An RNN-based method combined with bi-objective programming for tackling inverse facility line location problems

In most single facility location problems, a set of points is provided, and the objective is to determine the optimal location for a new facility based on criteria such as minimizing time, cost, and distances between clients and facilities. On the other side, inverse single facility location problems aim to adjust the problem's parameters at minimal cost to make a specific point optimal. We consider the inverse case of line location problem which tries to modify the coordinates of the given points with the minimum cost such that a given line becomes optimal. We model this problem in various cases as bi-objective linear programming problems with variable coordinates in the plane. At the first step, the bi-objective problem is converted into an equivalent single objective linear programming via the weighted sum method, where the Pareto front are obtained by using different values of weights. A neural network model with reduced model dimension and complexity is constructed for solving the obtained single objective problem. Based on Lyapunov theory, the suggested neural network is shown to be stable in the sense of Lyapunov and globally convergent to the optimal solution. The algorithm is subsequently tested on various instances to demonstrate its efficiency.