A novel approach for the solution of multiobjective optimization problem using hesitant fuzzy aggregation operator

Many decision-making problems can solve successfully by traditional optimization methods with a well-defined configuration. The formulation of such optimization problems depends on crisply objective functions and a specific system of constraints. Nevertheless, in reality, in any decision-making process, it is often observed that due to some doubt or hesitation, it is pretty tricky for decision-maker(s) to specify the precise/crisp value of any parameters and compelled to take opinions from different experts which leads towards a set of conflicting values regarding satisfaction level of decision-maker(s). Therefore the real decision-making problem cannot always be deterministic. Various types of uncertainties in parameters make it fuzzy. This paper presents a practical mathematical framework to reflect the reality involved in any decision-making process. The proposed method has taken advantage of the hesitant fuzzy aggregation operator and presents a particular way to emerge in a decision-making process. For this purpose, we have discussed a couple of different hesitant fuzzy aggregation operators and developed linear and hyperbolic membership functions under hesitant fuzziness, which contains the concept of hesitant degrees for different objectives. Finally, an example based on a multiobjective optimization problem is presented to illustrate the validity and applicability of our proposed models.

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A Multiobjective Genetic Algorithm for the Localization of Optimal and Nearly Optimal Solutions Which Are Potentially Useful: nevMOGA

Complexity ◽

10.1155/2018/1792420 ◽

2018 ◽

Vol 2018 ◽

pp. 1-22 ◽

Cited By ~ 7

Author(s):

Alberto Pajares ◽

Xavier Blasco ◽

Juan M. Herrero ◽

Gilberto Reynoso-Meza

Keyword(s):

Genetic Algorithm ◽

Decision Making ◽

Decision Maker ◽

Pareto Front ◽

Optimization Problem ◽

Engineering Problem ◽

Multiobjective Optimization Problem ◽

Optimal Solutions ◽

Multiobjective Genetic Algorithm ◽

Pi Controllers

Traditionally, in a multiobjective optimization problem, the aim is to find the set of optimal solutions, the Pareto front, which provides the decision-maker with a better understanding of the problem. This results in a more knowledgeable decision. However, multimodal solutions and nearly optimal solutions are ignored, although their consideration may be useful for the decision-maker. In particular, there are some of these solutions which we consider specially interesting, namely, the ones that have distinct characteristics from those which dominate them (i.e., the solutions that are not dominated in their neighborhood). We call these solutions potentially useful solutions. In this work, a new genetic algorithm called nevMOGA is presented, which provides not only the optimal solutions but also the multimodal and nearly optimal solutions nondominated in their neighborhood. This means that nevMOGA is able to supply additional and potentially useful solutions for the decision-making stage. This is its main advantage. In order to assess its performance, nevMOGA is tested on two benchmarks and compared with two other optimization algorithms (random and exhaustive searches). Finally, as an example of application, nevMOGA is used in an engineering problem to optimally adjust the parameters of two PI controllers that operate a plant.

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MultiObjective Genetic Modified Algorithm (MOGMA)

Cybernetics and Information Technologies ◽

10.2478/cait-2012-0010 ◽

2012 ◽

Vol 12 (2) ◽

pp. 23-33

Author(s):

Elica Vandeva

Keyword(s):

Genetic Algorithms ◽

Multiobjective Optimization ◽

Pareto Front ◽

Optimization Problem ◽

Optimization Problems ◽

Multiobjective Optimization Problem ◽

Multiobjective Optimization Problems ◽

Modified Algorithm

Abstract Multiobjective optimization based on genetic algorithms and Pareto based approaches in solving multiobjective optimization problems is discussed in the paper. A Pareto based fitness assignment is used − non-dominated ranking and movement of a population towards the Pareto front in a multiobjective optimization problem. A MultiObjective Genetic Modified Algorithm (MOGMA) is proposed, which is an improvement of the existing algorithm.

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Exact Penalization and Necessary Optimality Conditions for Multiobjective Optimization Problems with Equilibrium Constraints

Abstract and Applied Analysis ◽

10.1155/2014/630547 ◽

2014 ◽

Vol 2014 ◽

pp. 1-13

Author(s):

Shengkun Zhu ◽

Shengjie Li

Keyword(s):

Multiobjective Optimization ◽

Optimization Problem ◽

Optimization Problems ◽

Necessary Optimality Conditions ◽

Inequality Constraints ◽

Multiobjective Optimization Problem ◽

Equilibrium Constraints ◽

Exact Penalization ◽

Multiobjective Optimization Problems ◽

Weak Vector

A calmness condition for a general multiobjective optimization problem with equilibrium constraints is proposed. Some exact penalization properties for two classes of multiobjective penalty problems are established and shown to be equivalent to the calmness condition. Subsequently, a Mordukhovich stationary necessary optimality condition based on the exact penalization results is obtained. Moreover, some applications to a multiobjective optimization problem with complementarity constraints and a multiobjective optimization problem with weak vector variational inequality constraints are given.

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Nonemptiness and Compactness of Solutions Set for Nondifferentiable Multiobjective Optimization Problems

Journal of Applied Mathematics ◽

10.1155/2011/647489 ◽

2011 ◽

Vol 2011 ◽

pp. 1-16 ◽

Cited By ~ 1

Author(s):

Xin-kun Wu ◽

Jia-wei Chen ◽

Yun-zhi Zou

Keyword(s):

Fixed Point ◽

Multiobjective Optimization ◽

Optimization Problem ◽

Optimization Problems ◽

Efficient Solutions ◽

Multiobjective Optimization Problem ◽

Weakly Efficient Solutions ◽

Set Constraints ◽

Multiobjective Optimization Problems ◽

Problems And Solutions

A nondifferentiable multiobjective optimization problem with nonempty set constraints is considered, and the equivalence of weakly efficient solutions, the critical points for the nondifferentiable multiobjective optimization problems, and solutions for vector variational-like inequalities is established under some suitable conditions. Nonemptiness and compactness of the solutions set for the nondifferentiable multiobjective optimization problems are proved by using the FKKM theorem and a fixed-point theorem.

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Combining the cross-entropy algorithm and ∈-constraint method for multiobjective optimization

Moroccan Journal of Pure and Applied Analysis ◽

10.2478/mjpaa-2021-0019 ◽

2021 ◽

Vol 7 (2) ◽

pp. 299-311

Author(s):

Abdelmajid Ezzine ◽

Abdellah Alla ◽

Nadia Raissi

Keyword(s):

Multiobjective Optimization ◽

Local Search ◽

Optimization Problem ◽

Optimization Problems ◽

Cross Entropy ◽

Multiobjective Optimization Problem ◽

Cross Entropy Method ◽

The Cross ◽

Constraint Method ◽

Single Objective

Abstract This paper aims to propose a new hybrid approach for solving multiobjective optimization problems. This approach is based on a combination of global and local search procedures. The cross-entropy method is used as a stochastic model-based method to solve the multiobjective optimization problem and reach a first elite set of global solutions. In the local search step, an ∈-constraint method converts the multiobjective optimization problem to a series of parameterized single-objective optimization problems. Then, sequential quadratic programming (SQP) is used to solve the derived single-objective optimization problems allowing to reinforce and improve the global results. Numerical examples are used to demonstrate the efficiency and effectiveness of the proposed approach.

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Necessary optimality conditions for a fractional multiobjective optimization problem

RAIRO - Operations Research ◽

10.1051/ro/2020049 ◽

2020 ◽

Author(s):

Nazih Abderrazzak Gadhi ◽

khadija hamdaoui ◽

mohammed El idrissi ◽

Fatima zahra Rahou

Keyword(s):

Multiobjective Optimization ◽

Optimality Conditions ◽

Optimization Problem ◽

Constraint Qualification ◽

Optimization Problems ◽

Necessary Optimality Conditions ◽

Multiobjective Optimization Problem ◽

Support Functions

In this paper, we are concerned with a fractional multiobjective optimization problem (P). Using support functions together with a generalized Guignard constraint qualification, we give necessary optimality conditions in terms of convexificators and the Karush-Kuhn-Tucker multipliers. Several intermediate optimization problems have been introduced to help us in our investigation.

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Assessing the Performance of Interactive Multiobjective Optimization Methods

ACM Computing Surveys ◽

10.1145/3448301 ◽

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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MULTIPLE CRITERIA DECISION ANALYSIS USING PRIORITISED INTERVAL TYPE-2 FUZZY AGGREGATION OPERATORS AND ITS APPLICATION TO SITE SELECTION

Technological and Economic Development of Economy ◽

10.3846/20294913.2016.1209249 ◽

2017 ◽

Vol 23 (1) ◽

pp. 1-21 ◽

Cited By ~ 7

Author(s):

Ting-Yu CHEN

Keyword(s):

Decision Making ◽

Decision Analysis ◽

Site Selection ◽

Aggregation Operator ◽

Multiple Criteria ◽

Multiple Criteria Decision Analysis ◽

Landfill Site Selection ◽

Fuzzy Aggregation ◽

Interval Type

The theory of interval type-2 fuzzy sets provides an intuitive and computationally feasible method of addressing uncertain and ambiguous information in decision-making fields. This paper aims to develop a prioritised interval type-2 fuzzy aggregation operator and apply it to multiple criteria decision analysis with prioritised criteria. This paper considers situations in which a relationship between the criteria exists such that a lack of satisfaction by the higher priority criteria cannot be readily compensated by the satisfaction of lower priority criteria. This paper introduces the developed prioritised interval type-2 fuzzy aggregation operator to address the problem of criteria aggregation in this environment. To demonstrate the feasibility of the proposed operator, this paper provides a multiple criteria decision-making method that uses the prioritised interval type-2 fuzzy aggregation operator, and the method is illustrated with a practical application to landfill site selection.

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