A Scalable Test Suite for Continuous Dynamic Multiobjective Optimization

Dynamic multiobjective optimization (DMO) has gained increasing attention in recent years. Test problems are of great importance in order to facilitate the development of advanced algorithms that can handle dynamic environments well. However, many of the existing dynamic multiobjective test problems have not been rigorously constructed and analyzed, which may induce some unexpected bias when they are used for algorithmic analysis. In this paper, some of these biases are identified after a review of widely used test problems. These include poor scalability of objectives and, more important, problematic overemphasis of static properties rather than dynamics making it difficult to draw accurate conclusion about the strengths and weaknesses of the algorithms studied. A diverse set of dynamics and features is then highlighted that a good test suite should have. We further develop a scalable continuous test suite, which includes a number of dynamics or features that have been rarely considered in literature but frequently occur in real life. It is demonstrated with empirical studies that the proposed test suite is more challenging to the DMO algorithms found in the literature. The test suite can also test algorithms in ways that existing test suites cannot.

[1]  Lothar Thiele,et al.  Comparison of Multiobjective Evolutionary Algorithms: Empirical Results , 2000, Evolutionary Computation.

[2]  Min Liu,et al.  Novel prediction and memory strategies for dynamic multiobjective optimization , 2014, Soft Computing.

[3]  Shengxiang Yang,et al.  A Steady-State and Generational Evolutionary Algorithm for Dynamic Multiobjective Optimization , 2017, IEEE Transactions on Evolutionary Computation.

[4]  Kay Chen Tan,et al.  Evolutionary Dynamic Multiobjective Optimization Via Kalman Filter Prediction , 2016, IEEE Transactions on Cybernetics.

[5]  Maoguo Gong,et al.  Multi-Objective Self-Paced Learning , 2016, AAAI.

[6]  Shengxiang Yang,et al.  Ant Colony Optimization for Simulated Dynamic Multi-Objective Railway Junction Rescheduling , 2017, IEEE Transactions on Intelligent Transportation Systems.

[7]  Bernhard Sendhoff,et al.  Constructing Dynamic Optimization Test Problems Using the Multi-objective Optimization Concept , 2004, EvoWorkshops.

[8]  Hendrik Richter Change detection in dynamic fitness landscapes: An immunological approach , 2009, 2009 World Congress on Nature & Biologically Inspired Computing (NaBIC).

[9]  Marco Laumanns,et al.  Scalable Test Problems for Evolutionary Multiobjective Optimization , 2005, Evolutionary Multiobjective Optimization.

[10]  Zhongbao Zhou,et al.  A multi-objective approach for weapon selection and planning problems in dynamic environments , 2016 .

[11]  Walter Abrahão dos Santos,et al.  A Multidisciplinary Design Optimization Tool for Spacecraft Equipment Layout Conception , 2014 .

[12]  Hussein A. Abbass,et al.  A Benchmark Test Suite for Dynamic Evolutionary Multiobjective Optimization , 2017, IEEE Transactions on Cybernetics.

[13]  Shengxiang Yang,et al.  Shift-Based Density Estimation for Pareto-Based Algorithms in Many-Objective Optimization , 2014, IEEE Transactions on Evolutionary Computation.

[14]  Zhuhong Zhang,et al.  Immune Optimization Approach for Dynamic Constrained Multi-Objective Multimodal Optimization Problems , 2012 .

[15]  Yong Wang,et al.  Scalarizing Functions in Decomposition-Based Multiobjective Evolutionary Algorithms , 2018, IEEE Transactions on Evolutionary Computation.

[16]  Kay Chen Tan,et al.  A Competitive-Cooperative Coevolutionary Paradigm for Dynamic Multiobjective Optimization , 2009, IEEE Transactions on Evolutionary Computation.

[17]  Filip Logist,et al.  Dynamic optimization of biological networks under parametric uncertainty , 2016, BMC Systems Biology.

[18]  Francisco Rodríguez,et al.  Multiobjective hierarchical control architecture for greenhouse crop growth , 2012, Autom..

[19]  Haluk Topcuoglu,et al.  Sensor-based change detection schemes for dynamic multi-objective optimization problems , 2016, 2016 IEEE Symposium Series on Computational Intelligence (SSCI).

[20]  Andrea Castelletti,et al.  Many‐objective reservoir policy identification and refinement to reduce policy inertia and myopia in water management , 2014 .

[21]  Shengxiang Yang,et al.  A Strength Pareto Evolutionary Algorithm Based on Reference Direction for Multiobjective and Many-Objective Optimization , 2017, IEEE Transactions on Evolutionary Computation.

[22]  Francesco Pieri,et al.  A Fast Multiobjective Optimization Strategy for Single-Axis Electromagnetic MOEMS Micromirrors , 2017, Micromachines.

[23]  Ponnuthurai N. Suganthan,et al.  Evolutionary multiobjective optimization in dynamic environments: A set of novel benchmark functions , 2014, 2014 IEEE Congress on Evolutionary Computation (CEC).

[24]  Shengxiang Yang,et al.  Evolutionary dynamic optimization: A survey of the state of the art , 2012, Swarm Evol. Comput..

[25]  Qingfu Zhang,et al.  MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition , 2007, IEEE Transactions on Evolutionary Computation.

[26]  Qingfu Zhang,et al.  This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 1 RM-MEDA: A Regularity Model-Based Multiobjective Estimation of , 2022 .

[27]  R. K. Ursem Multi-objective Optimization using Evolutionary Algorithms , 2009 .

[28]  Shengxiang Yang,et al.  A prediction strategy based on center points and knee points for evolutionary dynamic multi-objective optimization , 2017, Appl. Soft Comput..

[29]  Kalyanmoy Deb,et al.  Dynamic Multi-objective Optimization and Decision-Making Using Modified NSGA-II: A Case Study on Hydro-thermal Power Scheduling , 2007, EMO.

[30]  Günter Rudolph,et al.  Evolutionary Optimization of Dynamic Multiobjective Functions , 2006 .

[31]  Xin Yao,et al.  Dynamic combinatorial optimisation problems: an analysis of the subset sum problem , 2011, Soft Comput..

[32]  Trung Thanh Nguyen,et al.  Dynamic Time-Linkage Problems - The Challenges , 2012, 2012 IEEE RIVF International Conference on Computing & Communication Technologies, Research, Innovation, and Vision for the Future.

[33]  Tapabrata Ray,et al.  A Pareto Corner Search Evolutionary Algorithm and Dimensionality Reduction in Many-Objective Optimization Problems , 2011, IEEE Transactions on Evolutionary Computation.

[34]  Xin Yao,et al.  Dynamic Multiobjectives Optimization With a Changing Number of Objectives , 2016, IEEE Transactions on Evolutionary Computation.

[35]  Qingfu Zhang,et al.  Multiobjective Optimization Problems With Complicated Pareto Sets, MOEA/D and NSGA-II , 2009, IEEE Transactions on Evolutionary Computation.

[36]  Shengxiang Yang,et al.  An Improved Multiobjective Optimization Evolutionary Algorithm Based on Decomposition for Complex Pareto Fronts , 2016, IEEE Transactions on Cybernetics.

[37]  Qingfu Zhang,et al.  Prediction-Based Population Re-initialization for Evolutionary Dynamic Multi-objective Optimization , 2007, EMO.

[38]  R. Lyndon While,et al.  A review of multiobjective test problems and a scalable test problem toolkit , 2006, IEEE Transactions on Evolutionary Computation.

[39]  Qingfu Zhang,et al.  Are All the Subproblems Equally Important? Resource Allocation in Decomposition-Based Multiobjective Evolutionary Algorithms , 2016, IEEE Transactions on Evolutionary Computation.

[40]  Steven Guan,et al.  Evolving Dynamic Multi-Objective Optimization Problems with Objective Replacement , 2005, Artificial Intelligence Review.

[41]  Qingfu Zhang,et al.  A Population Prediction Strategy for Evolutionary Dynamic Multiobjective Optimization , 2014, IEEE Transactions on Cybernetics.

[42]  Changhe Li,et al.  A clustering particle swarm optimizer for dynamic optimization , 2009, 2009 IEEE Congress on Evolutionary Computation.

[43]  Changhe Li,et al.  A Clustering Particle Swarm Optimizer for Locating and Tracking Multiple Optima in Dynamic Environments , 2010, IEEE Transactions on Evolutionary Computation.

[44]  Hisao Ishibuchi,et al.  Performance of Decomposition-Based Many-Objective Algorithms Strongly Depends on Pareto Front Shapes , 2017, IEEE Transactions on Evolutionary Computation.

[45]  Sanaz Mostaghim,et al.  Using ε-Dominance for Hidden and Degenerated Pareto-Fronts , 2015, 2015 IEEE Symposium Series on Computational Intelligence.

[46]  Jevgenijs Butans,et al.  Addressing real-time control problems in complex environments using dynamic multi-objective evolutionary approaches , 2011 .

[47]  Zbigniew Michalewicz,et al.  Multiobjective Resource-Constrained Project Scheduling with a Time-Varying Number of Tasks , 2014, TheScientificWorldJournal.

[48]  Peter J. Fleming,et al.  A Real-World Application of a Many-Objective Optimisation Complexity Reduction Process , 2013, EMO.

[49]  Xin Yao,et al.  Mathematical modeling and multi-objective evolutionary algorithms applied to dynamic flexible job shop scheduling problems , 2015, Inf. Sci..

[50]  Zhuhong Zhang,et al.  Multiobjective optimization immune algorithm in dynamic environments and its application to greenhouse control , 2008, Appl. Soft Comput..

[51]  Shengxiang Yang,et al.  Evolutionary Dynamic Multiobjective Optimization: Benchmarks and Algorithm Comparisons , 2017, IEEE Transactions on Cybernetics.

[52]  Kalyanmoy Deb,et al.  Dynamic multiobjective optimization problems: test cases, approximations, and applications , 2004, IEEE Transactions on Evolutionary Computation.

[53]  Kalyanmoy Deb,et al.  Investigating the Effect of Imbalance Between Convergence and Diversity in Evolutionary Multiobjective Algorithms , 2017, IEEE Transactions on Evolutionary Computation.

[54]  Gireeja Ranade,et al.  Verifying Controllers Against Adversarial Examples with Bayesian Optimization , 2018, 2018 IEEE International Conference on Robotics and Automation (ICRA).

[55]  Kay Chen Tan,et al.  A predictive gradient strategy for multiobjective evolutionary algorithms in a fast changing environment , 2010, Memetic Comput..

[56]  Yong Wang,et al.  A regularity model-based multiobjective estimation of distribution algorithm with reducing redundant cluster operator , 2012, Appl. Soft Comput..

[57]  Kourosh Behzadian,et al.  Rehabilitation of a Water Distribution System Using Sequential Multiobjective Optimization Models , 2016 .

[58]  Il Hong Suh,et al.  Dynamic multi-objective optimization based on membrane computing for control of time-varying unstable plants , 2011, Inf. Sci..