Backtracking Search Optimization Algorithm (BSA)
The BSA is a stochastic search algorithm developed by Civicioglu
[20]. The author of BSA was motivated by studies that attempt to
develop simpler and more effective search algorithm with as few control
parameters. The general structure of BSA can be explained by dividing
its functions into five segments: initialization, selection-I, mutation,
crossover and selection-II.
BSA initializes the population P by random selection between
lower and upper limits of the control variables. In Selection-I stage,
BSA determines the historical population oldP in order to
calculating the search direction. In the mutation process of BSA, a
trial population Mutant is formed as a function of Pand oldP . Because the historical population is used in the
calculation of the search-direction matrix, BSA generates a trial
population, taking partial advantage of its experiences from previous
generations. BSA’s crossover process generates crossover populationT as the final form of trial population. The initial value of
the trial population is Mutant , as obtained in the mutation
process. Crossover process contains of two steps. The first step
calculates a binary integer-valued matrix (map ) of sizeN‧n that indicates the individuals of T to be
manipulated by using the relevant individuals of P . In
Selection-II stage, the individual T ithat have better fitness values than the corresponding individualPi are used to update thePi based on a greedy selection. If the
best individual of P(Pbes t ) has a
better fitness value than the global minimum value obtained so far by
BSA, the global minimizer is updated to bePbes t , and the
global minimum value is updated to be the fitness value ofPbes t . Detailed
equation of BSA can be find in [20].