Multi-objective sine-cosine algorithm (MO-SCA) for multi-objective engineering design problems

AbstractThis paper proposes a novel and an effective multi-objective optimization algorithm named multi-objective sine-cosine algorithm (MO-SCA) which is based on the search technique of sine-cosine algorithm (SCA). MO-SCA employs the elitist non-dominated sorting and crowding distance approach for obtaining different non-domination levels and to preserve the diversity among the optimal set of solutions, respectively. The effectiveness of the method is measured by implementing it on multi-objective benchmark problems that have various characteristics of Pareto front such as convex, non-convex and discrete. This proposed algorithm is also checked for the multi-objective engineering design problems with distinctive features. Furthermore, we show the proposed algorithm effectively generates the Pareto front and is easy to implement and algorithmically simple.

[1]  Ali Kaveh Charged System Search Algorithm , 2014 .

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

[3]  Daniel Angus,et al.  Multiple objective ant colony optimisation , 2009, Swarm Intelligence.

[4]  Aniruddha Bhattacharya,et al.  Multi-objective economic emission load dispatch solution using gravitational search algorithm and considering wind power penetration , 2013 .

[5]  Singiresu S. Rao Engineering Optimization : Theory and Practice , 2010 .

[6]  G. Moslehi,et al.  A Pareto approach to multi-objective flexible job-shop scheduling problem using particle swarm optimization and local search , 2011 .

[7]  David E. Goldberg,et al.  Genetic algorithms and Machine Learning , 1988, Machine Learning.

[8]  Xavier Gandibleux,et al.  Multiobjective Combinatorial Optimization — Theory, Methodology, and Applications , 2003 .

[9]  Andrew Lewis,et al.  Grey Wolf Optimizer , 2014, Adv. Eng. Softw..

[10]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

[11]  Minghao Yin,et al.  Animal migration optimization: an optimization algorithm inspired by animal migration behavior , 2014, Neural Computing and Applications.

[12]  David Corne,et al.  The Pareto archived evolution strategy: a new baseline algorithm for Pareto multiobjective optimisation , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[13]  Ardeshir Bahreininejad,et al.  Mine blast algorithm: A new population based algorithm for solving constrained engineering optimization problems , 2013, Appl. Soft Comput..

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

[15]  C.A. Coello Coello,et al.  MOPSO: a proposal for multiple objective particle swarm optimization , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[16]  Dervis Karaboga,et al.  A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm , 2007, J. Glob. Optim..

[17]  Nima Amjady,et al.  Multi-objective electricity market clearing considering dynamic security by lexicographic optimization and augmented epsilon constraint method , 2011, Appl. Soft Comput..

[18]  Ali Kaveh,et al.  Advances in Metaheuristic Algorithms for Optimal Design of Structures , 2014 .

[19]  Hao Zhang,et al.  A hybrid multi-objective artificial bee colony algorithm for burdening optimization of copper strip production , 2012 .

[20]  Michel Gendreau,et al.  An exact epsilon-constraint method for bi-objective combinatorial optimization problems: Application to the Traveling Salesman Problem with Profits , 2009, Eur. J. Oper. Res..

[21]  Maoguo Gong,et al.  Multiobjective Immune Algorithm with Nondominated Neighbor-Based Selection , 2008, Evolutionary Computation.

[22]  Martin J. Oates,et al.  PESA-II: region-based selection in evolutionary multiobjective optimization , 2001 .

[23]  Vimal Savsani,et al.  Optimization of a plate-fin heat exchanger design through an improved multi-objective teaching-learning based optimization (MO-ITLBO) algorithm , 2014 .

[24]  Martin J. Oates,et al.  The Pareto Envelope-Based Selection Algorithm for Multi-objective Optimisation , 2000, PPSN.

[25]  Abdullah Al Mamun,et al.  An evolutionary artificial immune system for multi-objective optimization , 2008, Eur. J. Oper. Res..

[26]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[27]  Xin-She Yang,et al.  Engineering optimisation by cuckoo search , 2010 .

[28]  Kevin M. Passino,et al.  Biomimicry of bacterial foraging for distributed optimization and control , 2002 .

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

[30]  C. Lucas,et al.  A novel numerical optimization algorithm inspired from weed colonization , 2006, Ecol. Informatics.

[31]  Xin-She Yang,et al.  A New Metaheuristic Bat-Inspired Algorithm , 2010, NICSO.

[32]  Hussain Shareef,et al.  Lightning search algorithm , 2015, Appl. Soft Comput..

[33]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[34]  Vivek K. Patel,et al.  A multi-objective improved teaching-learning based optimization algorithm (MO-ITLBO) , 2016, Inf. Sci..

[35]  Alan S. Perelson,et al.  The immune system, adaptation, and machine learning , 1986 .

[36]  M Reyes Sierra,et al.  Multi-Objective Particle Swarm Optimizers: A Survey of the State-of-the-Art , 2006 .

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

[38]  Hossein Nezamabadi-pour,et al.  BGSA: binary gravitational search algorithm , 2010, Natural Computing.

[39]  Xin-She Yang,et al.  Multiobjective firefly algorithm for continuous optimization , 2012, Engineering with Computers.

[40]  Ashkan Rahimi-Kian,et al.  Multiobjective invasive weed optimization: Application to analysis of Pareto improvement models in electricity markets , 2012, Appl. Soft Comput..

[41]  Charles E. Taylor Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence. Complex Adaptive Systems.John H. Holland , 1994 .

[42]  S. S. Thakur,et al.  Biogeography based optimization for multi-constraint optimal power flow with emission and non-smooth cost function , 2010, Expert Syst. Appl..

[43]  Vivek K. Patel,et al.  Heat transfer search (HTS): a novel optimization algorithm , 2015, Inf. Sci..

[44]  Manoj Kumar Tiwari,et al.  Interactive Particle Swarm: A Pareto-Adaptive Metaheuristic to Multiobjective Optimization , 2008, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[45]  Mehmet Mutlu Yenisey,et al.  Ant colony optimization for multi-objective flow shop scheduling problem , 2008, Comput. Ind. Eng..

[46]  Xin-She Yang,et al.  Bat algorithm for multi-objective optimisation , 2011, Int. J. Bio Inspired Comput..

[47]  George Mavrotas,et al.  Effective implementation of the epsilon-constraint method in Multi-Objective Mathematical Programming problems , 2009, Appl. Math. Comput..

[48]  Ardeshir Bahreininejad,et al.  Water cycle algorithm - A novel metaheuristic optimization method for solving constrained engineering optimization problems , 2012 .

[49]  F. Merrikh Bayat,et al.  The runner-root algorithm: A metaheuristic for solving unimodal and multimodal optimization problems inspired by runners and roots of plants in nature , 2015, Appl. Soft Comput..

[50]  Ali Sadollah,et al.  Water cycle algorithm for solving constrained multi-objective optimization problems , 2015, Appl. Soft Comput..

[51]  Marco Laumanns,et al.  An efficient, adaptive parameter variation scheme for metaheuristics based on the epsilon-constraint method , 2006, Eur. J. Oper. Res..

[52]  Seyedali Mirjalili,et al.  SCA: A Sine Cosine Algorithm for solving optimization problems , 2016, Knowl. Based Syst..

[53]  Yujia Wang,et al.  Particle swarm optimization with preference order ranking for multi-objective optimization , 2009, Inf. Sci..

[54]  Bijaya K. Panigrahi,et al.  Application of Multi-Objective Teaching-Learning-Based Algorithm to an Economic Load Dispatch Problem with Incommensurable Objectives , 2011, SEMCCO.

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

[56]  Jürgen Teich,et al.  Covering Pareto-optimal fronts by subswarms in multi-objective particle swarm optimization , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[57]  Ali Ahrari,et al.  Grenade Explosion Method - A novel tool for optimization of multimodal functions , 2010, Appl. Soft Comput..

[58]  S. N. Omkar,et al.  Applied Soft Computing Artificial Bee Colony (abc) for Multi-objective Design Optimization of Composite Structures , 2022 .

[59]  Dan Simon,et al.  Biogeography-Based Optimization , 2022 .

[60]  Xin Yao,et al.  Parallel Problem Solving from Nature PPSN VI , 2000, Lecture Notes in Computer Science.

[61]  Reza Akbari,et al.  A multi-objective artificial bee colony algorithm , 2012, Swarm Evol. Comput..

[62]  Fariborz Jolai,et al.  Lion Optimization Algorithm (LOA): A nature-inspired metaheuristic algorithm , 2016, J. Comput. Des. Eng..

[63]  Marco Dorigo,et al.  Optimization, Learning and Natural Algorithms , 1992 .

[64]  Hossein Nezamabadi-pour,et al.  GSA: A Gravitational Search Algorithm , 2009, Inf. Sci..

[65]  Maghsoud Amiri,et al.  Solving binary-state multi-objective reliability redundancy allocation series-parallel problem using efficient epsilon-constraint, multi-start partial bound enumeration algorithm, and DEA , 2012, Reliab. Eng. Syst. Saf..

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

[67]  Farshad Merrikh-Bayat,et al.  The runner-root algorithm , 2015 .

[68]  R. Venkata Rao,et al.  Teaching-Learning-Based Optimization: An optimization method for continuous non-linear large scale problems , 2012, Inf. Sci..

[69]  Kevin E Lansey,et al.  Optimization of Water Distribution Network Design Using the Shuffled Frog Leaping Algorithm , 2003 .

[70]  R. Venkata Rao,et al.  Teaching-learning-based optimization: A novel method for constrained mechanical design optimization problems , 2011, Comput. Aided Des..

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

[72]  Xavier Gandibleux,et al.  Multiple Criteria Optimization: State of the Art Annotated Bibliographic Surveys , 2013 .

[73]  Mehmet Karaköse,et al.  A multi-objective artificial immune algorithm for parameter optimization in support vector machine , 2011, Appl. Soft Comput..

[74]  Xin-She Yang,et al.  Multiobjective cuckoo search for design optimization , 2013, Comput. Oper. Res..

[75]  K. S. Swarup,et al.  Multi-objective biogeography based optimization for optimal PMU placement , 2012, Appl. Soft Comput..

[76]  Vimal Savsani,et al.  Passing vehicle search (PVS): A novel metaheuristic algorithm , 2016 .

[77]  Xin-She Yang,et al.  Firefly Algorithms for Multimodal Optimization , 2009, SAGA.

[78]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.