This paper presents a novel binary monarch butterfly optimization (BMBO) method, intended for addressing the 0–1 knapsack problem (0–1 KP). Two tuples, consisting of real-valued vectors and binary vectors, are used to represent the monarch butterfly individuals in BMBO. Real-valued vectors constitute the search space, whereas binary vectors form the solution space. In other words, monarch butterfly optimization works directly on real-valued vectors, while solutions are represented by binary vectors. Three kinds of individual allocation schemes are tested in order to achieve better performance. Toward revising the infeasible solutions and optimizing the feasible ones, a novel repair operator, based on greedy strategy, is employed. Comprehensive numerical experimentations on three types of 0–1 KP instances are carried out. The comparative study of the BMBO with four state-of-the-art classical algorithms clearly points toward the superiority of the former in terms of search accuracy, convergent capability and stability in solving the 0–1 KP, especially for the high-dimensional instances.
This is a preview of subscription content, log in to check access.
This work was supported by National Natural Science Foundation of China (Nos. 61272297, 61402207, 61503165), Jiangsu Province Science Foundation for Youths (No. BK20150239) and R&D Program for Science and Technology of Shijiazhuang (No. 155790215).
Du DZ, Ko KI, Hu X (2011) Design and analysis of approximation algorithms. Springer, BerlinGoogle Scholar
Thiel J, Voss S (1994) Some experiences on solving multi constraint zero-one knapsack problems with genetic algorithms. INFOR 32(4):226–242zbMATHGoogle Scholar
Chen P, Li J, Liu ZM (2008) Solving 0–1 knapsack problems by a discrete binary version of differential evolution. In: Second international symposium on intelligent information technology application, vol 2, pp 513–516. doi:10.1109/IITA.2008.538
Fong S, Yang XS, Deb S (2013) Swarm search for feature selection in classification. In: Computational science and engineering (CSE), 2013 IEEE 16th international conference on. IEEE, pp 902–909Google Scholar
Wang G-G, Deb S, Coelho LDS (2015) Earthworm optimization algorithm: a bio-inspired metaheuristic algorithm for global optimization problems. Int J Bio-Inspired Comput in pressGoogle Scholar
Mirjalili SA, Hashim SZM (2011). BMOA: binary magnetic optimization algorithm. In: 2011 3rd international conference on machine learning and computing (ICMLC 2011), Singapore, pp 201–206Google Scholar
Wang G-G, Zhao XC, Deb S (2015). A novel monarch butterfly optimization with greedy strategy and self-adaptive crossover operator. In: the 2015 2nd international conference on soft computing & machine intelligence (ISCMI 2015), Hong Kong. IEEEGoogle Scholar
Yang XS (2010) Nature-inspired metaheuristic algorithms. Luniver Press, FromeGoogle Scholar
Joines JA, Houck CR (1994) On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with GA’s. In: Evolutionary computation, 1994. IEEE World Congress on computational intelligence. Proceedings of the first IEEE conference on. IEEE, pp 579–584. doi:10.1109/ICEC.1994.349995
Olsen AL (1994) Penalty functions and the knapsack problem. In: Evolutionary computation, 1994. IEEE World congress on computational intelligence. Proceedings of the first IEEE conference on. IEEE, pp 554–558. doi:10.1109/ICEC.1994.350000
Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, BostonzbMATHGoogle Scholar
Simon D (2013) Evolutionary optimization algorithms. Wiley, New YorkGoogle Scholar
Feng YH, Wang G-G (2015) An Improved hybrid encoding firefly algorithm for randomized time-varying knapsack problems. In: The 2015 2nd international conference on soft computing & machine intelligence (ISCMI 2015), Hong Kong. IEEEGoogle Scholar
Wang G-G, Hossein Gandomi A, Yang XS et al (2014) A novel improved accelerated particle swarm optimization algorithm for global numerical optimization. Eng Comput 31(7):1198–1220CrossRefGoogle Scholar