Hybird Evolutionary Multi-objective Algorithms Karthik Sindhya, PhD Postdoctoral Researcher Industrial Optimization Group Department of Mathematical Information Technology

Objectives The objectives of this lecture is to: Obtain an idea about hybrid algorithms

Hybrid EMO algorithm What is hybrid? The hybrid Prius runs on battery power up to 42 mph and while idling. When the car is moving above 42 mph, the gasoline engine kicks in. Toyota Prius

Global search+local search = Hybrid – Global search – Gasoline engine – Local search – Battery power Global search – EMO algorithm & Local search – Locally improve solutions in a population. Local search: Optimizing a scalarized function of a MOP using a suitable mathematical programming technique. Hybrid EMO algorithm

Hybrid EMO algorithms: – Increase in convergence speed. – Guaranteed convergence to the Pareto optimal front. – An efficient termination criterion. Classification: – Concurrent hybrid EMO algorithm – Serial hybrid EMO algorithm Hybrid EMO algorithm

Concurrent hybrid EMO algorithm: EMO algorithmLocal search Termination criterion ? Local search Pareto optimal front No Yes

Concurrent hybrid EMO algorithm (cont’d): – Locally improving a few solutions in a generation. Convergence speed can be increased. – A local search on final population is done to guarantee Pareto optimality. – Examples: Hybrid MOGA (Ishibuchi and Murata, 1998) MOGLS (Jaszkiewicz, 2002) etc. Hybrid EMO algorithm

Serial hybrid EMO algorithm (cont’d): – Local search applied only after the termination of an EMO algorithm. – Convergence speed is not improved. – Pareto optimality of the final population is guaranteed. – No clear termination criterion for stopping an EMO algorithm. – Examples: MSGA-LS1 & LS3 (Levi et al., 2000) Hybrid algorithm using PDM method (Harada et al., 2006) Hybrid EMO algorithm

Serial hybrid EMO algorithm: Hybrid EMO algorithm EMO algorithm Termination criterion ? Local search No Yes Pareto optimal front

Increase in convergence speed only possible in a concurrent hybrid EMO algorithm. Issues exist for a good implementation of a concurrent hybrid EMO algorithm: – Type of a scalarizing function: Several scalarizing functions exist – Weighted sum method (Gass, Saaty, 1955), achievement scalarizing function (Wierzbicki, 1980) etc. Hybrid EMO algorithm

– Frequency of local search Cyclic probability of local search P local. Balancing exploration and exploitation – Exploration – Crossover and mutation operators (global search). – Exploitation – local search. Periodically P local reduced to zero to allow global search. Generations Probability of local search P local 0 Hybrid EMO algorithm

– Termination criterion Using the optimal value of an ASF: – Using criterion of maximum number of function evaluations does not indicate proximity of solutions to the Pareto optimal front. – The optimal value of an ASF can be used to devise a new termination criterion for a hybrid EMO algorithm. – The optimal value of an ASF Ω at every generation t is stored in an archive. – Average of Ω (Ω avg ) after t+φ generations are calculated. – If Ω avg ≤ σ (σ – small postive scalar), hybrid algorithm is terminated. Hybrid EMO algorithm

Hybrid EMO algorithms Hybrid Original NSGA-II