Backtraking optimziation algorithm

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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 .

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LOGO Scientific Research Group in Egypt

www.egyptscience.net

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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

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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.

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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.

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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

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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.

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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).

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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

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LOGO BSA’s operators (Crossover) (cont.)

•The main steps of the BSA's crossover are presented in Algorithm 1 as follow.

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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.

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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 .

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LOGO Backtracking Search Optimization Algorithm (BSA)Parameter initialization

Initializing

population and

evaluation

Selection I

MutationCrossover

Boundary Control Mechanism

Selection II

Overall best solution

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LOGO References

P. Civicioglu, Backtracking search optimization algorithm for numerical optimization problems / Applied Mathematics and Computation 219, 8121–8144, 2013.

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LOGO

Thank you

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