Oppositional biogeography-based optimization

TLDR: A novel variation to biogeography-based optimization (BBO), which is an evolutionary algorithm (EA) developed for global optimization, employs opposition-based learning (OBL) alongside BBO's migration rates to create oppositional BBO (OB O), and a new opposition method named quasi-reflection is introduced.

Abstract: We propose a novel variation to biogeography-based optimization (BBO), which is an evolutionary algorithm (EA) developed for global optimization. The new algorithm employs opposition-based learning (OBL) alongside BBO's migration rates to create oppositional BBO (OB O). Additionally, a new opposition method named quasi-reflection is introduced. Quasi-reflection is based on opposite numbers theory and we mathematically prove that it has the highest expected probability of being closer to the problem solution among all OBL methods. The oppositional algorithm is further revised by the addition of dynamic domain scaling and weighted reflection. Simulations have been performed to validate the performance of quasi-opposition as well as a mathematical analysis for a single-dimensional problem. Empirical results demonstrate that with the assistance of quasi-reflection, OB O significantly outperforms BBO in terms of success rate and the number of fitness function evaluations required to find an optimal solution.

Figures

Figure 11. Fist ten generations of best results obtained for Schwefel 1.2s. Oppositional algorithms start strong.

Figure 43. fx̂Kr(z + y) in domain [a, b] where K is the reflection weight.

Table XXXII. Symmetric TSP benchmark problems and their optimal results as posted by TSPLIB [203].

Figure 76. Two dimensional plot of the Sphere function.

Figure 24. Opposite points defined in domain [a, b]. c is the center of the domain and x̂ is an EA individual, generated by an EA. x̂o is the opposite of x̂, and x̂qo and x̂qr are the quasi-opposite and quasi-reflected points, respectively.

Table IV. Distance to solution as a function of reflection weight, where the problem domain is [−b, b]

Full text

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OPPOSITIONAL
BIOGEOGRAPHY-BASED OPTIMIZATION
MEHMET ERGEZER
Bachelor of Engineering in Electrical and Computer Engineering
Youngstown State University
May, 2003
Master of Science in Electrical and Computer Engineering
Youngstown State University
May, 2006
submitted in partial fulfillment of the requirements for the degree
DOCTOR OF ENGINEERING
at the
CLEVELAND STATE UNIVERSITY
May 2014

c
Copyright Mehmet Ergezer 2014

We hereby approve the dissertation
of
Mehmet Ergezer
Candidate for the Doctor of Engineering degree.
This dissertation has been approved for the
Department of Electrical and Computer Engineering
and CLEVELAND STATE UNIVERSITY
College of Graduate Studies by
Dan Simon, Dissertation Committee Chairperson
Department/Date
Murad Hizlan, Dissertation Committee Member
Department/Date
Hanz Richter, Dissertation Committee Member
Department/Date
Iftikhar Sikder, Dissertation Committee Member
Department/Date

Sailai Shao, Dissertation Committee Member
Department/Date
Dan Simon, Doctoral Program Director
Department/Date
Chansu Yu, Department Chair
Department/Date
Student‘s Date of Defense