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].