Computational Intelligence and Neuroscience

Volume 2019, Article ID 2351591, 9 pages

https://doi.org/10.1155/2019/2351591

## PathGame: Crowdsourcing Time-Constrained Human Solutions for the Travelling Salesperson Problem

^{1}Department of Traffic Engineering, Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovica 6, 21000 Novi Sad, Serbia^{2}Faculty of Mathematics and Natural Sciences, University of Podgorica, Bulevar Džordža Vašingtona bb, 81000 Podgorica, Montenegro^{3}Department of Industrial Engineering and Management, Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovica 6, 21000 Novi Sad, Serbia

Correspondence should be addressed to Đorđije Dupljanin; sr.ca.snu@ijdrojdd

Received 11 July 2018; Revised 13 March 2019; Accepted 31 March 2019; Published 13 May 2019

Academic Editor: Amparo Alonso-Betanzos

Copyright © 2019 Slaviša Dumnić et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Human strategies for solving the travelling salesperson problem (TSP) continue to draw the attention of the researcher community, both to further understanding of human decision-making and inspiration for the design of automated solvers. Online games represent an efficient way of collecting large amounts of human solutions to the TSP, and PathGame is a game focusing on non-Euclideanclosed-form TSP. To capture the instinctive decision-making process of the users, PathGame requires users to solve the problem as quickly as possible, while still favouring more efficient tours. In the initial study presented here, we have used PathGame to collect a dataset of over 16,000 tours, containing over 22,000,000 destinations. Our analysis of the data revealed new insights related to ways in which humans solve TSP and the time it takes them when forced to solve TSPs of large complexity quickly.

#### 1. Introduction

Finding the shortest path to visit several destinations is one of the problems humans have evolved to solve on a daily basis. In the scientific literature, this problem is known as the TSP, as it can be thought of as a problem of finding ways in which one may find the shortest path for a “salesperson,” who needs to visit a predefined set of “cities”. The salesman is required to visit a city only once and, in the closed-form variant of the problem, to return to the starting node.

Since there are a number of applications in the domain of transport and delivery, which would benefit from ways to determine an optimal path through a set of points, the earliest published literature on the TSP dates to the 18th century [1], although it has probably been studied much earlier than that. Perhaps surprisingly, the research has revealed that it is a complex problem and one that belongs to a larger group of problems for which no algorithm that can solve them in polynomial time is known at this point. TSP is perhaps the best-studied example of a nondeterministic polynomial time (NP) problem and is known as NP-complete [1]. It is worth noting that there is also no theoretical proof that a good algorithm for solving this class of problems does not exist. Thus, we do not really know how hard of a problem TSP is, except through empirical evidence that we have been unable to solve it adequately for quite some time; despite the large interest, it continues to draw from the scientific community.

Despite the fact that computers are unable to solve the problem in polynomial time, humans are able to do so for relatively small instances of the problem (10–120 points), in time that is a close-to-linear function of the problem complexity [2, 3].

When solving the TSP, humans rely more on their perceptual skills than cognitive skills. In an early (1974) study aimed at examining this aspect of the problem, Polivanova compared human performance on geometrically represented instances of the problem versus performance on instances where the travel costs were given explicitly for each pair of cities. The participants showed significantly better results on geometric instances [4].

It is no surprise that there have been attempts to create computational models that would match human performance on TSP.

Best and Simon [5] showed early on 2000 that 80% of all subject choices as to what node to go to next can be explained by following the nearest neighbor path.

At about the same time, MacGregor et al. [6] created a model which starts from the convex hull of the destination points and iteratively refines it to include all the points. Since the refinement procedure starts from a random point on the convex hull and they consider two different point inclusion criteria, their model provides a number of solutions for a given set of points. The model was evaluated on a range of data gathered from humans in their and previous studies dealing with 10, 20, 40, and 60 node problems, a single 48-node problem, and a single 100-node problem. The data used to evaluate the model varied in terms of the number of instances and subjects that generated it. For the 10–60 node problems, 50 undergraduate students generated the data, for “several” random problems with each number of nodes. For the 48-node problem, 103 human solutions were gathered, while for the 100-node problem, just 8 subjects solved the problem. Although it was tested on limited data available, the model proposed by MacGregor et al. matches human performance well.

In the time following MacGregor et al.’s study, there has been a number of papers aimed at studying a different aspect of human TSP solving, often proposing and refining human-inspired computational models for TSP solving. In their 2011 paper, MacGregor and Chu provide a good overview of more recent results [7]. We limit our discussion to the studies closely related to our work.

Human performance on Euclidean and non-Euclidean TSPs was examined by Walwyn and Navarro [8]. Their experiments, conducted on 40 participants (mostly undergraduate students), each of whom solved 12 10-point and 6 40-point problems on paper, support the hypothesis that humans create near-optimal solutions for both types of the problem while being slightly better at solving the Euclidean version.

Despite the perhaps obvious benefits that might be gained through the uses of modern information technology and video games in terms of gathering much larger sets of experimental data, there have not been many such approaches reported in the literature. In fact, the only study taking this route that we could identify is reported on in a 2017 paper by Rach and Kirsch, who created an online game Perlentaucher [9]. The main goals of their study were to address a large number of participants, to collect data on different problem variants, to create a game that does not feel like a test and to collect data on human solution procedures when provided with tools, and to identify the ability to repeat a task. The first three goals dealing with gathering data from a large number of participants, data for different problem variants and creating a game that does not feel like a test, coincide with the goals of the study presented here. However, in the present study, we are interested in larger non-Euclidean problems, so our design choices have been made accordingly.

If one wants to collect large amounts of data, an online game, interesting enough for the participants is a good solution. The study conducted by Rach and Kirsch showed that the solutions collected through online gameplay corresponds well to the data previously reported in the literature and the validity of such an approach to data collection.

The work of Rach and Kirsch is the one most related to the work presented in this paper (PathGame). Both approaches are based on an online game that can be played on devices running a modern browser and required a mouse or touchpad as an input device. PathGame support for touchscreen devices is being developed but is still not available at the time of writing. However, significant differences exist between the two approaches. The study of Rach and Kirsch relied on 24 instances of Euclidean TSP as stimuli. In PathGame, the number of points ranges from 10 to 196 and is stochastically determined, by specifying only the probability of a point being a destination point. The playing field, shown in Figure 1, consists of a rectangular grid of 15 × 15 (225) points and the score is calculated based on Manhattan (block-based), not Euclidean distance. To induce the players to follow non-Euclidean-based strategies, the game plots the resulting block-based path between the last destination point visited and the current position of the mouse pointer.