DKPRG or how to succeed in the Kolkata Paise Restaurant gamevia TSP

Abstract

The Kolkata Paise Restaurant Problem is a challenging game, in which n agents must decide where to have lunch during their lunch break. The game is very interesting because there are exactly n restaurants and each restaurant can accommodate only one agent. If two or more agents happen to choose the same restaurant, only one gets served and the others have to return back to work hungry. In this paper we tackle this problem from an entirely new angle. We abolish certain implicit assumptions, which allows us to propose a novel strategy that results in greater utilization for the restaurants. We emphasize the spatially distributed nature of our approach, which, for the first time, perceives the locations of the restaurants as uniformly distributed in the entire city area. This critical change in perspective has profound ramifications in the topological layout of the restaurants, which now makes it completely realistic to assume that every agent has a second chance. Every agent now may visit, in case of failure, more than one restaurants, within the predefined time constraints. From the point of view of each agent, the situation now resembles more that of the iconic travelling salesman, who must compute an optimal route through n cities. Following this shift in paradigm, we advocate the use of metaheuristics. This is because exact solutions of the TSP are prohibitively expensive, whereas metaheuristics produce near-optimal solutions in a short amount of time. Thus, via metaheuristics each agent can compute her own personalized solution, incorporating her preferences, and providing alternative destinations in case of successive failures. We analyze rigorously the resulting situation, proving probabilistic formulas that confirm the advantages of this policy and the increase in utilization. The detailed mathematical analysis of our scheme demonstrates that it can achieve utilization ranging from 0.85 to 0.95 from the first day, while rapidly attaining steady state utilization 1.0. Finally, we note that the equations we derive generalize formulas that were previously presented in the literature, which can be seen as special cases of our results.

Stochastic Learning in Kolkata Paise Restaurant Problem: Classical and Quantum Strategies

“…Authors here had discussed and investigated the searchers' incentives following different strategies, including KPR, can maximize search success. Authors in Kastampolidou et al ( 2021 ) have discussed KPR problem as Traveling Salesman Problem (TSP) assuming restaurants are uniformly distributed on a two-dimensional plane and this topological layout of the restaurants can help provide each agent a second chance for choosing a better or less crowded restaurant. Additionally, they have proposed a meta-heuristics, producing near-optimal solutions in finite time (as exact solutions of the TSP are prohibitively expensive).…”

“…This, however, is not a true solution to the KPR problem, where each customer or agent decides on their own every evening, based on complete information about past events. Several recent applications of the classical KPR strategies to the Vehicle for Online Hire problem (Martin, 2017 ; Martin and Karaenke, 2017 ), resource allocation problem in the context of Internet-of-Things (IoT) (Park and Saad, 2017 ), development of a different strategy for solving the Traveling Salesman Problem (Kastampolidou et al, 2021 ), etc have been made.…”