An efficient hybrid technique for numerical optimization and applications

• The hybridization of two heuristics namely DE and PSO for constrained optimization problems.
• The population is broken into 3 sub-populations with inferior, mid and superior groups.
• DE–PSO–DE (abbreviated as DPD) is employed respectively on the above groups.
• DPD is tested over CEC2006 and CEC2010 test functions, engineering problems and CEC2011 Problems.
• The greater robustness of DPD is confirmed over the state-of-the-art algorithms.

Real World Optimization Problems is one of the major concerns to show the potential and effectiveness of an optimization algorithm. In this context, a hybrid algorithm of two popular heuristics namely Differential Evolution (DE) and Particle Swarm Optimization (PSO) engaged on a ‘tri-population’ environment. Initially, the whole population (in increasing order of fitness) is divided into three groups – Inferior Group, Mid Group and Superior Group. DE is employed in the inferior and superior groups, whereas PSO is used in the mid-group. The proposed method is abbreviated as DPD as it uses DE–PSO–DE on a population. Two strategies namely Elitism (to retain the best obtained values so far) and Non-redundant search (to improve the solution quality) have been additionally employed in DPD cycle. Moreover, the robustness of the mutation strategies of DE have been well studied and suitable mutation strategies for both DEs (for DPD) are investigated over a set of existing 8 popular mutation strategies which results 64 variants of DPD. The top DPD is further tested through the test functions of CEC2006, CEC2010 and 5 Engineering Design Problems. Also it is used to solve CEC2011 Real World Optimization problems. An excellent efficiency of the recommended DPD is confirmed over the state-of-the-art algorithms.