Abstract
In the literature, several variants of cat swarm optimization (CSO) algorithm are reported. However, CSO for integer multiobjective optimization problems (MOPs) has not yet been investigated. Owing to the frequent occurrence of integer MOPs and their importance in practical design problems, in this work, we investigate a new CSO approach for solving purely integer MOPs. This new approach named as multiobjective integer cat swarm optimization (MO-ICSO) algorithm incorporates the modified version of the CSO algorithm for MOPs. This approach is comprised of the concepts of rounding the floating points to the nearest integer numbers and the probabilistic updating (PU) technique. It uses the idea of Pareto dominance for finding the non-dominated solutions and an external archive for storing these solutions. We demonstrate the power of this new approach via its quantitative analysis and sensitivity test of its several parameters using different performance metrics performed over multiobjective multidimensional knapsack problem and several standard test functions. The simulation results argue that the proposed MO-ICSO approach can be a better candidate for solving the integer MOPs.
Similar content being viewed by others
References
Abualigah LMQ (2019) Feature selection and enhanced krill herd algorithm for text document clustering. Studies in computational intelligence. Springer, Berlin
Abualigah LMQ, Hanandeh ES (2015) Applying genetic algorithms to information retrieval using vector space model. Int J Comput Sci Eng Appl 5(1):19
Abualigah LM, Khader AT (2017) Unsupervised text feature selection technique based on hybrid particle swarm optimization algorithm with genetic operators for the text clustering. J Supercomput 73(11):4773–4795
Abualigah LM, Khader AT, Hanandeh ES, Gandomi AH (2017) A novel hybridization strategy for krill herd algorithm applied to clustering techniques. Appl Soft Comput 60:423–435
Abualigah LM, Khader AT, Hanandeh ES (2018a) A combination of objective functions and hybrid krill herd algorithm for text document clustering analysis. Eng Appl Artif Intell 73:111–125
Abualigah LM, Khader AT, Hanandeh ES (2018b) Hybrid clustering analysis using improved krill herd algorithm. Appl Intell 48(11):4047–4071
Abualigah LM, Khader AT, Hanandeh ES (2018c) A new feature selection method to improve the document clustering using particle swarm optimization algorithm. J Comput Sci 25:456–466
Ali MS, Ayaz A, Yasir QM, Qadri Nadia N, Jameel A (2018) Optimizing energy and throughput for mpsocs: an integer particle swarm optimization approach. Computing 100(3):227–244
Bacarisas ND, Yusiong JT (2011) The effects of varying the fitness function on the efficiency of the cat swarm optimization algorithm in solving the graph coloring problem. Ann Comput Sci Ser 9:1738
Banos R, Manzano-Agugliaro F, Montoya F, Gil C, Alcayde A, Gmez J (2011) Optimization methods applied to renewable and sustainable energy: a review. Renew Sustain Energy Rev 15(4):1753–1766
Chen J, Garcia HE (2016) Economic optimization of operations for hybrid energy systems under variable markets. Appl Energy 177:11–24
Chen JC, Hwang JC, Pan JS (2011) CSO algorithm for economic dispatch decision of hybrid generation system. J Energy Power Eng 5:73749
Chen J, Garcia HE, Kim JS, Bragg-Sitton SM (2016) Operations optimization of nuclear hybrid energy systems. Nucl Technol Am Nucl Soc 195(2):143–156
Chu S-C, Tsai P-W (2007) Computational intelligence based on the behavior of cats. Int J Innov Comput Inf Control 3(1):163–173
Cui S-Y, Wang Z-H, Tsai P-W, Chang C-C, Yue S (2013) Single bitmap block truncation coding of color images using cat swarm optimization. In: Pan J-S, Huang H-C, Jain LC, Zhao Y (eds) Recent advances in information hiding and applications. Springer, Berlin
Deb K (1999) Multi-objective genetic algorithms: problem difficulties and construction of test problems. Evol Comput 7(3):205–230
Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197
Deep K, Thakur M (2007) A new crossover operator for real coded genetic algorithms. Appl Math Comput 188(1):895–911
Deep K, Singh KP, Kansal M, Mohan C (2009) A real coded genetic algorithm for solving integer and mixed integer optimization problems. Appl Math Comput 212:505–518
Feldman AM, Serrano R (2006) Welfare economics and social choice theory. Springer, New York
Gujarati DN (2009) Basic econometrics. Tata McGraw-Hill Education, New York
Horst R, Tuy H (1996) Global optimization: deterministic approaches. Springer, New York
Hussain I, Ahmad A, Qadri MY, Qadri NN, Ahmed J (2016) Ant colony optimization for multicore re-configurable architecture. AI Commun 29(5):595–606
Ishfaq H, Abida P, Ayaz A, Yasir QM, Qadri Nadia N, Jameel A (2017) Nsga-ii-based design space exploration for energy and throughput aware multicore architectures. Cybern Syst 48(6–7):536–550
Jawad S, Ayaz A, Ali MS (2019) A multi-objective integer melody search algorithm. Appl Artif Intell 33(3):208–228
Kennedy J, Eberhart R (1995) Particle swarm optimization (PSO). In: Proceedings IEEE international conference on neural networks, pp 1942–1948
Kennedy J, Eberhart RC (1997) A discrete binary version of the particle swarm algorithm. In: 1997 IEEE international conference on computational cybernetics and simulation, systems, man, and cybernetics, vol 5. IEEE, pp 4104–4108
Kennedy J, Spears WM (1998) Matching algorithms to problems: an experimental test of the particle swarm and some genetic algorithms on the multimodal problem generator. In: Proceedings of the IEEE international conference on evolutionary computation, Citeseer, pp 78–83
Kim JS, Edgar TF (2014) Optimal scheduling of combined heat and power plants using mixed-integer nonlinear programming. Energy 77:675–690
Kita H, Yabumoto Y, Mori N, Nishikawa Y (1996) Multi-objective optimization by means of the thermodynamical genetic algorithm. In: Parallel problem solving from natureppsn IV. Springer, Berlin, pp 504–512
Kumar D, Samantaray S, Kamwa I, Sahoo N (2014) Reliability-constrained based optimal placement and sizing of multiple distributed generators in power distribution network using cat swarm optimization. Electric Power Compon Syst 42(2):149–164
Laskari EC, Parsopoulos KE, Vrahatis MN (2002) Particle swarm optimization for integer programming. In: Proceedings of the world on congress on computational intelligence, vol 2. IEEE, pp 1582–1587
Matsui T, Kato K, Sakawa M, Uno T, Matsumoto K (2008) Particle swarm optimization for nonlinear integer programming problems. In: Proceedings of international multiconference of engineers and computer scientists, pp 1874–1877
Mikki SM, Kishk AA (2006) Quantum particle swarm optimization for electromagnetics. IEEE Trans Antennas Propag 54(10):2764–2775
Palermo G, Silvano C, Zaccaria V (2008) Discrete particle swarm optimization for multiobjective design space exploration. In: 11th EUROMICRO conference on digital system design architectures, methods and tools, 2008, DSD’08. IEEE, pp 641–644
Pan Q-K, Tasgetiren MF, Liang Y-C (2008) A discrete particle swarm optimization algorithm for the no-wait flowshop scheduling problem. Comput Oper Res 35(9):2807–2839
Panda G, Pradhan PM, Majhi B (2011a) Direct and inverse modeling of plants using cat swarm optimization. In: Panigrahi BK, Shi Y, Lim M-H (eds) Handbook of swarm intelligence. Springer, Berlin
Panda G, Pradhan PM, Majhi B (2011b) IIR system identification using cat swarm optimization. Expert Syst Appl 38:1267112683
Petrie CJ, Webster TA, Cutkosky MR (1995) Using Pareto optimality to coordinate distributed agents. Artif Intell Eng Des Anal Manuf 9(4):269–281
Pradhan PM, Panda G (2012) Solving multiobjective problems using cat swarm optimization. Expert Syst Appl 39(3):2956–2964
Rao SS (1996) Engineering optimization-theory and practice. Wiley Eastern, New Delhi
Rao SS, Xiong Y (2005) A hybrid genetic algorithm for mixed-discrete design optimization. J Mech Des 127(6):1100–1112
Santosa B, Ningrum MK (2009) Cat swarm optimization for clustering. In: International conference of soft computing and pattern recognition, SOCPAR’09. IEEE pp 54–59
Schott JR (1995) Fault tolerant design using single and multicriteria genetic algorithm optimization. DTIC Document, Tech. Rep
Sharafi Y, Khanesar MA, Teshnehlab M (2013) Discrete binary cat swarm optimization algorithm. In: 2013 3rd international conference on computer, control & communication (IC4). IEEE, pp 1–6
Shi W, Zhang Q, Du H (2010) Quantum particle swarm optimization for integer programming of phased array feeds. In: 2010 international conference on. microwave and millimeter wave technology (ICMMT), pp 1386–1389
Tan Y, Gao H-M, Zeng J-C (2004) Particle swarm optimization for integer programming. Syst Eng Theory Pract 5:021
Tsai P-W, Pan J-S, Chen S-M, Liao B-Y, Hao S-P (2008) Parallel cat swarm optimization. In: IEEE seventh international conference on machine learning and cybernetics, Kunming, China, pp 3328–3333
Tsai P-W, Pan J-S, Chen S-M, Liao B-Y (2012) Enhanced parallel cat swarm optimization based on the Taguchi method. Expert Syst Appl 39:63096319
Van Veldhuizen DA (1999) Multiobjective evolutionary algorithms: classifications, analyses, and new innovations, DTIC Document, Tech. Rep
Wah BW, Wu Z (1999) The theory of discrete lagrange multipliers for nonlinear discrete optimization. Principles and practice of constraint programming-CP99. Springer, Berlin, pp 28–42
Wang G-G, Gandomi AH, Alavi AH, Gong D (2019) A comprehensive review of krill herd algorithm: variants, hybrids and applications. Artif Intell Rev 51(1):119–148
Wolsey LA, Nemhauser GL (2014) Integer and combinatorial optimization. John Wiley & Sons, London
Zhao X, Jin Y, Ji H, Geng J, Liang X, Jin R (2013) An improved mixed-integer multiobjective particle swarm optimization and its application in antenna array design. In: IEEE 5th international symposium on microwave, antenna, propagation and EMC technologies for wireless communications (MAPE). IEEE pp 412–415
Zitzler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans Evol Comput 3(4):257–271
Acknowledgements
We would like to acknowledge Dr. Abdul Qayyum Khan, from Department of Management Science, CUI, Wah Campus, for many useful discussions.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Ethical approval
This article does not contain any studies with human participants or animals performed by any of the authors.
Additional information
Communicated by V. Loia.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Ali Murtza, S., Ahmad, A. & Shafique, J. Integer cat swarm optimization algorithm for multiobjective integer problems. Soft Comput 24, 1927–1955 (2020). https://doi.org/10.1007/s00500-019-04023-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-019-04023-1