calculation structures in a multi-objective optimization framework. The Hydraulic and Risk Combined Model (HRCM) combines hydraulic performance and pipe breaking risk in a drainage system to provide optimal rehabilitation strategies. We evaluated different framework structures for the HRCM model. The results showed that the conventional framework structure used in engineering optimization research, which includes (1) constraint functions; (2) objective functions; and (3) multi-objective optimization, is inefficient for drainage rehabilitation problem. It was shown that the conventional framework can be significantly improved in terms of calculation speed and cost-effectiveness by removing the constraint function and adding more objective functions. The results indicated that the model performance improved remarkably, while the calculation speed was not changed substantially. In addition, we found that the mixed-integer optimization can decrease the optimization performance compared to using continuous variables and adding a post-processing module at the last stage to remove the unsatisfying results. This study (i) highlights the importance of the framework structure inefficiently solving engineering problems, and (ii) provides a simplified efficient framework for engineering optimization problems.

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A Novel Hybrid Multi-Objective Population Migration Algorithm

International Journal of Pattern Recognition and Artificial Intelligence ◽

10.1142/s0218001415590016 ◽

2015 ◽

Vol 29 (01) ◽

pp. 1559001 ◽

Cited By ~ 23

Author(s):

Aijia Ouyang ◽

Kenli Li ◽

Xiongwei Fei ◽

Xu Zhou ◽

Mingxing Duan

Keyword(s):

Optimization Problems ◽

Population Migration ◽

Mutation Operator ◽

Objective Functions ◽

Multi Objective Optimization ◽

Nsga Ii ◽

Multi Objective ◽

Good Point ◽

Point Set ◽

Good Point Set

This paper presents a multi-objective co-evolutionary population migration algorithm based on Good Point Set (GPSMCPMA) for multi-objective optimization problems (MOP) in view of the characteristics of MOPs. The algorithm introduces the theory of good point set (GPS) and dynamic mutation operator (DMO) and adopts the entire population co-evolutionary migration, based on the concept of Pareto nondomination and global best experience and guidance. The performance of the algorithm is tested through standard multi-objective functions. The experimental results show that the proposed algorithm performs much better in the convergence, diversity and solution distribution than SPEA2, NSGA-II, MOPSO and MOMASEA. It is a fast and robust multi-objective evolutionary algorithm (MOEA) and is applicable to other MOPs.

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A New Approach to Group Multi-Objective Optimization under Imperfect Information and Its Application to Project Portfolio Optimization

Applied Sciences ◽

10.3390/app11104575 ◽

2021 ◽

Vol 11 (10) ◽

pp. 4575

Author(s):

Eduardo Fernández ◽

Nelson Rangel-Valdez ◽

Laura Cruz-Reyes ◽

Claudia Gomez-Santillan

Keyword(s):

Portfolio Optimization ◽

Imperfect Information ◽

Model Parameters ◽

Final Decision ◽

Project Portfolio ◽

Objective Functions ◽

Multi Objective Optimization ◽

New Approach ◽

Multi Objective ◽

Group Member

This paper addresses group multi-objective optimization under a new perspective. For each point in the feasible decision set, satisfaction or dissatisfaction from each group member is determined by a multi-criteria ordinal classification approach, based on comparing solutions with a limiting boundary between classes “unsatisfactory” and “satisfactory”. The whole group satisfaction can be maximized, finding solutions as close as possible to the ideal consensus. The group moderator is in charge of making the final decision, finding the best compromise between the collective satisfaction and dissatisfaction. Imperfect information on values of objective functions, required and available resources, and decision model parameters are handled by using interval numbers. Two different kinds of multi-criteria decision models are considered: (i) an interval outranking approach and (ii) an interval weighted-sum value function. The proposal is more general than other approaches to group multi-objective optimization since (a) some (even all) objective values may be not the same for different DMs; (b) each group member may consider their own set of objective functions and constraints; (c) objective values may be imprecise or uncertain; (d) imperfect information on resources availability and requirements may be handled; (e) each group member may have their own perception about the availability of resources and the requirement of resources per activity. An important application of the new approach is collective multi-objective project portfolio optimization. This is illustrated by solving a real size group many-objective project portfolio optimization problem using evolutionary computation tools.

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