The Physical Travelling Salesman Problem: WCCI 2012 Competition Diego Perez School of Computer Science and Electronic Engineering University of Essex Colchester CO4 3SQ, UK Email: dperez@essex.ac.uk Philipp Rohlfshagen School of Computer Science and Electronic Engineering University of Essex Colchester CO4 3SQ, UK Email: prohlf@essex.ac.uk Simon M. Lucas School of Computer Science and Electronic Engineering University of Essex Colchester CO4 3SQ, UK Email: sml@essex.ac.uk Abstract—Numerous competitions have emerged in recent years that allow researchers to evaluate their algorithms on a variety of real-time video games with different degrees of complexity. These competitions, which vary from classical arcade games like Ms Pac-Man to racing simulations (Torcs) and real- time strategy games (StarCraft), are essential to establish a uni- form testbed that allows practitioners to refine their algorithms over time. In this paper we propose a new competition to be held for the first time at WCCI 2012: the Physical Travelling Salesman Problem is an open-ended single-player real-time game that removes some of the complexities evident in other video games while preserving some of the most fundamental challenges. This paper motivates and outlines the PTSP and discusses in detail the framework of the competition, including software interfaces, parameter settings, rules and details of submission. I. AN I NTRODUCTION TO THE PTSP Research in game AI has traditionally focussed on 2-player turn-taking board games of perfect information such as Chess and Go, and in many cases has produced algorithms capable of super-human play. Driven by past successes, practitioners have started to concentrate on more complex domains, including those characterised by hidden information, stochasticity, real- time elements and simultaneous moves, to name but a few. Amongst the wide variety of games considered, real-time video games are of particular interest, both academically and commercially: video games are immensely popular yet also notoriously complex and so far, efforts to produce convincing non-player characters (NPCs) have achieved some success but have been labour-intensive; there are some examples where modern Artificial Intelligence (AI) techniques have been applied to video games, as probabilistic techniques in the Halo series, or planning in FEAR and Skyrim. However, most successful video games continue to rely on scripts, animations, finite state machines (often hierarchical) or behaviour trees to convey a sense of intelligence to the gamer. In an ongoing effort to address this issue and offer a machine-learning based alternative, numerous video games competitions have been proposed in recent years, including, for instance, racing simulations (TORCS), Ms Pac-Man, Tron, Planet Wars and the Mario AI Challenge. Irrespective of any potential game applications, they are also interesting problems for academic study. In this paper we propose a new competition centred around the Physical Travelling Salesman Problem (PTSP), a modifica- tion of one of the most well-known combinatorial optimisation problems, the Travelling Salesman Problem (TSP). The goal of the competition is to allow practitioners to compete in a domain that is less complex than most other game-based competitions while retaining some of the essential aspects of modern video games. In particular, the PTSP requires real-time navigation of a single-point mass, an abstraction of a concept found in many modern video games. Despite its simplicity, the PTSP bears significant resemblance to some older video games, including CrystalQuest, XQuest and Crazy Taxi. 1 The PTSP is a single-player real-time variant of the classical TSP: the TSP consists of a set of spatially distributed cities n 0 ,n 1 ,...n N . A solution to the TSP is a sequence of cities (tour) that visits each city once, returning to the starting city at the end. The tour length is the sum of the distances between all consecutive pairs of cities and the goal is to find the tour with the minimum overall length [1]. The TSP may be converted into a single player real-time game: the agent (salesman; herein referred to as a ship) and the cities are positioned in two- dimensional continuous space as indicated by their respective coordinates (a pair of real values). The objective of the game is to direct the agent in real-time to visit all the cities (also referred to as waypoints in this text) as quickly (i.e., in as few time steps) as possible. This is done by providing an action in each execution step. The actions that govern the ship are summarised in Figure 1. There are two basic commands that can be used: thrusting and left / right rotation. The former can be seen as a boolean input (either the ship thrusts or not) while the latter is an integer value to indicate rotation to the left (−1), to the right (1) or no rotation at all (0). These two inputs may be supplied simultaneously for a total of six different actions that may be carried out at each time step. All actions can be understood as forces applied to the ship that update its position, orientation and speed. The equations shown below 1 Crazy Taxi and Mario Kart also have a bonus game in which the player drives the car around an open space with the aim of popping a set of balloons, or collecting items, within a given time limit; the PTSP is very similar to this.