Hybrid Dynamic Programming for Simultaneous Coalition Structure Generation and Assignment

Abstract

We present, analyze and benchmark two algorithms for simultaneous coalition structure generation and assignment: one based entirely on dynamic programming, and one anytime hybrid approach that uses branch-and-bound together with dynamic programming. To evaluate the algorithms' performance, we benchmark them against both CPLEX (an industry-grade solver) and the stateof-the-art using difficult randomized data sets of varying distribution and complexity. Our results show that our hybrid algorithm greatly outperforms CPLEX, pure dynamic programming and the current state-of-the-art in all of our benchmarks. For example, when solving one of the most difficult problem sets, our hybrid approach finds optimum in roughly 0.1% of the time that the current best method needs, and it generates 98% efficient interim solutions in milliseconds in all of our anytime benchmarks; a considerable improvement over what previous methods can achieve.

Dividing the Indivisible : Algorithms, Empirical Advances, and Complexity Results for Value-Maximizing Combinatorial Assignment Problems

“…These generate some of the most difficult known problems for the state-of-the-art UCA solvers (see e.g., our papers [143,144] for more examples). Variations of them have also been used extensively to benchmark various approaches for solving a number of different problems related to UCA in operations research, algorithmic game theory, and multi-agent systems, including coalition formation and combinatorial auctions [121,146,144,142,152,153,171,218]. In more detail, they generate problem instances as follows:…”

“…The first five distributions that we use for benchmarking are NPD (normal probability distribution), UPD (uniform probability distribution), SNPD (sparse NPD), SUPD (sparse UPD), and NRD (normal relational distribution). These generate some of the most difficult known problems for the state-of-the-art UCA solvers introduced in the previous sections (see e.g., [146,142]). Variations of them have also been used extensively to benchmark various approaches for solving a number of different problems related to UCA in operations research, algorithmic game theory, and multi-agent systems, including coalition formation and combinatorial auctions [121,146,144,142,157,153,171,218].…”

Anytime Index-Based Search Method for Large-Scale Simultaneous Coalition Structure Generation and Assignment

“…Very few algorithms [11,9,10] have been developed for the SCSGA problem. On the other, the closely related problem CSG has been extensively studied, and many algorithms have been developed to solve it, which are discussed in Section 1.…”

“…Among them, [9] introduces a search space representation based on multiset permutations of integer partitions [13] to prune large portions of the search space. Another work [10] proposes a dynamic programming algorithm for optimally solving the SC-SGA problem. These methods are optimal and outperform CPLEXa commercial state-of-the-art optimization software-when it comes to finding optimal solutions for small-scale problems.…”