Solving Dynamic Traveling Salesman Problems With Deep Reinforcement Learning

Exploring the Potential of DNA Computing for Complex Big Data Problems: A Case Study on the Traveling Car Renter Problem

The traveling car renter problem (TCRP) is a variant of the Traveling Salesman Problem (TSP) wherein the salesman utilizes rented cars for travel. The primary objective of this problem is to identify a solution that minimizes the cumulative operating costs. Given its classification as a non-deterministic polynomial (NP) problem, traditional computers are not proficient in effectively resolving it. Conversely, DNA computing exhibits unparalleled advantages when confronted with NP-hard problems. This paper presents a DNA algorithm, based on the Adleman-Lipton model, as a proposed approach to address TCRP. The solution for TCRP can be acquired by following a series of fundamental steps, including coding, interaction, and extraction. The time computing complexity of the proposed DNA algorithm is O(n2m) for TCRP with n cities and m types of cars. By conducting simulation experiments, the solutions for certain instances of TCRP are computed and compared to those obtained by alternative algorithms. The proposed algorithm further illustrates the potential of DNA computing, as a form of parallel computing, to address more intricate large-scale problems.

A Deep Reinforcement Learning-Based Scheme for Solving Multiple Knapsack Problems

A knapsack problem is to select a set of items that maximizes the total profit of selected items while keeping the total weight of the selected items no less than the capacity of the knapsack. As a generalized form with multiple knapsacks, the multi-knapsack problem (MKP) is to select a disjointed set of items for each knapsack. To solve MKP, we propose a deep reinforcement learning (DRL) based approach, which takes as input the available capacities of knapsacks, total profits and weights of selected items, and normalized profits and weights of unselected items and determines the next item to be mapped to the knapsack with the largest available capacity. To expedite the learning process, we adopt the Asynchronous Advantage Actor-Critic (A3C) for the policy model. The experimental results indicate that the proposed method outperforms the random and greedy methods and achieves comparable performance to an optimal policy in terms of the profit ratio of the selected items to the total profit sum, particularly when the profits and weights of items have a non-linear relationship such as quadratic forms.