An Artificial Bee Colony-Based Double Layered Neural Network Approach for Solving Quadratic Bi-Level Programming Problems

In the current work, we devised a hybrid method involving a Double-Layer Neural Network (DLNN) for solving a quadratic Bi-Level Programming Problem (BLPP). For an efficient and effective solution of such problems, the proposed potential methodology includes an improved Artificial Bee Colony (ABC) algorithm, a Hopfield Network (HN), and a Boltzmann Machine (BM). The improved ABC algorithm accommodates upper-level decision problems by selecting a set of potential solutions from all combinations of solutions. However, for lower-level decision problem, HN and BM are amalgamated to manifest a DLNN that initially generates its structure by choosing a limited number of units, and will subsequently converge to an optimal solution/unit among those units and hence, constitutes an effective, efficient solution technique.We compared the accuracy, computational time and effectiveness (ability to find the true optimum) of the proposed DLNN with improved-ABC, DLNN with PSO (where PSO replaces the improved-ABC in the upper-level problem of the proposed DLNN with improved-ABC), DLNN with GA (where GAreplaces the improved-ABC in the upper-level of the proposed algorithm) and other conventional approaches and found the proposed DLNN with improved-ABC can yield high quality global optimal solutions with higher accuracy in relatively smaller time.