scholarly journals Comparing interactive evolutionary multiobjective optimization methods with an artificial decision maker

2021 ◽  
Author(s):  
Bekir Afsar ◽  
Ana B. Ruiz ◽  
Kaisa Miettinen
Keyword(s):  
Multiobjective Optimization ◽  
Decision Maker ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Decision Makers ◽  
Interactive Methods ◽  
Preference Information ◽  
Evolutionary Methods ◽  
Solution Processes ◽  
Trade Offs

AbstractSolving multiobjective optimization problems with interactive methods enables a decision maker with domain expertise to direct the search for the most preferred trade-offs with preference information and learn about the problem. There are different interactive methods, and it is important to compare them and find the best-suited one for solving the problem in question. Comparisons with real decision makers are expensive, and artificial decision makers (ADMs) have been proposed to simulate humans in basic testing before involving real decision makers. Existing ADMs only consider one type of preference information. In this paper, we propose ADM-II, which is tailored to assess several interactive evolutionary methods and is able to handle different types of preference information. We consider two phases of interactive solution processes, i.e., learning and decision phases separately, so that the proposed ADM-II generates preference information in different ways in each of them to reflect the nature of the phases. We demonstrate how ADM-II can be applied with different methods and problems. We also propose an indicator to assess and compare the performance of interactive evolutionary methods.

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.

scholarly journals A Visualization Technique for Accessing Solution Pool in Interactive Methods of Multiobjective Optimization

2015 ◽  
Vol 10 (4) ◽  
pp. 508 ◽  
Author(s):  
Ernestas Filatovas ◽  
Dmitry Podkopaev ◽  
Olga Kurasova
Keyword(s):  
Multiobjective Optimization ◽  
Dimensionality Reduction ◽  
Decision Maker ◽  
Optimization Problem ◽  
Interactive Methods ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Visualization Technique ◽  
Preference Information ◽  
Optimal Set

<pre>Interactive methods of <span>multiobjective</span> optimization repetitively derive <span>Pareto</span> optimal solutions based on decision maker's preference information and present the obtained solutions for his/her consideration. Some interactive methods save the obtained solutions into a solution pool and, at each iteration, allow the decision maker considering any of solutions obtained earlier. This feature contributes to the flexibility of exploring the <span>Pareto</span> optimal set and learning about the optimization problem. However, in the case of many objective functions, the accumulation of derived solutions makes accessing the solution pool cognitively difficult for the decision maker. We propose to enhance interactive methods with visualization of the set of solution outcomes using dimensionality reduction and interactive mechanisms for exploration of the solution pool. We describe a proposed visualization technique and demonstrate its usage with an example problem solved using the interactive method NIMBUS.</pre>

Two-Decision-Maker Conflict Resolution with Fuzzy Preferences

2014 ◽  
Vol 2 (2) ◽  
pp. 40-59
Author(s):  
Mubarak S. Al-Mutairi
Keyword(s):  
Fuzzy Logic ◽  
Conflict Resolution ◽  
Decision Maker ◽  
Decision Makers ◽  
Fuzzy Approach ◽  
Model Uncertainties ◽  
Preference Information ◽  
Fuzzy Preferences ◽  
Illustrative Application ◽  
Fuzzy Preference

A unique fuzzy approach is developed to model uncertainties in the preferences of a decision maker involved in a conflict. Human judgments, including expressing preferences over a set of feasible outcomes or states in a conflict, are usually imprecise. Situations characterized by vagueness, impreciseness, incompleteness and ambiguity, are often reflected in the decision maker's preferences. When modeling a conflict, it is assumed that the decision makers, the courses of actions available for each, and the preferences of each decision maker are known. When the preferences of the decision maker over a certain set of actions are not known with certainty, this could affect the overall equilibria which are predicted in an analysis. Hence, fuzzy logic is used to handle imprecise or vague preference information so that realistic equilibria can be found. The well-known game of Prisoner's Dilemma, in which one must decide whether or not to cooperate, is employed as an illustrative application to demonstrate how the fuzzy preference methodology works in practice.

scholarly journals A Multiobjective Genetic Algorithm Based on a Discrete Selection Procedure

2015 ◽  
Vol 2015 ◽  
pp. 1-17 ◽  
Author(s):  
Qiang Long ◽  
Changzhi Wu ◽  
Xiangyu Wang ◽  
Lin Jiang ◽  
Jueyou Li
Keyword(s):  
Genetic Algorithm ◽  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Selection Procedure ◽  
Population Based ◽  
Pareto Solution ◽  
Multiobjective Genetic Algorithm ◽  
Trade Offs ◽  
Multiobjective Optimization Problems ◽  
Optimum Order

Multiobjective genetic algorithm (MOGA) is a direct search method for multiobjective optimization problems. It is based on the process of the genetic algorithm; the population-based property of the genetic algorithm is well applied in MOGAs. Comparing with the traditional multiobjective algorithm whose aim is to find a single Pareto solution, the MOGA intends to identify numbers of Pareto solutions. During the process of solving multiobjective optimization problems using genetic algorithm, one needs to consider the elitism and diversity of solutions. But, normally, there are some trade-offs between the elitism and diversity. For some multiobjective problems, elitism and diversity are conflicting with each other. Therefore, solutions obtained by applying MOGAs have to be balanced with respect to elitism and diversity. In this paper, we propose metrics to numerically measure the elitism and diversity of solutions, and the optimum order method is applied to identify these solutions with better elitism and diversity metrics. We test the proposed method by some well-known benchmarks and compare its numerical performance with other MOGAs; the result shows that the proposed method is efficient and robust.

scholarly journals A Novel Approach to Improve the Performance of Evolutionary Methods for Nonlinear Constrained Optimization

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Alireza Rowhanimanesh ◽  
Sohrab Efati
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Search Space ◽  
Global Optimum ◽  
Constrained Optimization Problems ◽  
Nonlinear Constrained Optimization ◽  
Evolutionary Methods ◽  
Space Reduction ◽  
Reduced Space

Evolutionary methods are well-known techniques for solving nonlinear constrained optimization problems. Due to the exploration power of evolution-based optimizers, population usually converges to a region around global optimum after several generations. Although this convergence can be efficiently used to reduce search space, in most of the existing optimization methods, search is still continued over original space and considerable time is wasted for searching ineffective regions. This paper proposes a simple and general approach based on search space reduction to improve the exploitation power of the existing evolutionary methods without adding any significant computational complexity. After a number of generations when enough exploration is performed, search space is reduced to a small subspace around the best individual, and then search is continued over this reduced space. If the space reduction parameters (red_gen and red_factor) are adjusted properly, reduced space will include global optimum. The proposed scheme can help the existing evolutionary methods to find better near-optimal solutions in a shorter time. To demonstrate the power of the new approach, it is applied to a set of benchmark constrained optimization problems and the results are compared with a previous work in the literature.

scholarly journals Surrogate Modeling Approaches for Multiobjective Optimization: Methods, Taxonomy, and Results

2020 ◽  
Vol 26 (1) ◽  
pp. 5
Author(s):  
Kalyanmoy Deb ◽  
Proteek Chandan Roy ◽  
Rayan Hussein
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Adaptive Strategy ◽  
Optimization Methods ◽  
Superior Performance ◽  
Pareto Optimal ◽  
Optimization Strategy ◽  
Conflicting Objectives ◽  
The Individual

Most practical optimization problems are comprised of multiple conflicting objectives and constraints which involve time-consuming simulations. Construction of metamodels of objectives and constraints from a few high-fidelity solutions and a subsequent optimization of metamodels to find in-fill solutions in an iterative manner remain a common metamodeling based optimization strategy. The authors have previously proposed a taxonomy of 10 different metamodeling frameworks for multiobjective optimization problems, each of which constructs metamodels of objectives and constraints independently or in an aggregated manner. Of the 10 frameworks, five follow a generative approach in which a single Pareto-optimal solution is found at a time and other five frameworks were proposed to find multiple Pareto-optimal solutions simultaneously. Of the 10 frameworks, two frameworks (M3-2 and M4-2) are detailed here for the first time involving multimodal optimization methods. In this paper, we also propose an adaptive switching based metamodeling (ASM) approach by switching among all 10 frameworks in successive epochs using a statistical comparison of metamodeling accuracy of all 10 frameworks. On 18 problems from three to five objectives, the ASM approach performs better than the individual frameworks alone. Finally, the ASM approach is compared with three other recently proposed multiobjective metamodeling methods and superior performance of the ASM approach is observed. With growing interest in metamodeling approaches for multiobjective optimization, this paper evaluates existing strategies and proposes a viable adaptive strategy by portraying importance of using an ensemble of metamodeling frameworks for a more reliable multiobjective optimization for a limited budget of solution evaluations.

scholarly journals A Comprehensive Study on Metaheuristic Techniques Using Genetic Approach

2019 ◽  
Vol 7 (8) ◽  
pp. 23-31
Author(s):  
G. Kalyani ◽  
K. Krishna Jyothi ◽  
T. Pratyusha
Keyword(s):  
Pareto Front ◽  
Optimization Problems ◽  
Real Life ◽  
Decision Makers ◽  
Benchmark Problems ◽  
Multiple Decision Makers ◽  
Trade Offs ◽  
Solution Methods ◽  
Metaheuristic Techniques ◽  
Comprehensive Study

Most real-life optimization problems involve multiple objective functions. Finding  a  solution  that  satisfies  the  decision-maker  is  very  difficult  owing  to  conflict  between  the  objectives.  Furthermore,  the  solution  depends  on  the  decision-maker’s preference.  Metaheuristic solution methods have become common tools to solve these problems.  The  task  of  obtaining  solutions  that  take  account  of  a  decision-maker’s preference  is  at  the  forefront  of  current  research.  It  is  also  possible  to  have  multiple decision-makers with different preferences and with different  decision-making  powers. It may not be easy to express a preference using crisp numbers. In this study, the preferences of multiple decision-makers were simulated  and  a solution based on  a genetic  algorithm was  developed  to  solve  multi-objective  optimization  problems.  The  preferences  were collected  as  fuzzy  conditional  trade-offs  and  they  were  updated  while  running  the algorithm interactively with the decision-makers. The proposed method was tested using well-known benchmark problems.  The solutions were found to converge around the Pareto front of the problems.

scholarly journals Interactive Multiobjective Procedure for Mixed Problems and Its Application to Capacity Planning

Entropy ◽  
2021 ◽  
Vol 23 (10) ◽  
pp. 1243
Author(s):  
Maciej Nowak ◽  
Tadeusz Trzaskalik ◽  
Sebastian Sitarz
Keyword(s):  
Decision Maker ◽  
Capacity Planning ◽  
Optimization Problems ◽  
Decision Models ◽  
Simultaneous Occurrence ◽  
Final Decision ◽  
Ordered Structures ◽  
Mixed Problems ◽  
Trade Offs ◽  
Dynamic Programming Problem

A problem that appears in many decision models is that of the simultaneous occurrence of deterministic, stochastic, and fuzzy values in the set of multidimensional evaluations. Such problems will be called mixed problems. They lead to the formulation of optimization problems in ordered structures and their scalarization. The aim of the paper is to present an interactive procedure with trade-offs for mixed problems, which helps the decision-maker to make a final decision. Its basic advantage consists of simplicity: after having obtained the solution proposed, the decision-maker should determine whether it is satisfactory and if not, how it should be improved by indicating the criteria whose values should be improved, the criteria whose values cannot be made worse, and the criteria whose values can be made worse. The procedure is applied in solving capacity planning treated as a mixed dynamic programming problem.

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

2022 ◽  
Author(s):  
Firoz Ahmad ◽  
Ahmad Yusuf Adhami ◽  
Boby John ◽  
Amit Reza
Keyword(s):  
Decision Making ◽  
Multiobjective Optimization ◽  
Decision Maker ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Aggregation Operator ◽  
Decision Making Process ◽  
Mathematical Framework ◽  
Multiobjective Optimization Problem ◽  
Fuzzy Aggregation

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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