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 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 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>

Domination Measure: A New Metric for Solving Multiobjective Optimization

2020 ◽  
Vol 32 (3) ◽  
pp. 565-581 ◽  
Author(s):  
Joshua Q. Hale ◽  
Helin Zhu ◽  
Enlu Zhou
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Solution Space ◽  
Optimization Methods ◽  
Pareto Optimal Set ◽  
Performance Metric ◽  
Multiobjective Optimization Problems ◽  
Global Optima ◽  
Benchmark Test Functions ◽  
Optimal Set

For general multiobjective optimization problems, the usual goal is finding the set of solutions not dominated by any other solutions, that is, a set of solutions as good as any other solution in all objectives and strictly better in at least one objective. In this paper, we propose a novel performance metric called the domination measure to measure the quality of a solution, which can be intuitively interpreted as the probability that an arbitrary solution in the solution space dominates that solution with respect to a predefined probability measure. We then reformulate the original problem as a stochastic and single-objective optimization problem. We further propose a model-based approach to solve it, which leads to an ideal version algorithm and an implementable version algorithm. We show that the ideal version algorithm converges to a set representation of the global optima of the reformulated problem; we demonstrate the numerical performance of the implementable version algorithm by comparing it with numerous existing multiobjective optimization methods on popular benchmark test functions. The numerical results show that the proposed approach is effective in generating a finite and uniformly spread approximation of the Pareto optimal set of the original multiobjective problem and is competitive with the tested existing methods. The concept of domination measure opens the door for potentially many new algorithms, and our proposed algorithm is an instance that benefits from domination measure.

scholarly journals The Evolutionary Algorithm to Find Robust Pareto-Optimal Solutions over Time

2015 ◽  
Vol 2015 ◽  
pp. 1-18 ◽  
Author(s):  
Meirong Chen ◽  
Yinan Guo ◽  
Haiyuan Liu ◽  
Chun Wang
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Multiobjective Optimization Problems ◽  
Dynamic Multiobjective Optimization ◽  
Pareto Fronts ◽  
Over Time

In dynamic multiobjective optimization problems, the environmental parameters change over time, which makes the true pareto fronts shifted. So far, most works of research on dynamic multiobjective optimization methods have concentrated on detecting the changed environment and triggering the population based optimization methods so as to track the moving pareto fronts over time. Yet, in many real-world applications, it is not necessary to find the optimal nondominant solutions in each dynamic environment. To solve this weakness, a novel method called robust pareto-optimal solution over time is proposed. It is in fact to replace the optimal pareto front at each time-varying moment with the series of robust pareto-optimal solutions. This means that each robust solution can fit for more than one time-varying moment. Two metrics, including the average survival time and average robust generational distance, are present to measure the robustness of the robust pareto solution set. Another contribution is to construct the algorithm framework searching for robust pareto-optimal solutions over time based on the survival time. Experimental results indicate that this definition is a more practical and time-saving method of addressing dynamic multiobjective optimization problems changing over time.

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.

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