An accelerated method for geometric programming problem subject to constraints of bipolar fuzzy relation equations with the max-product operator

In this paper, the minimization problem of a geometric objective function with a single-term exponent subject to bipolar fuzzy relation equations is studied with the max-product composition operator. This paper intends to update the lower bound of its objective function by simplifying the problem and design an algorithm to find the initial upper bound for the optimal objective value of the problem based on its initial (or updated) lower bound. We then develop a modified branch-and-bound method based on the bound to solve the above problem. We also design an efficient algorithm to solve the problem according to the above algorithm and the developed branch-and-bound method. According to the proposed upper and lower bound, the developed branch-and-bound method examines a much less number of nodes to find the optimal solution. Hence, the rate of computations is significantly reduced. Finally, a numerical example is provided to illustrate the algorithm and its performance.