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>

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 Multiobjective Optimization Scheduling Problems by Pareto-optimality in Agro-alimentaryWorkshop

2006 ◽  
Vol 1 (3) ◽  
pp. 71 ◽  
Author(s):  
Fatma Tangour ◽  
Ihsen Saad
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problem ◽  
Search Space ◽  
Multiobjective Optimization Problem ◽  
Optimal Solutions ◽  
Scheduling Problems ◽  
Objective Functions ◽  
Good Decision ◽  
Initial Cost ◽  
The Cost

This paper deals with the multiobjective optimization problem of an agroalimentary production workshop. Three criteria are considered in addition to this initial cost of production: the cost of the out-of-date products, the cost of the distribution discount and the makespan, and a new coding is proposed for this type of workshop. The adopted approach consists in generating optimal solutions diversified in the search space of solutions, and to help the decision maker when it cannot give a particular preference to one of the objective functions to make the good decision with respect to the quoted criteria.

scholarly journals Evaluation Method of Multiobjective Functions’ Combination and Its Application in Hydrological Model Evaluation

2020 ◽  
Vol 2020 ◽  
pp. 1-23 ◽  
Author(s):  
Jiuyuan Huo ◽  
Liqun Liu
Keyword(s):  
Objective Function ◽  
Parameter Optimization ◽  
Optimization Problem ◽  
Hydrological Model ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Hydrological Forecasting ◽  
Model Parameter Optimization

Parameter optimization of a hydrological model is intrinsically a high dimensional, nonlinear, multivariable, combinatorial optimization problem which involves a set of different objectives. Currently, the assessment of optimization results for the hydrological model is usually made through calculations and comparisons of objective function values of simulated and observed variables. Thus, the proper selection of objective functions’ combination for model parameter optimization has an important impact on the hydrological forecasting. There exist various objective functions, and how to analyze and evaluate the objective function combinations for selecting the optimal parameters has not been studied in depth. Therefore, to select the proper objective function combination which can balance the trade-off among various design objectives and achieve the overall best benefit, a simple and convenient framework for the comparison of the influence of different objective function combinations on the optimization results is urgently needed. In this paper, various objective functions related to parameters optimization of hydrological models were collected from the literature and constructed to nine combinations. Then, a selection and evaluation framework of objective functions is proposed for hydrological model parameter optimization, in which a multiobjective artificial bee colony algorithm named RMOABC is employed to optimize the hydrological model and obtain the Pareto optimal solutions. The parameter optimization problem of the Xinanjiang hydrological model was taken as the application case for long-term runoff prediction in the Heihe River basin. Finally, the technique for order preference by similarity to ideal solution (TOPSIS) based on the entropy theory is adapted to sort the Pareto optimal solutions to compare these combinations of objective functions and obtain the comprehensive optimal objective functions’ combination. The experiments results demonstrate that the combination 2 of objective functions can provide more comprehensive and reliable dominant options (i.e., parameter sets) for practical hydrological forecasting in the study area. The entropy-based method has been proved that it is effective to analyze and evaluate the performance of different combinations of objective functions and can provide more comprehensive and impersonal decision support for hydrological forecasting.

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

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-22 ◽  
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.

AN INTELLIGENT DECISION SUPPORT BASED ON A SUBTRACTIVE CLUSTERING AND FUZZY INFERENCE SYSTEM FOR MULTIOBJECTIVE OPTIMIZATION PROBLEM IN SERIOUS GAME

2011 ◽  
Vol 10 (05) ◽  
pp. 793-810 ◽  
Author(s):  
I. G. P. ASTO BUDITJAHJANTO ◽  
HAJIME MIYAUCHI
Keyword(s):  
Decision Support ◽  
Multiobjective Optimization ◽  
Optimization Problem ◽  
Fuzzy Inference ◽  
Subtractive Clustering ◽  
Multiobjective Optimization Problem ◽  
Optimal Solutions ◽  
Inference System ◽  
Intelligent Decision ◽  
Intelligent Decision Support

Learning decision making through playing a game is an interesting activity for the decision maker or player. In this paper, a multiobjective optimization problem for economic and emission dispatch in which the player can learn about the tradeoff between fuel cost (economic) and emission problems to achieve optimal decisions is considered. A nonplayer character (NPC) is an entity that is built to provide intelligent decision support for the player. The proposed approach is carried out in two stages for the NPC module: the first stage uses the nondominated sorting genetic algorithm II method to solve the multiobjective optimization problem; this stage produces some optimal solutions. The next stage uses subtractive clustering to cluster optimal solutions; furthermore, these clusters are used to build a fuzzy inference system based on the Mamdani type. In this stage, players can select the best decision offered by the NPC.

A Newton method for capturing Pareto optimal solutions of fuzzy multiobjective optimization problems

2019 ◽  
Vol 53 (3) ◽  
pp. 867-886
Author(s):  
Mehrdad Ghaznavi ◽  
Narges Hoseinpoor ◽  
Fatemeh Soleimani
Keyword(s):  
Multiobjective Optimization ◽  
Newton Method ◽  
Optimization Problems ◽  
Order Relation ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Multiobjective Optimization Problems ◽  
Generalized Hukuhara Differentiability

In this study, a Newton method is developed to obtain (weak) Pareto optimal solutions of an unconstrained multiobjective optimization problem (MOP) with fuzzy objective functions. For this purpose, the generalized Hukuhara differentiability of fuzzy vector functions and fuzzy max-order relation on the set of fuzzy vectors are employed. It is assumed that the objective functions of the fuzzy MOP are twice continuously generalized Hukuhara differentiable. Under this assumption, the relationship between weakly Pareto optimal solutions of a fuzzy MOP and critical points of the related crisp problem is discussed. Numerical examples are provided to demonstrate the efficiency of the proposed methodology. Finally, the convergence analysis of the method under investigation is discussed.

scholarly journals Surrogate assisted interactive multiobjective optimization in energy system design of buildings

2021 ◽  
Author(s):  
Pouya Aghaei Pour ◽  
Tobias Rodemann ◽  
Jussi Hakanen ◽  
Kaisa Miettinen
Keyword(s):  
Decision Maker ◽  
Management Strategy ◽  
Computation Time ◽  
Energy System ◽  
Surrogate Models ◽  
Model Management ◽  
Interactive Methods ◽  
Objective Functions ◽  
Interactive Method ◽  
Computationally Expensive

AbstractIn this paper, we develop a novel evolutionary interactive method called interactive K-RVEA, which is suitable for computationally expensive problems. We use surrogate models to replace the original expensive objective functions to reduce the computation time. Typically, in interactive methods, a decision maker provides some preferences iteratively and the optimization algorithm narrows the search according to those preferences. However, working with surrogate models will introduce some inaccuracy to the preferences, and therefore, it would be desirable that the decision maker can work with the solutions that are evaluated with the original objective functions. Therefore, we propose a novel model management strategy to incorporate the decision maker’s preferences to select some of the solutions for both updating the surrogate models (to improve their accuracy) and to show them to the decision maker. Moreover, we solve a simulation-based computationally expensive optimization problem by finding an optimal configuration for an energy system of a heterogeneous business building complex. We demonstrate how a decision maker can interact with the method and how the most preferred solution is chosen. Finally, we compare our method with another interactive method, which does not have any model management strategy, and shows how our model management strategy can help the algorithm to follow the decision maker’s preferences.

scholarly journals A Decision Making Approach for Multi-Objective Optimization Considering A Trade-off Method

2017 ◽  
Vol 11 (2) ◽  
pp. 178-189
Author(s):  
Tipwimol Sooktip ◽  
Naruemon Wattanapongsakorn
Keyword(s):  
Decision Maker ◽  
Optimization Problem ◽  
Benchmark Problems ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Trade Off ◽  
Multi Objective ◽  
Component Allocation ◽  
Objective Value ◽  
Preferred Solutions

In multi-objective optimization problem, a set of optimal solutions is obtained from an optimization algorithm. There are many trade-off optimal solutions. However, in practice, a decision maker or user only needs one or very few solutions for implementation. Moreover, these solutions are difficult to determine from a set of optimal solutions of complex system. Therefore, a trade-off method for multi-objective optimization is proposed for identifying the preferred solutions according to the decision maker’s preference. The preference is expressed by using the trade-off between any two objectives where the decision maker is willing to worsen in one objective value in order to gain improvement in the other objective value. The trade-off method is demonstrated by using well-known two-objective and three-objective benchmark problems. Furthermore, a system design problem with component allocation is also considered to illustrate the applicability of the proposed method. The results show that the trade-off method can be applied for solving practical problems to identify the final solution(s) and easy to use even when the decision maker lacks some knowledge or not an expert in the problem solving. The decision maker only gives his/her preference information.  Then, the corresponding optimal solutions will be obtained, accordingly.

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.

Sign in / Sign up

Export Citation Format

Share Document