A Benchmark-Suite of real-World constrained multi-objective optimization problems and some baseline results

Abstract Generally, Synthetic Benchmark Problems (SBPs) are utilized to assess the performance of metaheuristics. However, these SBPs may include various unrealistic properties. As a consequence, performance assessment may lead to underestimation or overestimation. To address this issue, few benchmark suites containing real-world problems have been proposed for all kinds of metaheuristics except for Constrained Multi-objective Metaheuristics (CMOMs). To fill this gap, we develop a benchmark suite of Real-world Constrained Multi-objective Optimization Problems (RWCMOPs) for performance assessment of CMOMs. This benchmark suite includes 50 problems collected from various streams of research. We also present the baseline results of this benchmark suite by using state-of-the-art algorithms. Besides, for comparative analysis, a ranking scheme is also proposed.

[1]  Ye Tian,et al.  An Indicator-Based Multiobjective Evolutionary Algorithm With Reference Point Adaptation for Better Versatility , 2018, IEEE Transactions on Evolutionary Computation.

[2]  Gonzalo Guillén-Gosálbez,et al.  A novel MILP-based objective reduction method for multi-objective optimization: Application to environmental problems , 2011, Comput. Chem. Eng..

[3]  G. Chiandussi,et al.  Comparison of multi-objective optimization methodologies for engineering applications , 2012, Comput. Math. Appl..

[4]  Panos M. Pardalos,et al.  A Collection of Test Problems for Constrained Global Optimization Algorithms , 1990, Lecture Notes in Computer Science.

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

[6]  Akshay Kumar Rathore,et al.  Fundamental Switching Frequency Optimal Pulsewidth Modulation of Medium-Voltage Cascaded Seven-Level Inverter , 2015 .

[7]  Guohua Wu,et al.  A test-suite of non-convex constrained optimization problems from the real-world and some baseline results , 2020, Swarm Evol. Comput..

[8]  Bablesh Kumar Jha,et al.  A New Current Injection Based Power Flow Formulation , 2020 .

[9]  I. Grossmann,et al.  Global optimization of nonconvex mixed-integer nonlinear programming (MINLP) problems in process synthesis , 1988 .

[10]  James N. Siddall,et al.  Optimal Engineering Design: Principles and Applications , 1982 .

[11]  Joachim Holtz,et al.  Optimal pulsewidth modulation of multilevel inverters for low switching frequency control of medium voltage high power industrial AC drives , 2010, 2010 IEEE Energy Conversion Congress and Exposition.

[12]  Javier Del Ser,et al.  A Tutorial On the design, experimentation and application of metaheuristic algorithms to real-World optimization problems , 2021, Swarm Evol. Comput..

[13]  Kalyanmoy Deb,et al.  Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms , 1994, Evolutionary Computation.

[14]  F. Cheng,et al.  GENERALIZED CENTER METHOD FOR MULTIOBJECTIVE ENGINEERING OPTIMIZATION , 1999 .

[15]  Tapabrata Ray,et al.  A Swarm Metaphor for Multiobjective Design Optimization , 2002 .

[16]  Akshay Kumar Rathore,et al.  Optimal pulsewidth modulation of cascade nine-level (9L) inverter for medium voltage high power industrial AC drives , 2015, IECON 2015 - 41st Annual Conference of the IEEE Industrial Electronics Society.

[17]  Yong Peng,et al.  A hybrid multi-objective optimization approach for energy-absorbing structures in train collisions , 2019, Inf. Sci..

[18]  S. N. Kramer,et al.  An Augmented Lagrange Multiplier Based Method for Mixed Integer Discrete Continuous Optimization and Its Applications to Mechanical Design , 1994 .

[19]  John E. Dennis,et al.  Normal-Boundary Intersection: A New Method for Generating the Pareto Surface in Nonlinear Multicriteria Optimization Problems , 1998, SIAM J. Optim..

[20]  P. N. Suganthan,et al.  Multi-objective optimal power flow solutions using a constraint handling technique of evolutionary algorithms , 2019, Soft Computing.

[21]  Michael G. Parsons,et al.  Formulation of Multicriterion Design Optimization Problems for Solution With Scalar Numerical Optimization Methods , 2004 .

[22]  Yong Wang,et al.  Handling Constrained Multiobjective Optimization Problems With Constraints in Both the Decision and Objective Spaces , 2019, IEEE Transactions on Evolutionary Computation.

[23]  Carlos A. Coello Coello,et al.  Constraint-handling in nature-inspired numerical optimization: Past, present and future , 2011, Swarm Evol. Comput..

[24]  Qingfu Zhang,et al.  Comparison between MOEA/D and NSGA-III on a set of novel many and multi-objective benchmark problems with challenging difficulties , 2019, Swarm Evol. Comput..

[25]  Abhishek Kumar,et al.  A Nested-Iterative Newton-Raphson based Power Flow Formulation for Droop-based Islanded Microgrids , 2020 .

[26]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[27]  Kalyanmoy Deb,et al.  Constrained Test Problems for Multi-objective Evolutionary Optimization , 2001, EMO.

[28]  Qingfu Zhang,et al.  Multiobjective evolutionary algorithms: A survey of the state of the art , 2011, Swarm Evol. Comput..

[29]  Hisao Ishibuchi,et al.  An easy-to-use real-world multi-objective optimization problem suite , 2020, Appl. Soft Comput..

[30]  A. Osyczka,et al.  A new method to solve generalized multicriteria optimization problems using the simple genetic algorithm , 1995 .

[31]  Swagatam Das,et al.  The spherical search algorithm for bound-constrained global optimization problems , 2019, Appl. Soft Comput..

[32]  Swagatam Das,et al.  A υ-Constrained Matrix Adaptation Evolution Strategy With Broyden-Based Mutation for Constrained Optimization. , 2021, IEEE transactions on cybernetics.

[33]  S. Azarm,et al.  On improving multiobjective genetic algorithms for design optimization , 1999 .

[34]  C. Floudas.  Nonlinear and Mixed-Integer Optimization: Fundamentals and Applications , 1995 .

[35]  Ivan Zelinka,et al.  A self-adaptive spherical search algorithm for real-world constrained optimization problems , 2020, GECCO Companion.

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

[37]  Ye Tian,et al.  PlatEMO: A MATLAB Platform for Evolutionary Multi-Objective Optimization [Educational Forum] , 2017, IEEE Computational Intelligence Magazine.

[38]  Min Zhang,et al.  Infeasible Elitists and Stochastic Ranking Selection in Constrained Evolutionary Multi-objective Optimization , 2006, SEAL.

[39]  Devender Singh,et al.  Improving the local search capability of Effective Butterfly Optimizer using Covariance Matrix Adapted Retreat Phase , 2017, 2017 IEEE Congress on Evolutionary Computation (CEC).

[40]  Siamak Talatahari,et al.  Stochastic paint optimizer: theory and application in civil engineering , 2020, Engineering with Computers.

[41]  Yong Wang,et al.  Evolutionary Constrained Multiobjective Optimization: Test Suite Construction and Performance Comparisons , 2019, IEEE Transactions on Evolutionary Computation.

[42]  Andrzej Osyczka,et al.  Evolutionary Algorithms for Single and Multicriteria Design Optimization , 2001 .

[43]  Xin Yao,et al.  A New Dominance Relation-Based Evolutionary Algorithm for Many-Objective Optimization , 2016, IEEE Transactions on Evolutionary Computation.

[44]  N. Sahinidis,et al.  Global optimization of nonconvex NLPs and MINLPs with applications in process design , 1995 .

[45]  Akshay Kumar Rathore,et al.  Synchronous Optimal Pulsewidth Modulation for Low-Switching-Frequency Control of Medium-Voltage Multilevel Inverters , 2010, IEEE Transactions on Industrial Electronics.

[46]  J. Carrasco,et al.  Recent Trends in the Use of Statistical Tests for Comparing Swarm and Evolutionary Computing Algorithms: Practical Guidelines and a Critical Review , 2020, Swarm Evol. Comput..

[47]  Gary G. Yen,et al.  Constraint Handling in Multiobjective Evolutionary Optimization , 2009, IEEE Transactions on Evolutionary Computation.

[48]  Tao Zhang,et al.  A Coevolutionary Framework for Constrained Multiobjective Optimization Problems , 2021, IEEE Transactions on Evolutionary Computation.

[49]  Jun Zhang,et al.  Tri-Goal Evolution Framework for Constrained Many-Objective Optimization , 2020, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[50]  Kalyanmoy Deb,et al.  An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point Based Nondominated Sorting Approach, Part II: Handling Constraints and Extending to an Adaptive Approach , 2014, IEEE Transactions on Evolutionary Computation.

[51]  Francisco Rivas-Dávalos,et al.  An Approach Based on the Strength Pareto Evolutionary Algorithm 2 for Power Distribution System Planning , 2005, EMO.

[52]  Bablesh Kumar Jha,et al.  A modified current injection load flow method under different load model of EV for distribution system , 2020 .

[53]  Devender Singh,et al.  Nested backward/forward sweep algorithm for power flow analysis of droop regulated islanded microgrids , 2019, IET Generation, Transmission & Distribution.

[54]  Rammohan Mallipeddi,et al.  An Inversion-Free Robust Power-Flow Algorithm for Microgrids , 2021, IEEE Transactions on Smart Grid.

[55]  Hong-Zhong Huang,et al.  An interactive fuzzy multi-objective optimization method for engineering design , 2006, Eng. Appl. Artif. Intell..

[56]  Lothar Thiele,et al.  The Hypervolume Indicator Revisited: On the Design of Pareto-compliant Indicators Via Weighted Integration , 2007, EMO.

[57]  Yong Wang,et al.  A Many-Objective Evolutionary Algorithm with Angle-Based Selection and Shift-Based Density Estimation , 2017, ArXiv.

[58]  Devender Singh,et al.  Butterfly Optimizer for Placement and Sizing of Distributed Generation for Feeder Phase Balancing , 2018, Advances in Intelligent Systems and Computing.

[59]  Eckart Zitzler,et al.  HypE: An Algorithm for Fast Hypervolume-Based Many-Objective Optimization , 2011, Evolutionary Computation.

[60]  Qingfu Zhang,et al.  Multiobjective optimization Test Instances for the CEC 2009 Special Session and Competition , 2009 .

[61]  Tao Xu,et al.  A Novel Hybrid Algorithm for Solving Multiobjective Optimization Problems with Engineering Applications , 2018 .

[62]  Shapour Azarm,et al.  Tradeoff-driven optimization-based design of mechanical systems , 1992 .

[63]  Abhishek Kumar,et al.  A Reference Vector-Based Simplified Covariance Matrix Adaptation Evolution Strategy for Constrained Global Optimization , 2020, IEEE Transactions on Cybernetics.

[64]  Akshay Kumar Rathore,et al.  Optimal Pulsewidth Modulation for Common-Mode Voltage Elimination Scheme of Medium-Voltage Modular Multilevel Converter-Fed Open-End Stator Winding Induction Motor Drives , 2017, IEEE Transactions on Industrial Electronics.

[65]  Masahiro Tanaka,et al.  GA-based decision support system for multicriteria optimization , 1995, 1995 IEEE International Conference on Systems, Man and Cybernetics. Intelligent Systems for the 21st Century.

[66]  Siamak Talatahari,et al.  Chaos Game Optimization: a novel metaheuristic algorithm , 2020, Artificial Intelligence Review.

[67]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[68]  Ignacio E. Grossmann,et al.  A modelling and decomposition strategy for the MINLP optimization of process flowsheets , 1989 .

[69]  Kiyoshi Tanaka,et al.  A Review of Features and Limitations of Existing Scalable Multiobjective Test Suites , 2019, IEEE Transactions on Evolutionary Computation.

[70]  Vijay Kumar,et al.  Multi-objective spotted hyena optimizer: A Multi-objective optimization algorithm for engineering problems , 2018, Knowl. Based Syst..

[71]  Rammohan Mallipeddi,et al.  Power Flow Analysis of Islanded Microgrids: A Differential Evolution Approach , 2021, IEEE Access.

[72]  Devender Singh,et al.  Current injection‐based Newton–Raphson power‐flow algorithm for droop‐based islanded microgrids , 2019, IET Generation, Transmission & Distribution.

[73]  Ivan Zelinka,et al.  A modified covariance matrix adaptation evolution strategy for real-world constrained optimization problems , 2020, GECCO Companion.