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Using Choquet integral as preference model in interactive evolutionary multiobjective optimization

Published on May 1, 2016in European Journal of Operational Research3.81
· DOI :10.1016/j.ejor.2015.10.027
Juergen Branke16
Estimated H-index: 16
(Warw.: University of Warwick),
Salvatore Corrente15
Estimated H-index: 15
(University of Catania)
+ 2 AuthorsPiotr Zielniewicz9
Estimated H-index: 9
(PUT: Poznań University of Technology)
Cite
Abstract
We propose an interactive multiobjective evolutionary algorithm that attempts to discover the most preferred part of the Pareto-optimal set. Preference information is elicited by asking the user to compare some solutions pairwise. This information is then used to curb the set of compatible user’s value functions, and the multiobjective evolutionary algorithm is run to simultaneously search for all solutions that could potentially be the most preferred. Compared to previous similar approaches, we implement a much more efficient way of determining potentially preferred solutions, that is, solutions that are best for at least one value function compatible with the preference information provided by the decision maker. For the first time in the context of evolutionary computation, we apply the Choquet integral as a user’s preference model, allowing us to capture interactions between objectives. As there is a trade-off between the flexibility of the value function model and the complexity of learning a faithful model of user’s preferences, we propose to start the interactive process with a simple linear model but then to switch to the Choquet integral as soon as the preference information can no longer be represented using the linear model. An experimental analysis demonstrates the effectiveness of the approach.
  • References (45)
  • Citations (29)
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References45
Newest
Published on Jan 1, 2016
Juergen Branke16
Estimated H-index: 16
(Warw.: University of Warwick)
Evolutionary multiobjective optimization promises to efficiently generate a representative set of Pareto optimal solutions in a single optimization run. This allows the decision maker to select the most preferred solution from the generated set, rather than having to specify preferences a priori. In recent years, there has been a growing interest in combining the ideas of evolutionary multiobjective optimization and MCDA. MCDA can be used before optimization, to specify partial user preferences,...
Published on Feb 1, 2015in IEEE Transactions on Evolutionary Computation8.51
Jürgen Branke34
Estimated H-index: 34
(Warw.: University of Warwick),
Salvatore Greco52
Estimated H-index: 52
(University of Catania)
+ 1 AuthorsPiotr Zielniewicz9
Estimated H-index: 9
(PUT: Poznań University of Technology)
This paper proposes an interactive multiobjective evolutionary algorithm (MOEA) that attempts to learn a value function capturing the users’ true preferences. At regular intervals, the user is asked to rank a single pair of solutions. This information is used to update the algorithm’s internal value function model, and the model is used in subsequent generations to rank solutions incomparable according to dominance. This speeds up evolution toward the region of the Pareto front that is most desi...
Published on Nov 1, 2013in Machine Learning2.81
Salvatore Corrente15
Estimated H-index: 15
(University of Catania),
Salvatore Greco52
Estimated H-index: 52
(University of Portsmouth)
+ 1 AuthorsRoman Slowifiski67
Estimated H-index: 67
(PUT: Poznań University of Technology)
Multiple Criteria Decision Aiding (MCDA) offers a diversity of approaches designed for providing the decision maker (DM) with a recommendation concerning a set of alternatives (items, actions) evaluated from multiple points of view, called criteria. This paper aims at drawing attention of the Machine Learning (ML) community upon recent advances in a representative MCDA methodology, called Robust Ordinal Regression (ROR). ROR learns by examples in order to rank a set of alternatives, thus conside...
Published on Jun 1, 2011 in CEC (Congress on Evolutionary Computation)
Antonio López Jaimes11
Estimated H-index: 11
(CINVESTAV),
Alfredo Arias Montaño5
Estimated H-index: 5
(CINVESTAV),
Carlos A. Coello-Coello65
Estimated H-index: 65
(CINVESTAV)
In this paper, we assess the convenience of applying a previously proposed interactive method to solve three aerodynamic airfoil shape optimization problems with 2, 3, and 6 objectives, respectively. The expensive simulations required to evaluate the objective functions makes these problems an excellent example in which the use of interactive methods is very advantageous. First, the search can be focused on the decision maker's region of interest, saving this way, valuable function evaluations. ...
Published on Apr 5, 2011
Karthik Sindhya13
Estimated H-index: 13
(Information Technology University),
Ana Belen Ruiz9
Estimated H-index: 9
(UMA: University of Málaga),
Kaisa Miettinen39
Estimated H-index: 39
(Information Technology University)
This paper describes a new Preference-based Interactive Evolutionary (PIE) algorithm for multi-objective optimization which exploits the advantages of both evolutionary algorithms and multiple criteria decision making approaches. Our algorithm uses achievement scalarizing functions and the potential of population based evolutionary algorithms to help the decision maker to direct the search towards the desired Pareto optimal solution. Starting from an approximated nadir point, the PIE algorithm i...
Published on Oct 1, 2010in IEEE Transactions on Evolutionary Computation8.51
Roberto Battiti33
Estimated H-index: 33
,
Andrea Passerini25
Estimated H-index: 25
The centrality of the decision maker (DM) is widely recognized in the multiple criteria decision-making community. This translates into emphasis on seamless human-computer interaction, and adaptation of the solution technique to the knowledge which is progressively acquired from the DM. This paper adopts the methodology of reactive search optimization (RSO) for evolutionary interactive multiobjective optimization. RSO follows to the paradigm of “learning while optimizing,” through the use of onl...
Published on Oct 1, 2010in IEEE Transactions on Evolutionary Computation8.51
Tobias Wagner18
Estimated H-index: 18
,
Heike Trautmann17
Estimated H-index: 17
In this paper, a concept for efficiently approximating the practically relevant regions of the Pareto front (PF) is introduced. Instead of the original objectives, desirability functions (DFs) of the objectives are optimized, which express the preferences of the decision maker. The original problem formulation and the optimization algorithm do not have to be modified. DFs map an objective to the domain [0, 1] and nonlinearly increase with better objective quality. By means of this mapping, value...
Published on Oct 1, 2010in IEEE Transactions on Evolutionary Computation8.51
Lamjed Ben Said12
Estimated H-index: 12
(Tunis University),
Slim Bechikh14
Estimated H-index: 14
(Tunis University),
Khaled Ghedira14
Estimated H-index: 14
(Tunis University)
Evolutionary multiobjective optimization (EMO) methodologies have gained popularity in finding a representative set of Pareto optimal solutions in the past decade and beyond. Several techniques have been proposed in the specialized literature to ensure good convergence and diversity of the obtained solutions. However, in real world applications, the decision maker is not interested in the overall Pareto optimal front since the final decision is a unique solution. Recently, there has been an incr...
Published on Oct 1, 2010in European Journal of Operational Research3.81
John W. Fowler36
Estimated H-index: 36
(ASU: Arizona State University),
Esma Senturk Gel15
Estimated H-index: 15
(ASU: Arizona State University)
+ 3 AuthorsJyrki Wallenius14
Estimated H-index: 14
(Aalto University)
We present a new hybrid approach to interactive evolutionary multi-objective optimization that uses a partial preference order to act as the fitness function in a customized genetic algorithm. We periodically send solutions to the decision maker (DM) for her evaluation and use the resulting preference information to form preference cones consisting of inferior solutions. The cones allow us to implicitly rank solutions that the DM has not considered. This technique avoids assuming an exact form f...
Published on Oct 1, 2010in IEEE Transactions on Evolutionary Computation8.51
Kalyanmoy Deb91
Estimated H-index: 91
(IITK: Indian Institute of Technology Kanpur),
Ankur Sinha19
Estimated H-index: 19
(Aalto University)
+ 1 AuthorsJyrki Wallenius26
Estimated H-index: 26
(Aalto University)
This paper suggests a preference-based methodology, which is embedded in an evolutionary multiobjective optimization algorithm to lead a decision maker (DM) to the most preferred solution of her or his choice. The progress toward the most preferred solution is made by accepting preference based information progressively from the DM after every few generations of an evolutionary multiobjective optimization algorithm. This preference information is used to model a strictly monotone value function,...
Cited By29
Newest
Published on Aug 1, 2019in Computers & Operations Research3.00
Michał K. Tomczyk2
Estimated H-index: 2
,
Miłosz Kadziński16
Estimated H-index: 16
Abstract We propose a family of algorithms, called EMOSOR, combining Evolutionary Multiple Objective Optimization with Stochastic Ordinal Regression. The proposed methods ask the Decision Maker (DM) to holistically compare, at regular intervals, a pair of solutions, and use the Monte Carlo simulation to construct a set of preference model instances compatible with such indirect and incomplete information. The specific variants of EMOSOR are distinguished by the following three aspects. Firstly, ...
Published on Jul 23, 2019
Michael S. Bittermann (ITU: Istanbul Technical University), Ecenur Yavuz (ITU: Istanbul Technical University), Özer Ciftcioglu10
Estimated H-index: 10
(TU Delft: Delft University of Technology)
A learning strategy for fuzzy neural tree is presented that is based on combining the knowledge-driven and data-driven modeling paradigms. The knowledge-driven aspect of the strategy is expressing knowledge via the connection topology of a neural tree. The tree is driven by inputs associated with fuzzy logic. In this type of neural tree, the connection weights are determined in an unsupervised manner. However, the fuzzy logic related parameters are subject to data-driven identification, and they...
Published on May 12, 2019in Journal of Intelligent and Fuzzy Systems1.64
Xin Liu1
Estimated H-index: 1
(CSU: Central South University),
Yanju Zhou3
Estimated H-index: 3
(CSU: Central South University),
Zongrun Wang3
Estimated H-index: 3
(CSU: Central South University)
Published on Jun 1, 2019in Expert Systems With Applications4.29
Mengzhuo Guo (Ministry of Education), Mengzhuo Guo (Ministry of Education)+ 0 AuthorsJiapeng Liu4
Estimated H-index: 4
(Ministry of Education)
Abstract A new decision-aiding approach for multiple criteria sorting problems is proposed for considering the non-monotonic relationship between the preference and evaluations of the alternatives on specific criteria. The approach employs a value function as the preference model and requires the decision maker (DM) to provide assignment examples of a subset of reference alternatives as preference information. We assume that the marginal value function of a non-monotonic criterion is non-decreas...
Published on Feb 1, 2019
Marcelo Karanik5
Estimated H-index: 5
(National Technological University (United States)),
Rubén Bernal3
Estimated H-index: 3
(National Technological University (United States))
+ 1 AuthorsJosé Antonio Gómez-Ruiz8
Estimated H-index: 8
(UMA: University of Málaga)
Customers strongly base their e-commerce decisions on the opinions of others by checking reviews and ratings provided by other users. These assessments are overall opinions about the product or service, and it is not possible to establish why they perceive it as good or bad. To understand this “why”, it is necessary an expert’s analysis concerning the relevant factors of the product or service. Frequently, these two visions are not coincident and the best product for experts may not be the best ...
Published on Jan 1, 2019
Michał K. Tomczyk2
Estimated H-index: 2
(PUT: Poznań University of Technology),
Miłosz Kadziński16
Estimated H-index: 16
(PUT: Poznań University of Technology)
Published on Dec 1, 2018in Knowledge Based Systems5.10
Xiaoyang Yao (China Jiliang University), Jianping LiXiaolei19
Estimated H-index: 19
(CAS: Chinese Academy of Sciences)
+ 1 AuthorsDengsheng Wu10
Estimated H-index: 10
(CAS: Chinese Academy of Sciences)
Abstract A perfect combination of fact-based and value-based judgments is what multiple criteria decision-making (MCDM) issues pursue. Tolerability constraints, an important part of value-based judgments, are easily observable and have drawn attention in theory. However, their practical applications in the MCDM process are still in their infancy. This paper aims to fill the gap between theory and application. A framework for tolerability constraints in the context of non-independent criteria is ...
Published on Oct 1, 2018in Journal of Intelligent and Fuzzy Systems1.64
Xiaoxu Cui (Beijing Jiaotong University), Meimei Xia25
Estimated H-index: 25
(Beijing Jiaotong University)
Published on Sep 1, 2018in Natural Computing1.33
Michael Emmerich22
Estimated H-index: 22
(LEI: Leiden University),
André H. Deutz10
Estimated H-index: 10
(LEI: Leiden University)
In almost no other field of computer science, the idea of using bio-inspired search paradigms has been so useful as in solving multiobjective optimization problems. The idea of using a population of search agents that collectively approximate the Pareto front resonates well with processes in natural evolution, immune systems, and swarm intelligence. Methods such as NSGA-II, SPEA2, SMS-EMOA, MOPSO, and MOEA/D became standard solvers when it comes to solving multiobjective optimization problems. T...