Correlation Clustering Based Coalition Formation For Multi-Robot Task Allocation

In this paper, we study the multi-robot task allocation problem where a group of robots needs to be allocated to a set of tasks so that the tasks can be finished optimally. One task may need more than one robot to finish it. Therefore the robots need to form coalitions to complete these tasks. Multi-robot coalition formation for task allocation is a well-known NP-hard problem. To solve this problem, we use a linear-programming based graph partitioning approach along with a region growing strategy which allocates (near) optimal robot coalitions to tasks in a negligible amount of time. Our proposed algorithm is fast (only taking 230 secs. for 100 robots and 10 tasks) and it also finds a near-optimal solution (up to 97.66% of the optimal). We have empirically demonstrated that the proposed approach in this paper always finds a solution which is closer (up to 9.1 times) to the optimal solution than a theoretical worst-case bound proved in an earlier work

A Polynomial Time Algorithm for Spatio-Temporal Security Games

An ever-important issue is protecting infrastructure and other valuable targets from a range of threats from vandalism to theft to piracy to terrorism. The "defender" can rarely afford the needed resources for a 100% protection. Thus, the key question is, how to provide the best protection using the limited available resources. We study a practically important class of security games that is played out in space and time, with targets and "patrols" moving on a real line. A central open question here is whether the Nash equilibrium (i.e., the minimax strategy of the defender) can be computed in polynomial time. We resolve this question in the affirmative. Our algorithm runs in time polynomial in the input size, and only polylogarithmic in the number of possible patrol locations (M). Further, we provide a continuous extension in which patrol locations can take arbitrary real values. Prior work obtained polynomial-time algorithms only under a substantial assumption, e.g., a constant number of rounds. Further, all these algorithms have running times polynomial in M, which can be very large

Anytime Coalition Structure Generation with Worst Case Guarantees

Coalition formation is a key topic in multiagent systems. One would prefer a coalition structure that maximizes the sum of the values of the coalitions, but often the number of coalition structures is too large to allow exhaustive search for the optimal one. But then, can the coalition structure found via a partial search be guaranteed to be within a bound from optimum? We show that none of the previous coalition structure generation algorithms can establish any bound because they search fewer nodes than a threshold that we show necessary for establishing a bound. We present an algorithm that establishes a tight bound within this minimal amount of search, and show that any other algorithm would have to search strictly more. The fraction of nodes needed to be searched approaches zero as the number of agents grows. If additional time remains, our anytime algorithm searches further, and establishes a progressively lower tight bound. Surprisingly, just searching one more node drops the bound in half. As desired, our algorithm lowers the bound rapidly early on, and exhibits diminishing returns to computation. It also drastically outperforms its obvious contenders. Finally, we show how to distribute the desired search across self-interested manipulative agents

Social Network Based Substance Abuse Prevention via Network Modification (A Preliminary Study)

Substance use and abuse is a significant public health problem in the United States. Group-based intervention programs offer a promising means of preventing and reducing substance abuse. While effective, unfortunately, inappropriate intervention groups can result in an increase in deviant behaviors among participants, a process known as deviancy training. This paper investigates the problem of optimizing the social influence related to the deviant behavior via careful construction of the intervention groups. We propose a Mixed Integer Optimization formulation that decides on the intervention groups, captures the impact of the groups on the structure of the social network, and models the impact of these changes on behavior propagation. In addition, we propose a scalable hybrid meta-heuristic algorithm that combines Mixed Integer Programming and Large Neighborhood Search to find near-optimal network partitions. Our algorithm is packaged in the form of GUIDE, an AI-based decision aid that recommends intervention groups. Being the first quantitative decision aid of this kind, GUIDE is able to assist practitioners, in particular social workers, in three key areas: (a) GUIDE proposes near-optimal solutions that are shown, via extensive simulations, to significantly improve over the traditional qualitative practices for forming intervention groups; (b) GUIDE is able to identify circumstances when an intervention will lead to deviancy training, thus saving time, money, and effort; (c) GUIDE can evaluate current strategies of group formation and discard strategies that will lead to deviancy training. In developing GUIDE, we are primarily interested in substance use interventions among homeless youth as a high risk and vulnerable population. GUIDE is developed in collaboration with Urban Peak, a homeless-youth serving organization in Denver, CO, and is under preparation for deployment

Coalition structure generation in cooperative games with compact representations

This paper presents a new way of formalizing the coalition structure generation problem (CSG) so that we can apply constraint optimization techniques to it. Forming effective coalitions is a major research challenge in AI and multi-agent systems. CSG involves partitioning a set of agents into coalitions to maximize social surplus. Traditionally, the input of the CSG problem is a black-box function called a characteristic function, which takes a coalition as input and returns the value of the coalition. As a result, applying constraint optimization techniques to this problem has been infeasible. However, characteristic functions that appear in practice often can be represented concisely by a set of rules, rather than treating the function as a black box. Then we can solve the CSG problem more efficiently by directly applying constraint optimization techniques to this compact representation. We present new formalizations of the CSG problem by utilizing recently developed compact representation schemes for characteristic functions. We first characterize the complexity of CSG under these representation schemes. In this context, the complexity is driven more by the number of rules than by the number of agents. As an initial step toward developing efficient constraint optimization algorithms for solving the CSG problem, we also develop mixed integer programming formulations and show that an off-the-shelf optimization package can perform reasonably well