A data-driven game theoretic multi-objective hybrid algorithm for the Dial-A-Ride Problem with multiple time windows

Abstract

The Dial-A-Ride Problem (DARP) designs pick-up and delivery routes for a set of customers. It arises in door-to-door transport services tailored to elderly and impaired people. It minimizes operational costs while accommodating as many drivers’ and customers’ constraints as possible; e.g., constraints on transit time and time windows on pick up and drop off.This paper develops a two-layer and a three-layer artificial neural network (ANN) to predict DARP parameters. The ANN is trained with real data provided by a transit agency from the Canadian city/region of Vancouver. Experimental results show that a three-layer ANN with rectified linear activation functions in conjunction with a stochastic gradient descent optimizer provides the most accurate output forecasts.Utilizing the predictions as parameter estimates for a deterministic mean DARP with multiple time windows (DARPMTW), this paper models the problem as a Company-Drivers-Customers’ theoretic game that minimizes the total route duration and maximizes the minimal satisfaction of the drivers and the customers. It shows that non-dominated Pareto feasible solutions satisfy the Nash equilibrium conditions of the game-theoretic model. It then creates a multi-objective hybrid adaptive large neighborhood search (DD-HALNS) to estimate the Pareto front. The multi-objective DD-HALNS algorithm confines its search to feasible solutions that satisfy the Nash equilibrium conditions and employs local search operators based on their success rates. The operators are controlled by a learning mechanism that utilizes previous successful moves, cost savings, and utility maximization. Four hybridization operators are applied, namely Simulated Annealing, Tabu Lists, Genetic Crossover, and Restarts. The results of experiments conducted on real-world DARPMTW instances demonstrate the ability of the multi-objective DD-HALNS to enhance the best-known routing solutions, as well as its implementability.