Multi-Population Adaptive Inflationary Differential Evolution - PowerPoint PPT Presentation

- - - - Multi-Population Adaptive Inflationary Differential Evolution Marilena Di Carlo, Massimiliano Vasile, Edmondo Minisci Department of Mechanical and Aerospace Engineering University of Strathclyde marilena.di-carlo@strath.ac.uk PPSN BIOMA - Bioinspired Optimization Methods and their Applications Ljubljana, 13 September 2014 Marilena Di Carlo, Massimiliano Vasile, Edmondo Minisci Multi-Population Adaptive Inflationary Differential Evolution

Introduction IDEA & AIDEA Multi-Population AIDEA Test Results Conclusions Introduction ◮ Differential Evolution (DE) is a very efficient population-based stochastic algorithm for global numerical optimization problems Marilena Di Carlo, Massimiliano Vasile, Edmondo Minisci Multi-Population Adaptive Inflationary Differential Evolution

Introduction IDEA & AIDEA Multi-Population AIDEA Test Results Conclusions Introduction ◮ Differential Evolution (DE) is a very efficient population-based stochastic algorithm for global numerical optimization problems ◮ Its performance can be enhanced by combining it with others optimizer: Marilena Di Carlo, Massimiliano Vasile, Edmondo Minisci Multi-Population Adaptive Inflationary Differential Evolution

Introduction IDEA & AIDEA Multi-Population AIDEA Test Results Conclusions Introduction ◮ Differential Evolution (DE) is a very efficient population-based stochastic algorithm for global numerical optimization problems ◮ Its performance can be enhanced by combining it with others optimizer: Inflationary Differential Evolution Algorithm, IDEA Marilena Di Carlo, Massimiliano Vasile, Edmondo Minisci Multi-Population Adaptive Inflationary Differential Evolution

Introduction IDEA & AIDEA Multi-Population AIDEA Test Results Conclusions Introduction ◮ Differential Evolution (DE) is a very efficient population-based stochastic algorithm for global numerical optimization problems ◮ Its performance can be enhanced by combining it with others optimizer: Inflationary Differential Evolution Algorithm, IDEA ◮ DE performance are strongly influenced by setting of the algorithm parameter: Marilena Di Carlo, Massimiliano Vasile, Edmondo Minisci Multi-Population Adaptive Inflationary Differential Evolution

Introduction IDEA & AIDEA Multi-Population AIDEA Test Results Conclusions Introduction ◮ Differential Evolution (DE) is a very efficient population-based stochastic algorithm for global numerical optimization problems ◮ Its performance can be enhanced by combining it with others optimizer: Inflationary Differential Evolution Algorithm, IDEA ◮ DE performance are strongly influenced by setting of the algorithm parameter: Adaptive Inflationary Differential Evolution Algorithm, AIDEA Marilena Di Carlo, Massimiliano Vasile, Edmondo Minisci Multi-Population Adaptive Inflationary Differential Evolution

Introduction IDEA & AIDEA Multi-Population AIDEA Test Results Conclusions Introduction ◮ Differential Evolution (DE) is a very efficient population-based stochastic algorithm for global numerical optimization problems ◮ Its performance can be enhanced by combining it with others optimizer: Inflationary Differential Evolution Algorithm, IDEA ◮ DE performance are strongly influenced by setting of the algorithm parameter: Adaptive Inflationary Differential Evolution Algorithm, AIDEA ◮ Multi-population version of AIDEA (MP-AIDEA) Marilena Di Carlo, Massimiliano Vasile, Edmondo Minisci Multi-Population Adaptive Inflationary Differential Evolution

Introduction IDEA & AIDEA Multi-Population AIDEA Test Results Conclusions Contents Marilena Di Carlo, Massimiliano Vasile, Edmondo Minisci Multi-Population Adaptive Inflationary Differential Evolution

Introduction IDEA & AIDEA Multi-Population AIDEA Test Results Conclusions Contents - Differential Evolution Marilena Di Carlo, Massimiliano Vasile, Edmondo Minisci Multi-Population Adaptive Inflationary Differential Evolution

Introduction IDEA & AIDEA Multi-Population AIDEA Test Results Conclusions Contents - Differential Evolution - IDEA Marilena Di Carlo, Massimiliano Vasile, Edmondo Minisci Multi-Population Adaptive Inflationary Differential Evolution

Introduction IDEA & AIDEA Multi-Population AIDEA Test Results Conclusions Contents - Differential Evolution - IDEA - AIDEA Marilena Di Carlo, Massimiliano Vasile, Edmondo Minisci Multi-Population Adaptive Inflationary Differential Evolution

Introduction IDEA & AIDEA Multi-Population AIDEA Test Results Conclusions Contents - Differential Evolution - IDEA - AIDEA - Multi-Population AIDEA Marilena Di Carlo, Massimiliano Vasile, Edmondo Minisci Multi-Population Adaptive Inflationary Differential Evolution

Introduction IDEA & AIDEA Multi-Population AIDEA Test Results Conclusions Contents - Differential Evolution - IDEA - AIDEA - Multi-Population AIDEA - Test Results Marilena Di Carlo, Massimiliano Vasile, Edmondo Minisci Multi-Population Adaptive Inflationary Differential Evolution

Introduction IDEA & AIDEA Differential Evolution Multi-Population AIDEA IDEA Test Results AIDEA Conclusions Differential Evolution ◮ Initialize population in the search space 6 5 4 3 2 1 0 0 1 2 3 4 5 Marilena Di Carlo, Massimiliano Vasile, Edmondo Minisci Multi-Population Adaptive Inflationary Differential Evolution

Introduction IDEA & AIDEA Differential Evolution Multi-Population AIDEA IDEA Test Results AIDEA Conclusions Differential Evolution ◮ Initialize population in the search space ◮ Select three individuals x 1 , x 2 and x 3 6 5 4 3 2 1 0 0 1 2 3 4 5 Marilena Di Carlo, Massimiliano Vasile, Edmondo Minisci Multi-Population Adaptive Inflationary Differential Evolution

Introduction IDEA & AIDEA Differential Evolution Multi-Population AIDEA IDEA Test Results AIDEA Conclusions Differential Evolution ◮ Initialize population in the search space ◮ Select three individuals x 1 , x 2 and x 3 6 x 2 5 4 x 3 3 2 1 x 1 0 0 1 2 3 4 5 Marilena Di Carlo, Massimiliano Vasile, Edmondo Minisci Multi-Population Adaptive Inflationary Differential Evolution

Introduction IDEA & AIDEA Differential Evolution Multi-Population AIDEA IDEA Test Results AIDEA Conclusions Differential Evolution ◮ Initialize population in the search space ◮ Select three individuals x 1 , x 2 and x 3 6 ◮ Apply mutation: 5 (x 2 −x 3 ) x 2 v 1 = x 1 + F · ( x 2 − x 3 ) 4 x 3 3 2 F (x 2 −x 3 ) v 1 1 x 1 0 0 1 2 3 4 5 Marilena Di Carlo, Massimiliano Vasile, Edmondo Minisci Multi-Population Adaptive Inflationary Differential Evolution

Introduction IDEA & AIDEA Differential Evolution Multi-Population AIDEA IDEA Test Results AIDEA Conclusions Differential Evolution ◮ Initialize population in the search space ◮ Select three individuals x 1 , x 2 and x 3 6 ◮ Apply mutation: 5 v 1 = x 1 + F · ( x 2 − x 3 ) 4 ◮ Apply crossover to obtain trial vector 3 u 1 : � v j 1 , if rand(0,1) ≤ CR or j = j rand 2 u 1 u j 1 = x j v 1 1 , otherwise 1 x 1 0 0 1 2 3 4 5 Marilena Di Carlo, Massimiliano Vasile, Edmondo Minisci Multi-Population Adaptive Inflationary Differential Evolution

Introduction IDEA & AIDEA Differential Evolution Multi-Population AIDEA IDEA Test Results AIDEA Conclusions Differential Evolution ◮ Initialize population in the search space ◮ Select three individuals x 1 , x 2 and x 3 6 ◮ Apply mutation: 5 v 1 = x 1 + F · ( x 2 − x 3 ) 4 ◮ Apply crossover to obtain trial vector 3 u 1 : � v j 1 , if rand(0,1) ≤ CR or j = j rand 2 u j 1 = x j 1 , otherwise 1 ◮ Repeat operation for all the individuals 0 0 1 2 3 4 5 Marilena Di Carlo, Massimiliano Vasile, Edmondo Minisci Multi-Population Adaptive Inflationary Differential Evolution

Introduction IDEA & AIDEA Differential Evolution Multi-Population AIDEA IDEA Test Results AIDEA Conclusions Differential Evolution ◮ Initialize population in the search space ◮ Select three individuals x 1 , x 2 and x 3 6 ◮ Apply mutation: 5 v 1 = x 1 + F · ( x 2 − x 3 ) 4 ◮ Apply crossover to obtain trial vector 3 u 1 : � v j 1 , if rand(0,1) ≤ CR or j = j rand 2 u j 1 = x j 1 , otherwise 1 ◮ Repeat operation for all the individuals 0 0 1 2 3 4 5 ◮ Survival selection: � u i , if f ( u i ) ≤ f ( x i ) x ′ i = x i , otherwise Marilena Di Carlo, Massimiliano Vasile, Edmondo Minisci Multi-Population Adaptive Inflationary Differential Evolution

Introduction IDEA & AIDEA Differential Evolution Multi-Population AIDEA IDEA Test Results AIDEA Conclusions IDEA ◮ DE drawbacks: - Stagnation of the optimization process - CR and F difficult to tune and heavily problem dependent Marilena Di Carlo, Massimiliano Vasile, Edmondo Minisci Multi-Population Adaptive Inflationary Differential Evolution

Introduction IDEA & AIDEA Differential Evolution Multi-Population AIDEA IDEA Test Results AIDEA Conclusions IDEA ◮ DE drawbacks: - Stagnation of the optimization process - CR and F difficult to tune and heavily problem dependent ◮ IDEA (Inflationary Differential Evolution Algorithm) M. Vasile, E. Minisci, M. Locatelli, 2011 - Hybridization of DE with the restarting procedure of Monotonic Basin Hopping (MBH) algorithm Marilena Di Carlo, Massimiliano Vasile, Edmondo Minisci Multi-Population Adaptive Inflationary Differential Evolution