Use of cooperative coevolution for solving large scale multiobjective optimization problems

2013 ◽  
Author(s):  
Luis Miguel Antonio ◽  
Carlos A. Coello Coello
Keyword(s):  
Multiobjective Optimization ◽  
Large Scale ◽  
Optimization Problems ◽  
Cooperative Coevolution ◽  
Multiobjective Optimization Problems

Lagrangian Relaxation Method in Approximating the Pareto Front of Multiobjective Optimization Problems

2021 ◽  
Vol 40 (2) ◽  
pp. 126-133
Author(s):  
MM Rizvi ◽  
HS Faruque Alam ◽  
Ganesh Chandra Ray
Keyword(s):  
Multiobjective Optimization ◽  
Lagrangian Relaxation ◽  
Large Scale ◽  
Pareto Front ◽  
Original Problem ◽  
Necessary Conditions ◽  
Optimization Problems ◽  
Relaxation Method ◽  
Optimization Techniques ◽  
Multiobjective Optimization Problems

In this paper, we propose that the Lagrangian relaxation approach can be used to approximate the Pareto front of the multiobjective optimization problems. We introduce Lagrangian relaxation approach to solve scalarized subproblems. The scalarization is a technique employed to transform multiple objectives optimization problems into single-objective optimization problems so that existing optimization techniques are used to solve the problems. The relaxation approach exploits transformation and creates a Lagrangian problem in which some of the constraints are replaced from the original problem to make the problem easier to solve.  The method is very effective when the problem is large scale and difficult to solve; this means if the problem has nonconvex and nonsmooth structure, then our proposed method efficiently solves the problem. We succeed in establishing proper Karush Kuhn-Tucker type necessary conditions for our proposed approach. We establish the relation between our proposed approach and the well-known existing approach weighted-sum scalarization methods. We conduct extensive numerical experiments and demonstrated the advantages of the proposed method of adopting a test problem. GANIT J. Bangladesh Math. Soc. 40.2 (2020) 126-133

scholarly journals Cooperative multiobjective optimization with bounds on objective functions

2020 ◽  
Author(s):  
I. Kaliszewski ◽  
J. Miroforidis
Keyword(s):  
Multiobjective Optimization ◽  
Large Scale ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Knapsack Problems ◽  
Mixed Integer ◽  
Pareto Optimal ◽  
Multidimensional Knapsack ◽  
Multiobjective Optimization Problems ◽  
Time Limitations

Abstract When solving large-scale multiobjective optimization problems, solvers can get stuck because of memory and/or time limitations. In such cases, one is left with no information on the distance to the best feasible solution, found before the optimization process has stopped, to the true Pareto optimal solution. In this work, we show how to provide such information. To this aim we make use of the concept of lower shells and upper shells, developed in our earlier works. No specific assumptions about the problems to be solved are made. We illustrate the proposed approach on biobjective multidimensional knapsack problems derived from single-objective multidimensional knapsack problems in the Beasley OR Library. We address cases when a top-class commercial mixed-integer linear solver fails to provide Pareto optimal solutions attempted to be derived by scalarization.

scholarly journals Duality Theorems for (ρ,ψ,d)-Quasiinvex Multiobjective Optimization Problems with Interval-Valued Components

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 894
Author(s):  
Savin Treanţă
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Integral Functional ◽  
Multiple Integral ◽  
Control Problems ◽  
Duality Theorems ◽  
New Class ◽  
Duality Results ◽  
Multiobjective Optimization Problems ◽  
Interval Valued

The present paper deals with a duality study associated with a new class of multiobjective optimization problems that include the interval-valued components of the ratio vector. More precisely, by using the new notion of (ρ,ψ,d)-quasiinvexity associated with an interval-valued multiple-integral functional, we formulate and prove weak, strong, and converse duality results for the considered class of variational control problems.

scholarly journals Robust neutrosophic programming approach for solving intuitionistic fuzzy multiobjective optimization problems

2021 ◽  
Author(s):  
Firoz Ahmad
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Practical Implication ◽  
Real Life ◽  
Future Research ◽  
Programming Approach ◽  
Solution Approach ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Multiobjective Optimization Problems

AbstractThis study presents the modeling of the multiobjective optimization problem in an intuitionistic fuzzy environment. The uncertain parameters are depicted as intuitionistic fuzzy numbers, and the crisp version is obtained using the ranking function method. Also, we have developed a novel interactive neutrosophic programming approach to solve multiobjective optimization problems. The proposed method involves neutral thoughts while making decisions. Furthermore, various sorts of membership functions are also depicted for the marginal evaluation of each objective simultaneously. The different numerical examples are presented to show the performances of the proposed solution approach. A case study of the cloud computing pricing problem is also addressed to reveal the real-life applications. The practical implication of the current study is also discussed efficiently. Finally, conclusions and future research scope are suggested based on the proposed work.

scholarly journals Assessing the Performance of Interactive Multiobjective Optimization Methods

2021 ◽  
Vol 54 (4) ◽  
pp. 1-27
Author(s):  
Bekir Afsar ◽  
Kaisa Miettinen ◽  
Francisco Ruiz
Keyword(s):  
Multiobjective Optimization ◽  
Decision Maker ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Interactive Methods ◽  
Value Functions ◽  
Technical Aspects ◽  
Preference Information ◽  
Multiobjective Optimization Problems ◽  
Human Decision

Interactive methods are useful decision-making tools for multiobjective optimization problems, because they allow a decision-maker to provide her/his preference information iteratively in a comfortable way at the same time as (s)he learns about all different aspects of the problem. A wide variety of interactive methods is nowadays available, and they differ from each other in both technical aspects and type of preference information employed. Therefore, assessing the performance of interactive methods can help users to choose the most appropriate one for a given problem. This is a challenging task, which has been tackled from different perspectives in the published literature. We present a bibliographic survey of papers where interactive multiobjective optimization methods have been assessed (either individually or compared to other methods). Besides other features, we collect information about the type of decision-maker involved (utility or value functions, artificial or human decision-maker), the type of preference information provided, and aspects of interactive methods that were somehow measured. Based on the survey and on our own experiences, we identify a series of desirable properties of interactive methods that we believe should be assessed.

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