Abstract
Cuckoo search algorithm is a promising metaheuristic population based method. It has been applied to solve many real life problems. In this paper, we propose a new cuckoo search algorithm by combining the cuckoo search algorithm with the Nelder–Mead method in order to solve the integer and minimax optimization problems. We call the proposed algorithm by hybrid cuckoo search and Nelder–Mead method (HCSNM). HCSNM starts the search by applying the standard cuckoo search for number of iterations then the best obtained solution is passing to the Nelder–Mead algorithm as an intensification process in order to accelerate the search and overcome the slow convergence of the standard cuckoo search algorithm. The proposed algorithm is balancing between the global exploration of the Cuckoo search algorithm and the deep exploitation of the Nelder–Mead method. We test HCSNM algorithm on seven integer programming problems and ten minimax problems and compare against eight algorithms for solving integer programming problems and seven algorithms for solving minimax problems. The experiments results show the efficiency of the proposed algorithm and its ability to solve integer and minimax optimization problems in reasonable time.
Highlights
Cuckoo search (CS) is a population based meta-heuristic algorithm that was developed by Yang et al (2007)
Conclusion and future work In this paper, a new hybrid cuckoo search algorithm with Nelder–Mead algorithm (NM) method is proposed in order to solve integer programming and minimax problems
The NM algorithm helps the proposed algorithm to overcome the slow convergence of the standard by refining the best obtained solution from the cuckoo search instead of keeping the algorithm running with more iterations without any improvements in the results
Summary
Cuckoo search (CS) is a population based meta-heuristic algorithm that was developed by Yang et al (2007). Few works have been applied to solve minimax and integer programming problems via these algorithms. The main drawback of applying swarm intelligence algorithms for solving minimax and integer programming problems is the slow convergence and the expensive computation time for these algorithms. The authors in Chang et al (2015), Jovanovic et al (2014) have invoked the Nelder– Mead method in the cuckoo search algorithm instead of the levy Flight operator The drawback of this idea is the computation time because the calling for NM method at each iteration in the Cuckoo search algorithm. Definition of the problems and an overview of the applied algorithms we present the definitions of the integer programming and the minimax problems as follows. 15: Build new nests at new locations using Levy flight a fraction pa of worse nests
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