An anytime algorithm for optimal simultaneous coalition structure generation and assignment

Abstract

An important research problem in artificial intelligence is how to organize multiple agents, and coordinate them, so that they can work together to solve problems. Coordinating agents in a multi-agent system can significantly affect the system's performance-the agents can, in many instances, be organized so that they can solve tasks more efficiently, and consequently benefit collectively and individually. Central to this endeavor is coalition formation-the process by which heterogeneous agents organize and form disjoint groups (coalitions). Coalition formation often involves finding a coalition structure (an exhaustive set of disjoint coalitions) that maximizes the system's potential performance (e.g., social welfare) through coalition structure generation. However, coalition structure generation typically has no notion of goals. In cooperative settings, where coordination of multiple coalitions is important, this may generate suboptimal teams for achieving and accomplishing the tasks and goals at hand. With this in mind, we consider simultaneously generating coalitions of agents and assigning the coalitions to independent alternatives (e.g., tasks/goals), and present an anytime algorithm for the simultaneous coalition structure generation and assignment problem. This combinatorial optimization problem has many real-world applications, including forming goal-oriented teams. To evaluate the presented algorithm's performance, we present five methods for synthetic problem set generation, and benchmark the algorithm against the industry-grade solver CPLEX using randomized data sets of varying distribution and complexity. To test its anytimeperformance, we compare the quality of its interim solutions against those generated by a greedy algorithm and pure random search. Finally, we also apply the algorithm to solve the problem of assigning agents to regions in a major commercial strategy game, and show that it can be used in game-playing to coordinate smaller sets of agents in real-time.

Towards Utilitarian Combinatorial Assignment with Deep Neural Networks and Heuristic Algorithms

“…We use the problem set distributions NPD (3) and TRAP (4) for generating difficult problem instances for evaluating our method. NPD is one of the more difficult standardized problem instances for optimal solvers [11], and it is defined as follows:…”

“…The only UCA algorithm in the literature is an optimal branch-and-bound algorithm [10,11]. Although this algorithm greatly outperforms industry-grade solvers like CPLEX in difficult benchmarks, it can only solve fairly small problems.…”

“…Note that there are applications for which it is realistic (or even preferred) to have the value function given in this type of fashion. Examples of this include the strategy game Europa Universalis 4, where it is given by the game's programmers to enforce a certain behaviour from its game-playing agents [11]. Other such examples include when it can be defined concisely but e.g., not given as an explicit list due to the problem's size, such as in winner determination for combinatorial auctions [13], or when the value function is a result of machine (e.g., reinforcement) learning.…”

Hybrid Dynamic Programming for Simultaneous Coalition Structure Generation and Assignment

“…Although this algorithm performs fairly well in practice and greatly outperforms the industry-grade solver CPLEX, it suffers from there being no proven guarantee that it can find an optimum without first evaluating all the m n possible feasible solutions. [7] To address these issues, we develop an algorithm with a proven worst-case time complexity better (lower) than O(m n ), and devise a second algorithm that finds both optimal and anytime (interim) solutions faster than the state-of-the-art. More specifically, we focus on the paradigm dynamic programming to accomplish this, and investigate how dynamic programming can be combined with branch-and-bound to obtain the best features of both.…”

Avoiding collaborative paradox in multi‐agent reinforcement learning

“…These approaches have been proven effective in a large set of multi-agent cooperation tasks [13][14][15]. However, collaboration in real-world applications can still be improved where two aspects of highly competitive and cooperative settings exist simultaneously [16].…”