Applications of new hybrid algorithm based on advanced cuckoo search and adaptive Gaussian quantum behaved particle swarm optimization in solving ordinary differential equations - Kumar, Nirmal; Shaikh, Ali Akbar; Mahato, Sanat Kumar; Bhunia, Asoke Kumar (Expert systems with applications, 2021)
•Transformation of ordinary differential equation to optimization problem.•Hybrid algorithm based on cuckoo search & advanced particle swarm optimization.•Testing of stability of the algorithm by convergence graph & statistical analysis.•Finding superiority of the algorithm by non-parametrical statistical test. This article solves first and second order differential equations with initial and/or boundary conditions by transforming these equations into unconstrained/bound constrained optimization problems. In order to solve these problems, a hybrid algorithm based on advanced cuckoo search (CS) algorithm and adaptive Gaussian quantum behaved particle swarm optimization (AGQPSO) is proposed. The CS algorithm is modified first by changing the step size in the simplified version. After that half of the total population is upgraded by this modified CS algorithm and another half is upgraded by AGQPSO algorithm. Then deletion strategy of CS algorithm is applied on the whole updated population. Next, to test the performance of the proposed hybrid algorithm, a number of benchmarks bound constrained optimization problems with different dimensions are considered and solved. Then this algorithm is applied fruitfully in first and second order initial value problems and boundary value problems by expressing the said problems in the form of bound constrained optimization problems.