A review of multi-objective optimization: Methods and its applications

Gunantara, Nyoman

doi:10.1080/23311916.2018.1502242

Cited by 609 publications

(292 citation statements)

References 26 publications

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“…The multi-objective optimization by WSM converts objective functions into scalar-based objective functions by defining them as weighted sums of various objectives, Ref. [31][32][33].…”

Section: Step 4: Multi-objective Optimizationmentioning

confidence: 99%

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An Integrated Multi-Criteria and Multi-Objective Optimization Approach for Establishing the Transport Plan of Intercity Trains

Stoilova

2020

Sustainability

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The development of the transport plan must take into account various criteria impacting the transport process. The main objective of the study is to propose an integrated approach to determine the transport plan of passenger trains. The methodology consists of five steps. In the first step, the criteria for optimization of the transport plan were defined. In the second step, variants of the transport plan were formulated. In the third step, the weights of the criteria are determined by applying the step-wise weight assessment ratio analysis method (SWARA) multi-criteria method. The multi-objective optimization was conducted in the fourth step. The following multi-objective optimization approaches were used and compared: weighted sum method (WSM), compromise programming method (CP), and the epsilon–constraint method (EC). The study proposes a modified epsilon–constraint method (MEC) by applying normalization of each objective function according to the maximal value of the solution by individual optimization for each objective function, and hybrid methods: hybrid WSM and EC, hybrid WSM and MEC, hybrid CP and EC, and Hybrid CP and MEC. The impact of the variation of passenger flows on the choice of an optimal transport plan was studied in the fifth step. The Laplace’s criterion, Hurwitz’s criterion, and Savage’s criterion were applied to come to a decision. The approbation of the methodology was demonstrated through the case study of Bulgaria’s railway network. Suitable variant of transport plan is proposed.

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“…The multi-objective optimization by WSM converts objective functions into scalar-based objective functions by defining them as weighted sums of various objectives, Ref. [31][32][33].…”

Section: Step 4: Multi-objective Optimizationmentioning

confidence: 99%

“…• Hybrid WSM and EC-it uses objective function (23) and conditions (24), (18)-(22), (28)- (33), and:…”

Section: Step 4: Multi-objective Optimizationmentioning

confidence: 99%

An Integrated Multi-Criteria and Multi-Objective Optimization Approach for Establishing the Transport Plan of Intercity Trains

Stoilova

2020

Sustainability

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“…Decision-making methods based on optimality were introduced by Pareto in 1896 and applied to a wide range of problems. The Multi-Objective Evolutionary Algorithm (MOEA) [24] is used to find the optimal Pareto solutions for specific problems [25]. Keeney and Raiffa [26] and Fishburn [27] introduced the Multi-Attribute Value Theory (MAVT), the Multi-Attribute Value Analysis (MAVA) and Multi-Attribute Utility Theory (MAUT) methods.…”

Section: Literature Reviewmentioning

confidence: 99%

Multi-Attribute Decision-Making Methods as a Part of Mathematical Optimization

Vinogradova

2019

Mathematics

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Optimization problems are relevant to various areas of human activity. In different cases, the problems are solved by applying appropriate optimization methods. A range of optimization problems has resulted in a number of different methods and algorithms for reaching solutions. One of the problems deals with the decision-making area, which is an optimal option selected from several options of comparison. Multi-Attribute Decision-Making (MADM) methods are widely applied for making the optimal solution, selecting a single option or ranking choices from the most to the least appropriate. This paper is aimed at providing MADM methods as a component of mathematics-based optimization. The theoretical part of the paper presents evaluation criteria of methods as the objective functions. To illustrate the idea, some of the most frequently used methods in practice—Simple Additive Weighting (SAW), Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), Complex Proportional Assessment Method (COPRAS), Multi-Objective Optimization by Ratio Analysis (MOORA) and Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE)—were chosen. These methods use a finite number of explicitly given alternatives. The research literature does not propose the best or most appropriate MADM method for dealing with a specific task. Thus, several techniques are frequently applied in parallel to make the right decision. Each method differs in the data processing, and therefore the results of MADM methods are obtained on different scales. The practical part of this paper demonstrates how to combine the results of several applied methods into a single value. This paper proposes a new approach for evaluating that involves merging the results of all applied MADM methods into a single value, taking into account the suitability of the methods for the task to be solved. Taken as a basis is the fact that if a method is more stable to a minor data change, the greater importance (weight) it has for the merged result. This paper proposes an algorithm for determining the stability of MADM methods by applying the statistical simulation method using a sequence of random numbers from the given distribution. This paper shows the different approaches to normalizing the results of MADM methods. For arranging negative values and making the scales of the results of the methods equal, Weitendorf’s linear normalization and classical and author-proposed transformation techniques have been illustrated in this paper.

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“…Thus, the multiobjetive problem becomes uniobjective and the general optimization methods could be applied to solve the scalarized problem. In which, the objective function incorporates performance indicators of different objectives [21].…”

Section: Related Workmentioning

confidence: 99%

Swarm Robotics and Rapidly Exploring Random Graph Algorithms Applied to Environment Exploration and Path Planning

Calderón-Arce¹,

Solis-Ortega²

2019

IJACSA

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We propose an efficient scheme based on a swarm robotics approach for exploring unknown environments. The initial goal is to trace a map which is later used to find optimal paths. The algorithm minimizes distance and danger. The proposed scheme consists in three phases: exploration, mapping and path optimization. A cellular automata approach is used for the simulation of the fist two phases. For the exploration phase, a stigmergy approach is applied in order to allow for swarm communication in a implicit way. For the path planning phase a hybrid method is proposed. First an adapted Rapidlyexploring Random Graph algorithm is used and then a scalarized multiobjective technique is applied to find the shortest path.

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A review of multi-objective optimization: Methods and its applications

Cited by 609 publications

References 26 publications

An Integrated Multi-Criteria and Multi-Objective Optimization Approach for Establishing the Transport Plan of Intercity Trains

An Integrated Multi-Criteria and Multi-Objective Optimization Approach for Establishing the Transport Plan of Intercity Trains

Multi-Attribute Decision-Making Methods as a Part of Mathematical Optimization

Swarm Robotics and Rapidly Exploring Random Graph Algorithms Applied to Environment Exploration and Path Planning

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