An Efficient Algorithm for Unconstrained Optimization

This paper presents an original and efficient PSO algorithm, which is divided into three phases: (1) stabilization, (2) breadth-first search, and (3) depth-first search. The proposed algorithm, called PSO-3P, was tested with 47 benchmark continuous unconstrained optimization problems, on a total of 82 instances. The numerical results show that the proposed algorithm is able to reach the global optimum. This work mainly focuses on unconstrained optimization problems from 2 to 1,000 variables.

[1]  Pauline Ong,et al.  Adaptive Cuckoo Search Algorithm for Unconstrained Optimization , 2014, TheScientificWorldJournal.

[2]  M. Imran,et al.  An Overview of Particle Swarm Optimization Variants , 2013 .

[3]  Novruz Allahverdi,et al.  Particle Swarm Optimization with Flexible Swarm for Unconstrained Optimization , 2013 .

[4]  Ping-Hung Tang,et al.  Adaptive directed mutation for real-coded genetic algorithms , 2013, Appl. Soft Comput..

[5]  Zhao Xinchao A perturbed particle swarm algorithm for numerical optimization , 2010 .

[6]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[7]  Xia Li,et al.  An improved shuffled frog-leaping algorithm with extremal optimisation for continuous optimisation , 2012, Inf. Sci..

[8]  Yuxin Zhao,et al.  A modified particle swarm optimization via particle visual modeling analysis , 2009, Comput. Math. Appl..

[9]  Jui-Yu Wu,et al.  Solving Unconstrained Global Optimization Problems via Hybrid Swarm Intelligence Approaches , 2013 .

[10]  A. Rezaee Jordehi,et al.  Enhanced leader PSO (ELPSO): A new PSO variant for solving global optimisation problems , 2015, Appl. Soft Comput..

[11]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[12]  Chia-Chong Chen,et al.  Two-layer particle swarm optimization for unconstrained optimization problems , 2011, Appl. Soft Comput..

[13]  Fred Glover,et al.  Tabu Search - Part II , 1989, INFORMS J. Comput..

[14]  Fred W. Glover,et al.  A Template for Scatter Search and Path Relinking , 1997, Artificial Evolution.

[15]  Fred W. Glover,et al.  Tabu Search - Part I , 1989, INFORMS J. Comput..

[16]  M. Pierini,et al.  Global optimization test problems based on random field composition , 2017, Optim. Lett..

[17]  Xia Li,et al.  A novel particle swarm optimizer hybridized with extremal optimization , 2010, Appl. Soft Comput..

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

[19]  Ellips Masehian,et al.  Particle Swarm Optimization Methods, Taxonomy and Applications , 2009 .

[20]  M. A. El-Shorbagy,et al.  Integrating particle swarm optimization with genetic algorithms for solving nonlinear optimization problems , 2011, Journal of Computational and Applied Mathematics.

[21]  Sergio Gerardo De los Cobos Silva SC-Sistema de convergencia: teoría y fundamentos , 2015 .

[22]  Jie Chen,et al.  An Improved Real-Coded Population-Based Extremal Optimization Method for Continuous Unconstrained Optimization Problems , 2014 .

[23]  Kusum Deep,et al.  A new mutation operator for real coded genetic algorithms , 2007, Appl. Math. Comput..