Upload
ahmed-fouad
View
162
Download
1
Tags:
Embed Size (px)
Citation preview
Company
LOGO
Scientific Research Group in Egypt (SRGE)
Backtracking Search Optimization
Algorithm (BSA)
Dr. Ahmed Fouad AliSuez Canal University,
Dept. of Computer Science, Faculty of Computers and informatics
Member of the Scientific Research Group in Egypt .
Company
LOGO Outline
1. Backtracking search optimization algorithm (BSA) (main idea)
3. BSA’s operators (selection-I, mutation, crossover, selection II)
2. Initializing population
6. References
4. Boundary control mechanism
5. Backtracking search optimization Algorithm
Company
LOGOBacktracking search optimization algorithm (BSA) (main idea)
•Backtracking search optimization algorithm (BSA) is arecent population-based evolutionary algorithm proposedby P. Civicioglu for solving numerical optimizationproblems.
•BSA is different from other evolutionary algorithmsbecause it has a single control parameter and it generates atrail population, which enables it to solve numericaloptimization problems rapidly.
Company
LOGO Initializing population
•The initial population P in the BSA is generated randomlyand consists of N individuals and D variables.
•The initial population can be represented as follow.
For i=1,2,3,…, N and j=1,2,3,…, D, where N, D are thepopulation size and the problem dimension, respectively, Uis the uniform distribution.
Company
LOGO BSA’s operators (selection-I)
•BSA has two selection operators, the first selection is calledselection-I, which is used to determine the historicalpopulation (Pold ) in order to calculate the search direction.
• The initial historical population is generated randomly asfollow.
•The Pold is redefined at the beginning of each iterationthrough the following rule
Company
LOGO BSA’s operators (selection-I)
Where := is the update operation, a, b are random numbers.
• After the historical population is determined, the order ofits individuals is changed as follow.
The permuting function is a random shuffling function.
Company
LOGO BSA’s operators (Mutation)
BSA generates the initial trail population Mutant byapplying the mutation operator as follow.
Where F controls the amplitude of the search direction matrix (P old- P).
Company
LOGO BSA’s operators (Crossover)
•The final form of the trial population T is generated by usingBSA's crossover operator.
•There are two steps in BSA's crossover process.
The first step generates a binary integer-valued matrix (map),where map size is N X D, which indicates the individuals of thetrail population T.
The initial value of the binary integer matrix is set to 1, wheren ϵ {1,2,3,…,N} and m ϵ {1,2,3,…,D}.
•The T is updated as follow
Company
LOGO BSA’s operators (Crossover) (cont.)
•The main steps of the BSA's crossover are presented in Algorithm 1 as follow.
Company
LOGO Boundary Control Mechanism of BSA
•The obtained individuals from BSA's crossover mayoverflow the allowed search space limit;
•These individuals are regenerated using Algorithm 2.
Company
LOGO BSA's Selection-II
•The second selection operator in the BSA is a greedyselection, which is called selection-II.
•The individual of the trail population T are replaced withthe individuals in the population P, when their fitnessvalues are better than the fitness values of the individuals ofthe population P.
•The overall best individual with the best fitness value isselected to be the global best solution .
Company
LOGO Backtracking Search Optimization Algorithm (BSA)Parameter initialization
Initializing
population and
evaluation
Selection I
MutationCrossover
Boundary Control Mechanism
Selection II
Overall best solution
Company
LOGO References
P. Civicioglu, Backtracking search optimization algorithm for numerical optimization problems / Applied Mathematics and Computation 219, 8121–8144, 2013.