IEEE Transactions on Evolutionary Computation, 2017
Measuring the performance of an algorithm for solving multiobjective optimization problem has alw... more Measuring the performance of an algorithm for solving multiobjective optimization problem has always been challenging simply due to two conflicting goals, i.e., convergence and diversity of obtained tradeoff solutions. There are a number of metrics for evaluating the performance of a multiobjective optimizer that approximates the whole Paretooptimal front. However, for evaluating the quality of a preferred subset of the whole front, the existing metrics are inadequate. In this paper, we suggest a systematic way to adapt the existing metrics to quantitatively evaluate the performance of a preference-based evolutionary multiobjective optimization algorithm using reference points. The basic idea is to preprocess the preferred solution set according to a multicriterion decision making approach before using a regular metric for performance assessment. Extensive experiments on several artificial scenarios, and benchmark problems fully demonstrate its effectiveness in evaluating the quality of different preferred solution sets with regard to various reference points supplied by a decision maker.
Rather than a whole Pareto-optimal front, which demands too many points (especially in a high-dim... more Rather than a whole Pareto-optimal front, which demands too many points (especially in a high-dimensional space), the decision maker (DM) may only be interested in a partial region, called the region of interest (ROI). In this case, solutions outside this region can be noisy to the decision-making procedure. Even worse, there is no guarantee that we can find the preferred solutions when tackling problems with complicated properties or many objectives. In this paper, we develop a systematic way to incorporate the DM's preference information into the decomposition-based evolutionary multiobjective optimization methods. Generally speaking, our basic idea is a nonuniform mapping scheme by which the originally evenly distributed reference points on a canonical simplex can be mapped to new positions close to the aspiration-level vector supplied by the DM. By this means, we are able to steer the search process toward the ROI either directly or interactively and also handle many objecti...
Ieee Transactions on Evolutionary Computation, Oct 1, 2010
This paper suggests a preference-based methodology, which is embedded in an evolutionary multiobj... more 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, which is used for the subsequent iterations of the evolutionary multiobjective optimization (EMO) algorithm. In addition to the development of the value function which satisfies DM's preference information, the proposed progressively interactive EMO-approach utilizes the constructed value function in directing EMO algorithm's search to more preferred solutions. This is accomplished using a preference-based domination principle and utilizing a preference-based termination criterion. Results on two-to five-objective optimization problems using the progressively interactive NSGA-II approach show the simplicity of the proposed approach and its future promise. A parametric study involving the algorithm's parameters reveals interesting insights of parameter interactions and indicates useful parameter values. A number of extensions to this paper are also suggested.
We present a new hybrid approach to interactive evolutionary multi-objective optimization that us... more 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 for the preference function, but does assume that the preference function is quasi-concave. This paper describes the genetic algorithm and demonstrates its performance on the multi-objective knapsack problem.
In this paper, we propose a new evolutionary algorithm for multi-objective optimization. The prop... more In this paper, we propose a new evolutionary algorithm for multi-objective optimization. The proposed algorithm benefits from the existing literature and borrows several concepts from existing multi-objective optimization algorithms. The proposed algorithm employs a new kind of selection procedure which benefits from the search history of the algorithm and attempts to minimize the number of function evaluations required to achieve the desired convergence.
IEEE Transactions on Evolutionary Computation, 2017
Measuring the performance of an algorithm for solving multiobjective optimization problem has alw... more Measuring the performance of an algorithm for solving multiobjective optimization problem has always been challenging simply due to two conflicting goals, i.e., convergence and diversity of obtained tradeoff solutions. There are a number of metrics for evaluating the performance of a multiobjective optimizer that approximates the whole Paretooptimal front. However, for evaluating the quality of a preferred subset of the whole front, the existing metrics are inadequate. In this paper, we suggest a systematic way to adapt the existing metrics to quantitatively evaluate the performance of a preference-based evolutionary multiobjective optimization algorithm using reference points. The basic idea is to preprocess the preferred solution set according to a multicriterion decision making approach before using a regular metric for performance assessment. Extensive experiments on several artificial scenarios, and benchmark problems fully demonstrate its effectiveness in evaluating the quality of different preferred solution sets with regard to various reference points supplied by a decision maker.
Rather than a whole Pareto-optimal front, which demands too many points (especially in a high-dim... more Rather than a whole Pareto-optimal front, which demands too many points (especially in a high-dimensional space), the decision maker (DM) may only be interested in a partial region, called the region of interest (ROI). In this case, solutions outside this region can be noisy to the decision-making procedure. Even worse, there is no guarantee that we can find the preferred solutions when tackling problems with complicated properties or many objectives. In this paper, we develop a systematic way to incorporate the DM's preference information into the decomposition-based evolutionary multiobjective optimization methods. Generally speaking, our basic idea is a nonuniform mapping scheme by which the originally evenly distributed reference points on a canonical simplex can be mapped to new positions close to the aspiration-level vector supplied by the DM. By this means, we are able to steer the search process toward the ROI either directly or interactively and also handle many objecti...
Ieee Transactions on Evolutionary Computation, Oct 1, 2010
This paper suggests a preference-based methodology, which is embedded in an evolutionary multiobj... more 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, which is used for the subsequent iterations of the evolutionary multiobjective optimization (EMO) algorithm. In addition to the development of the value function which satisfies DM's preference information, the proposed progressively interactive EMO-approach utilizes the constructed value function in directing EMO algorithm's search to more preferred solutions. This is accomplished using a preference-based domination principle and utilizing a preference-based termination criterion. Results on two-to five-objective optimization problems using the progressively interactive NSGA-II approach show the simplicity of the proposed approach and its future promise. A parametric study involving the algorithm's parameters reveals interesting insights of parameter interactions and indicates useful parameter values. A number of extensions to this paper are also suggested.
We present a new hybrid approach to interactive evolutionary multi-objective optimization that us... more 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 for the preference function, but does assume that the preference function is quasi-concave. This paper describes the genetic algorithm and demonstrates its performance on the multi-objective knapsack problem.
In this paper, we propose a new evolutionary algorithm for multi-objective optimization. The prop... more In this paper, we propose a new evolutionary algorithm for multi-objective optimization. The proposed algorithm benefits from the existing literature and borrows several concepts from existing multi-objective optimization algorithms. The proposed algorithm employs a new kind of selection procedure which benefits from the search history of the algorithm and attempts to minimize the number of function evaluations required to achieve the desired convergence.
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Papers by Kalyanmoy Deb