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Kalyanmoy Deb - One of the best experts on this subject based on the ideXlab platform.

  • an improved visual analytics framework for high dimensional Pareto Optimal Front a case for multi objective portfolio optimization
    Journal of Banking and Financial Technology, 2021
    Co-Authors: Akm Khaled Ahsan Talukder, Kalyanmoy Deb
    Abstract:

    Visual representation of a many-objective Pareto-Optimal Front in a high-dimensional (four or more) objective space requires a large number of data points. Choosing a single point from a large number of data points even with preference information is problematic, as it causes a large cognitive burden on the part of the decision-makers. Therefore, many-objective optimization and analytics practitioners have been interested in practical visualization methods that enable them to filter down a large set of data points to a few critical points for further analysis. Most existing visualization methods are borrowed from other data analytics domain and they are too generic to be effective for many-criteria decision making. In this paper, we propose a visualization method, following an earlier concept, using star-coordinate plots for effectively visualizing many-objective trade-off solutions (data points). We demonstrate the use of the proposed method to a couple of high-dimensional test problems and a 4-objective portfolio optimization problem. We also show a case of interactive exploratory data analytics where we use the ‘Pareto Race’ technique from the multi-criteria decision analysis (MCDA) literature to demonstrate the ease and advantage of the proposed visualization method.

  • paletteviz with star coordinates an improved method for high dimensional Pareto Optimal Front visualization and decision making
    IEEE Symposium Series on Computational Intelligence, 2020
    Co-Authors: Akm Khaled Ahsan Talukder, Kalyanmoy Deb
    Abstract:

    Visual representation of a many-objective Pareto-Optimal Front in four or more dimensional objective space requires a large number of data points. Moreover, choosing a single point from a large set even with certain preference information is problematic, as it causes a large cognitive burden on the part of the decision-makers. Therefore, many-objective optimization and decision-making practitioners have been interested in effective visualization methods to enable them to filter down a large set to a few critical points for further analysis. Most existing visualization methods are borrowed from other data analytics domain and they are too generic to be effective for manycriteria decision making. In this paper, we propose a visualization method, following an earlier concept, using star-coordinate plots for effectively visualizing many-objective trade-off solutions. The proposed method respects some basic topological, geometric and functional decision-making properties of high-dimensional tradeoff points mapped to a three-dimensional space. We demonstrate the use of the proposed method to a number large-dimensional test problems and a 10-objective real-world problem. The use of `Pareto Race’ concept from MCDM literature is introduced within the proposed visualization method to demonstrate the ease and advantage of the visualization method.

  • palettestarviz a visualization method for multi criteria decision making from high dimensional Pareto Optimal Front
    Genetic and Evolutionary Computation Conference, 2020
    Co-Authors: A Khaled K M Talukder, Kalyanmoy Deb
    Abstract:

    Visual representation of a many-objective Pareto-Optimal Front in four or more dimensional objective space requires a large number of data points. Moreover, choosing a single point from a large set even with certain preference information is problematic, as it causes a large cognitive burden on the part of the decision-makers. Therefore, many-objective optimization and decision-making practitioners have been interested in effective visualization methods to enable them to filter down a large set to a few critical points for further analysis. Most existing visualization methods are borrowed from other data analytic domains and they are too generic to be effective for many-criteria decision making. In this paper, we propose an alternative visualization method, following an earlier concept, using star-coordinate plots for effectively visualizing many-objective trade-off solutions. The proposed PaletteStarViz respects some basic topological, geometric, and functional decision-making properties of high-dimensional trade-off points mapped to a "two-and-a-half" dimensional space. We demonstrate the use of PaletteStarViz to a number high-dimensional Pareto-Optimal Fronts.

  • paletteviz a visualization method for functional understanding of high dimensional Pareto Optimal data sets to aid multi criteria decision making
    IEEE Computational Intelligence Magazine, 2020
    Co-Authors: Akm Khaled Ahsan Talukder, Kalyanmoy Deb
    Abstract:

    To represent a many-objective Pareto-Optimal Front having four or more dimensions of the objective space, a large number of points are necessary. However, for choosing a single preferred point from a large set is problematic and time-consuming, as they provide a large cognitive burden on the part of the decision-makers (DMs). Hence, many-objective optimization and decision-making researchers and practitioners have been interested in effective visualization methods to filter down a few critical points for further analysis. While some ideas are borrowed from data analytics and visualization literature, they are generic and do not exploit the functionalities that DMs are usually interested. In this paper, we outline some such functionalities: a point's trade-off among conflicting objectives in its neighborhood, closeness of a point to the boundary or core of the high-dimensional Pareto set, specific desired geometric properties of points, spatial distance of one point to another, closeness of a point to constraint boundary, and others, in developing a new visualization technique. We propose a novel way to map a high-dimensional Pareto-Optimal Front (points or data-set) into two-and-half dimensions by revealing functional features of points that may be of great interest to DMs. As a proof-of-principle demonstration, we apply our proposed palette visualization (PaletteViz) technique to a number of different structures of Pareto-Optimal data-sets and discuss how the proposed technique is different from a few popularly used visualization techniques.

  • r metric evaluating the performance of preference based evolutionary multiobjective optimization using reference points
    IEEE Transactions on Evolutionary Computation, 2018
    Co-Authors: Kalyanmoy Deb, Xin Yao
    Abstract:

    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 Pareto-Optimal 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.

S Fatemi M T Ghomi - One of the best experts on this subject based on the ideXlab platform.

  • a multi phase covering Pareto Optimal Front method to multi objective parallel machine scheduling
    International Journal of Production Research, 2010
    Co-Authors: J Behnamian, M Zandieh, S Fatemi M T Ghomi
    Abstract:

    This paper considers the problem of parallel machine scheduling with sequence-dependent setup times to minimise both makespan and total earliness/tardiness in the due window. To tackle the problem considered, a multi-phase algorithm is proposed. The goal of the initial phase is to obtain a good approximation of the Pareto-Front. In the second phase, to improve the Pareto-Front, non-dominated solutions are unified to constitute a big population. In this phase, based on the local search in the Pareto space concept, three multi-objective hybrid metaheuristics are proposed. Covering the whole set of Pareto-Optimal solutions is a desired task of multi-objective optimisation methods. So in the third phase, a new method using an e-constraint hybrid metaheuristic is proposed to cover the gaps between the non-dominated solutions and improve the Pareto-Front. Appropriate combinations of multi-objective methods in various phases are considered to improve the total performance. The multi-phase algorithm iterates over...

  • a multi phase covering Pareto Optimal Front method to multi objective scheduling in a realistic hybrid flowshop using a hybrid metaheuristic
    Expert Systems With Applications, 2009
    Co-Authors: J Behnamian, S Fatemi M T Ghomi, M Zandieh
    Abstract:

    This paper considers the problem of sequence-dependent setup time hybrid flowshop scheduling with the objectives of minimizing the makespan and sum of the earliness and tardiness of jobs, and present a multi-phase method. In initial phase, the population will be decomposed into several subpopulations. In this phase we develop a random key genetic algorithm and the goal is to obtain a good approximation of the Pareto-Front. In the second phase, for improvement the Pareto-Front, non-dominant solutions will be unified as one big population. In this phase, based on the local search in Pareto space concept, we propose multi-objective hybrid metaheuristic. Finally in phase 3, we propose a novel method using e-constraint covering hybrid metaheuristic to cover the gaps between the non-dominated solutions and improve Pareto-Front. Generally in three phases, we consider appropriate combinations of multi-objective methods to improve the total performance. The hybrid algorithm used in phases 2 and 3 combines elements from both simulated annealing and a variable neighborhood search. The aim of using a hybrid metaheuristic is to raise the level of generality so as to be able to apply the same solution method to several problems. Furthermore, in this study to evaluate non-dominated solution sets, we suggest several new approaches. The non-dominated sets obtained from each phase and global archive sub-population genetic algorithm presented previously in the literature are compared. The results obtained from the computational study have shown that the multi-phase algorithm is a viable and effective approach.

M Zandieh - One of the best experts on this subject based on the ideXlab platform.

  • a multi phase covering Pareto Optimal Front method to multi objective parallel machine scheduling
    International Journal of Production Research, 2010
    Co-Authors: J Behnamian, M Zandieh, S Fatemi M T Ghomi
    Abstract:

    This paper considers the problem of parallel machine scheduling with sequence-dependent setup times to minimise both makespan and total earliness/tardiness in the due window. To tackle the problem considered, a multi-phase algorithm is proposed. The goal of the initial phase is to obtain a good approximation of the Pareto-Front. In the second phase, to improve the Pareto-Front, non-dominated solutions are unified to constitute a big population. In this phase, based on the local search in the Pareto space concept, three multi-objective hybrid metaheuristics are proposed. Covering the whole set of Pareto-Optimal solutions is a desired task of multi-objective optimisation methods. So in the third phase, a new method using an e-constraint hybrid metaheuristic is proposed to cover the gaps between the non-dominated solutions and improve the Pareto-Front. Appropriate combinations of multi-objective methods in various phases are considered to improve the total performance. The multi-phase algorithm iterates over...

  • a multi phase covering Pareto Optimal Front method to multi objective scheduling in a realistic hybrid flowshop using a hybrid metaheuristic
    Expert Systems With Applications, 2009
    Co-Authors: J Behnamian, S Fatemi M T Ghomi, M Zandieh
    Abstract:

    This paper considers the problem of sequence-dependent setup time hybrid flowshop scheduling with the objectives of minimizing the makespan and sum of the earliness and tardiness of jobs, and present a multi-phase method. In initial phase, the population will be decomposed into several subpopulations. In this phase we develop a random key genetic algorithm and the goal is to obtain a good approximation of the Pareto-Front. In the second phase, for improvement the Pareto-Front, non-dominant solutions will be unified as one big population. In this phase, based on the local search in Pareto space concept, we propose multi-objective hybrid metaheuristic. Finally in phase 3, we propose a novel method using e-constraint covering hybrid metaheuristic to cover the gaps between the non-dominated solutions and improve Pareto-Front. Generally in three phases, we consider appropriate combinations of multi-objective methods to improve the total performance. The hybrid algorithm used in phases 2 and 3 combines elements from both simulated annealing and a variable neighborhood search. The aim of using a hybrid metaheuristic is to raise the level of generality so as to be able to apply the same solution method to several problems. Furthermore, in this study to evaluate non-dominated solution sets, we suggest several new approaches. The non-dominated sets obtained from each phase and global archive sub-population genetic algorithm presented previously in the literature are compared. The results obtained from the computational study have shown that the multi-phase algorithm is a viable and effective approach.

J Behnamian - One of the best experts on this subject based on the ideXlab platform.

  • a multi phase covering Pareto Optimal Front method to multi objective parallel machine scheduling
    International Journal of Production Research, 2010
    Co-Authors: J Behnamian, M Zandieh, S Fatemi M T Ghomi
    Abstract:

    This paper considers the problem of parallel machine scheduling with sequence-dependent setup times to minimise both makespan and total earliness/tardiness in the due window. To tackle the problem considered, a multi-phase algorithm is proposed. The goal of the initial phase is to obtain a good approximation of the Pareto-Front. In the second phase, to improve the Pareto-Front, non-dominated solutions are unified to constitute a big population. In this phase, based on the local search in the Pareto space concept, three multi-objective hybrid metaheuristics are proposed. Covering the whole set of Pareto-Optimal solutions is a desired task of multi-objective optimisation methods. So in the third phase, a new method using an e-constraint hybrid metaheuristic is proposed to cover the gaps between the non-dominated solutions and improve the Pareto-Front. Appropriate combinations of multi-objective methods in various phases are considered to improve the total performance. The multi-phase algorithm iterates over...

  • a multi phase covering Pareto Optimal Front method to multi objective scheduling in a realistic hybrid flowshop using a hybrid metaheuristic
    Expert Systems With Applications, 2009
    Co-Authors: J Behnamian, S Fatemi M T Ghomi, M Zandieh
    Abstract:

    This paper considers the problem of sequence-dependent setup time hybrid flowshop scheduling with the objectives of minimizing the makespan and sum of the earliness and tardiness of jobs, and present a multi-phase method. In initial phase, the population will be decomposed into several subpopulations. In this phase we develop a random key genetic algorithm and the goal is to obtain a good approximation of the Pareto-Front. In the second phase, for improvement the Pareto-Front, non-dominant solutions will be unified as one big population. In this phase, based on the local search in Pareto space concept, we propose multi-objective hybrid metaheuristic. Finally in phase 3, we propose a novel method using e-constraint covering hybrid metaheuristic to cover the gaps between the non-dominated solutions and improve Pareto-Front. Generally in three phases, we consider appropriate combinations of multi-objective methods to improve the total performance. The hybrid algorithm used in phases 2 and 3 combines elements from both simulated annealing and a variable neighborhood search. The aim of using a hybrid metaheuristic is to raise the level of generality so as to be able to apply the same solution method to several problems. Furthermore, in this study to evaluate non-dominated solution sets, we suggest several new approaches. The non-dominated sets obtained from each phase and global archive sub-population genetic algorithm presented previously in the literature are compared. The results obtained from the computational study have shown that the multi-phase algorithm is a viable and effective approach.

T. Meyarivan - One of the best experts on this subject based on the ideXlab platform.

  • A fast and elitist multiobjective genetic algorithm: NSGA-II
    IEEE Transactions on Evolutionary Computation, 2002
    Co-Authors: Kalyanmoy Deb, Amrit Pratap, Sameer Agarwal, T. Meyarivan
    Abstract:

    Multi-objective evolutionary algorithms (MOEAs) that use non-dominated sorting and sharing have been criticized mainly for: (1) their O(MN3) computational complexity (where M is the number of objectives and N is the population size); (2) their non-elitism approach; and (3) the need to specify a sharing parameter. In this paper, we suggest a non-dominated sorting-based MOEA, called NSGA-II (Non-dominated Sorting Genetic Algorithm II), which alleviates all of the above three difficulties. Specifically, a fast non-dominated sorting approach with O(MN2) computational complexity is presented. Also, a selection operator is presented that creates a mating pool by combining the parent and offspring populations and selecting the best N solutions (with respect to fitness and spread). Simulation results on difficult test problems show that NSGA-II is able, for most problems, to find a much better spread of solutions and better convergence near the true Pareto-Optimal Front compared to the Pareto-archived evolution strategy and the strength-Pareto evolutionary algorithm - two other elitist MOEAs that pay special attention to creating a diverse Pareto-Optimal Front. Moreover, we modify the definition of dominance in order to solve constrained multi-objective problems efficiently. Simulation results of the constrained NSGA-II on a number of test problems, including a five-objective, seven-constraint nonlinear problem, are compared with another constrained multi-objective optimizer, and the much better performance of NSGA-II is observed

  • a fast elitist non dominated sorting genetic algorithm for multi objective optimisation nsga ii
    Parallel Problem Solving from Nature, 2000
    Co-Authors: Samir Agrawal, Amrit Pratap, T. Meyarivan
    Abstract:

    Multi-objective evolutionary algorithms which use non-dominated sorting and sharing have been mainly criticized for their (i) O(MN3) computational complexity (where M is the number of objectives and N is the population size), (ii) non-elitism approach, and (iii) the need for specifying a sharing parameter. In this paper, we suggest a non-dominated sorting based multi-objective evolutionary algorithm (we called it the Non-dominated Sorting GA-II or NSGA-II) which alleviates all the above three difficulties. Specifically, a fast non-dominated sorting approach with O(MN2) computational complexity is presented. Second, a selection operator is presented which creates a mating pool by combining the parent and child populations and selecting the best (with respect to fitness and spread) N solutions. Simulation results on five difficult test problems show that the proposed NSGA-II, in most problems, is able to find much better spread of solutions and better convergence near the true Pareto-Optimal Front compared to PAES and SPEA--two other elitist multi-objective EAs which pay special attention towards creating a diverse Pareto-Optimal Front. Because of NSGA-II's low computational requirements, elitist approach, and parameter-less sharing approach, NSGA-II should find increasing applications in the years to come.