An Approximate Algorithm for Resource Allocation Using Combinatorial Auctions

Combinatorial auctions (CAs), where users bid on combination of items, have emerged as a useful tool for resource allocation in distributed systems. However, two main difficulties exist to the adoption of CAs in time-constrained environments. The first difficulty involves the computational complexity of winner determination. The second difficulty entails the computational complexity of eliciting utility valuations for all possible combinations of resources to different tasks. To address both issues, we developed a new algorithm, seeded genetic algorithm (SGA) for finding high quality solutions quickly. SGA uses a novel representational schema that produces only feasible solutions. We compare the winner determination performance of our algorithm with Casanova, another local stochastic search procedure, on typically hard-to-solve bid distributions. We show that SGA converges to a better solution than Casanova for large problem sizes. However, for many bid distributions, exact winner determination using integer programming approaches is very fast, even for large problem sizes. In these cases, SGA can still provide significant time savings by eliminating the requirement for formulating all possible bids.