Generalized incremental orthant search: towards efficient steady-state evolutionary multiobjective algorithms
Pages 1357 - 1365
Abstract
Some of the modern evolutionary multiobjective algorithms have a high computational complexity of the internal data processing. To further complicate this problem, researchers often wish to alter some of these procedures, and to do it with little effort.
The problem is even more pronounced for steady-state algorithms, which update the internal information as each single individual is computed. In this paper we explore the applicability of the principles behind the existing framework, called generalized offline orthant search, to the typical problems arising in steady-state evolutionary multiobjective algorithms.
We show that the variety of possible problem formulations is higher than in the offline setting. In particular, we state a problem which cannot be solved in an incremental manner faster than from scratch. We present an efficient algorithm for one of the simplest possible settings, incremental dominance counting, and formulate the set of requirements that enable efficient solution of similar problems. We also present an algorithm to evaluate fitness within the IBEA algorithm and show when it is efficient in practice.
Supplementary Material
Supplemental material.
- Download
- 91.51 KB
References
[1]
Hussein A. Abbass, Ruhul Sarker, and Charles Newton. 2001. PDE: A Pareto Frontier Differential Evolution Approach for Multiobjective Optimization Problems. In Proceedings of the Congress on Evolutionary Computation. IEEE Press, 971--978.
[2]
Anne Auger, Johannes Bader, Dimo Brockhoff, and Eckart Zitzler. 2012. Hypervolume-based multiobjective optimization: Theoretical foundations and practical implications. Theoretical Computer Science 425 (2012), 75--103.
[3]
Jon Louis Bentley. 1975. Multidimensional binary search trees used for associative searching. Commun. ACM 18, 9 (1975), 509--517.
[4]
Jon Louis Bentley. 1980. Multidimensional Divide-and-conquer. Communications of ACM 23, 4 (1980), 214--229.
[5]
Karl Bringmann and Tobias Friedrich. 2009. Approximating the Least Hypervolume Contributor: NP-Hard in General, But Fast in Practice. In Proceedings of the 5th International Conference on Evolutionary Multi-Criterion Optimization. 6--20.
[6]
Dimo Brockhoff, Tobias Wagner, and Heike Trautmann. 2012. On the properties of the R2 indicator. In Proceedings of Genetic and Evolutionary Computation Conference. 465--472.
[7]
Adam L. Buchsbaum and Michael T. Goodrich. 2004. Three-Dimensional Layers of Maxima. Algorithmica 39 (2004), 275--286.
[8]
Maxim Buzdalov. 2018. Generalized offline orthant search: One code for many problems in multiobjective optimization. In Proceedings of Genetic and Evolutionary Computation Conference. 593--600.
[9]
Maxim Buzdalov. 2019. Make Evolutionary Multiobjective Algorithms Scale Better with Advanced Data Structures: Van Emde Boas Tree for Non-Dominated Sorting. In Proceedings of International Conference on Evolutionary Multi-Criterion Optimization. Number 11411 in Lecture Notes in Computer Science. 66--77.
[10]
Alexander W. Churchill, Phil Husbands, and Andrew Philippides. 2013. Tool Sequence Optimization using Synchronous and Asynchronous Parallel Multi-Objective Evolutionary Algorithms with Heterogeneous Evaluations. In Proceedings of IEEE Congress on Evolutionary Computation. 2924--2931.
[11]
David W. Corne, Nick R. Jerram, Joshua D. Knowles, and Martin J. Oates. 2001. PESA-II: Region-based Selection in Evolutionary Multiobjective Optimization. In Proceedings of Genetic and Evolutionary Computation Conference. Morgan Kaufmann Publishers, 283--290.
[12]
Kalyanmoy Deb and Himanshu Jain. 2013. An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints. IEEE Transactions on Evolutionary Computation 18, 4 (2013), 577--601.
[13]
Kalyanmoy Deb, Amrit Pratap, Sameer Agarwal, and T. Meyarivan. 2002. A Fast and Elitist Multi-Objective Genetic Algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6, 2 (2002), 182--197.
[14]
M. Drozdik, Y. Akimoto, H. Aguirre, and K. Tanaka. 2015. Computational cost reduction of nondominated sorting using the M-front. IEEE Transactions on Evolutionary Computation 19, 5 (2015), 659--678.
[15]
Peter M. Fenwick. 1994. A new data structure for cumulative frequency tables. Software: Practice and Experience 24, 3 (1994), 327--336.
[16]
Tobias Glasmachers. 2017. A Fast Incremental BSP Tree Archive for Non-dominated Points. In Proceedings of Evolutionary Multiobjective Optimization. Number 10173 in Lecture Notes in Computer Science. 252--266.
[17]
Patrik Gustavsson and Anna Syberfeldt. 2018. A New Algorithm Using the Non-dominated Tree to Improve Non-dominated Sorting. Evolutionary Computation 26, 1 (2018), 89--116.
[18]
Nikolaus Hansen, Sibylle D. Müller, and Petros Koumoutsakos. 2003. Reducing the Time Complexity of the Derandomized Evolution Strategy with Covariance Matrix Adaptation (CMA-ES). Evolutionary Computation 11, 1 (2003), 1--18.
[19]
Nikolaus Hansen and Andreas Ostermeier. 2001. Completely Derandomized Self-Adaptation in Evolution Strategies. Evolutionary Computation 9 (2001), 159--195.
[20]
Hisao Ishibuchi, Ryo Imada, Yu Setoguchi, and Yusuke Nojima. 2018. How to Specify a Reference Point in Hypervolume Calculation for Fair Performance Comparison. Evolutionary Computation 26, 3 (2018), 411--440.
[21]
Andrzej Jaszkiewicz. 2018. Improved quick hypervolume algorithm. Computers & Operations Research 90 (2018), 72--83.
[22]
Mikkel T. Jensen. 2003. Reducing the Run-time Complexity of Multiobjective EAs: The NSGA-II and Other Algorithms. IEEE Transactions on Evolutionary Computation 7, 5 (2003), 503--515.
[23]
Hsiang-Tsung Kung, Fabrizio Luccio, and Franco P. Preparata. 1975. On Finding the Maxima of a Set of Vectors. journal of ACM 22, 4 (1975), 469--476.
[24]
Renaud Lacour, Kathrin Klamroth, and Carlos M. Fonseca. 2017. A Box Decomposition Algorithm to Compute the Hypervolume Indicator. Computers & Operations Research 79 (2017), 347--360.
[25]
Marco Laumanns, Lothar Thiele, Kalyanmoy Deb, and Eckart Zitzler. 2002. Combining Convergence and Diversity in Evolutionary Multi-Objective Optimization. Evolutionary Computation 10, 3 (2002), 263--282.
[26]
Ke Li, Kalyanmoy Deb, Qingfu Zhang, and Qiang Zhang. 2017. Efficient Non-domination Level Update Method for Steady-State Evolutionary Multiobjective Optimization. IEEE Transactions on Cybernetics 47, 9 (2017), 2838--2849.
[27]
Sumit Mishra, Samrat Mondal, and Sriparna Saha. 2017. Improved solution to the non-domination level update problem. Applied Soft Computing 60 (2017), 336--362.
[28]
Antonio J. Nebro and Juan J. Durillo. 2009. On the Effect of Applying a Steady-State Selection Scheme in the Multi-Objective Genetic Algorithm NSGA-II. In Nature-Inspired Algorithms for Optimisation. Number 193 in Studies in Computational Intelligence. Springer Berlin Heidelberg, 435--456.
[29]
Yakov Nekrich. 2011. A Fast Algorithm for Three-Dimensional Layers of Maxima Problem. In Algorithms and Data Structures. Number 6844 in Lecture Notes in Computer Science. 607--618.
[30]
Niyaz Nigmatullin, Maxim Buzdalov, and Andrey Stankevich. 2016. Efficient Removal of Points with Smallest Crowding Distance in Two-dimensional Incremental Non-dominated Sorting. In Proceedings of Genetic and Evolutionary Computation Conference Companion. 1121--1128.
[31]
Proteek Chandan Roy, Kalyanmoy Deb, and Md. Monirul Islam. 2019. An Efficient Nondominated Sorting Algorithm for Large Number of Fronts. IEEE Transactions on Cybernetics 49, 3 (2019), 859--869.
[32]
Proteek Chandan Roy, Md. Monirul Islam, and Kalyanmoy Deb. 2016. Best Order Sort: A New Algorithm to Non-dominated Sorting for Evolutionary Multi-objective Optimization. In Proceedings of Genetic and Evolutionary Computation Conference Companion. 1113--1120.
[33]
Luis M. S. Russo and Alexandre P. Francisco. 2014. Quick Hypervolume. IEEE Transactions on Evolutionary Computation 18, 4 (2014).
[34]
Ke Shang, Hisao Ishibuchi, Min-Ling Zhang, and Yiping Liu. 2018. A new R2 indicator for better hypervolume approximation. In Proceedings of Genetic and Evolutionary Computation Conference. 745--752.
[35]
N. Srinivas and Kalyanmoy Deb. 1994. Multiobjective Optimization Using Non-dominated Sorting in Genetic Algorithms. Evolutionary Computation 2, 3 (1994), 221--248.
[36]
Frank van Harmelen, Vladimir Lifschitz, and Bruce Porter (Eds.). 2007. Handbook of Knowledge Representation. Vol. 1. Elsevier Science.
[37]
Andrey Vasin and Maxim Buzdalov. 2016. A Faster Algorithm for the Binary Epsilon Indicator Based on Orthant Minimum Search. In Proceedings of Genetic and Evolutionary Computation Conference. 613--620.
[38]
Ilya Yakupov and Maxim Buzdalov. 2015. Incremental Non-Dominated Sorting with O(N) Insertion for the Two-Dimensional Case. In Proceedings of IEEE Congress on Evolutionary Computation. 1853--1860.
[39]
Ilya Yakupov and Maxim Buzdalov. 2017. Improved Incremental Non-dominated Sorting for Steady-State Evolutionary Multiobjective Optimization. In Proceedings of Genetic and Evolutionary Computation Conference. 649--656.
[40]
Quingfu Zhang and Hui Li. 2007. MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition. IEEE Transactions on Evolutionary Computation 11, 6 (2007), 712--731.
[41]
Eckart Zitzler and Simon Künzli. 2004. Indicator-Based Selection in Multiobjective Search. In Parallel Problem Solving from Nature - PPSN VIII. Number 3242 in Lecture Notes in Computer Science. 832--842.
[42]
Eckart Zitzler, Marco Laumanns, and Lothar Thiele. 2001. SPEA2: Improving the Strength Pareto Evolutionary Algorithm for Multiobjective Optimization. In Proceedings of the EUROGEN'2001 Conference. 95--100.
[43]
Eckart Zitzler and Lothar Thiele. 1999. Multiobjective Evolutionary Algorithms: A Comparative Case Study and the Strength Pareto Approach. IEEE Transactions on Evolutionary Computation 3, 4 (1999), 257--271.
[44]
Eckart Zitzler, Lothar Thiele, Marco Laumanns, Carlos M. Fonseca, and Viviane Grunert da Fonseca. 2003. Performance assessment of multiobjective optimizers: An analysis and review. IEEE Transactions on Evolutionary Computation 7, 2 (2003), 117--132.
Index Terms
- Generalized incremental orthant search: towards efficient steady-state evolutionary multiobjective algorithms
Recommendations
Generalized offline orthant search: one code for many problems in multiobjective optimization
GECCO '18: Proceedings of the Genetic and Evolutionary Computation ConferenceWe introduce generalized offline orthant search, an algorithmic framework that can be used to solve many problems coming from evolutionary multiobjective optimization using a common well-optimized algorithmic core and relatively cheap reduction ...
Improved incremental non-dominated sorting for steady-state evolutionary multiobjective optimization
GECCO '17: Proceedings of the Genetic and Evolutionary Computation ConferenceWe present an algorithm for incremental non-dominated sorting, a procedure to use with steady-state multiobjective algorithms, with the complexity of O(N(log N)M−2) for a single insertion, where N is the number of points and M is the number of ...
Multi-objective modified differential evolution algorithm with archive-base mutation for solving multi-objective $$p$$p-xylene oxidation process
Maximizing the diversity of the obtained objective vectors and increasing the convergence speed to the true Pareto front are two important issues in the design of multi-objective evolutionary algorithms (MOEAs). To solve complex multi-objective ...
Comments
Information & Contributors
Information
Published In
July 2019
2161 pages
ISBN:9781450367486
DOI:10.1145/3319619
- Editor:
- Manuel López-Ibáñez,
- General Chairs:
- Anne Auger,
- Thomas Stützle
Copyright © 2019 ACM.
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].
Sponsors
Publisher
Association for Computing Machinery
New York, NY, United States
Publication History
Published: 13 July 2019
Check for updates
Author Tags
Qualifiers
- Research-article
Funding Sources
Conference
GECCO '19
Sponsor:
Acceptance Rates
Overall Acceptance Rate 1,669 of 4,410 submissions, 38%
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 52Total Downloads
- Downloads (Last 12 months)1
- Downloads (Last 6 weeks)0
Reflects downloads up to 05 Mar 2025
Other Metrics
Citations
View Options
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in