Multi-task Combinatorial Optimization: Inter-task Distance Metric and Benchmark

Peng Li, Bo Liu

Abstract: Operations research has indeed gone far in the direction of siloing tasks without explicitly using inter-task synergies which makes optimizing a new task a Sisyphean challenge. The existence of dependences across tasks constitutes the fundamental premise of impelling knowledge transfer to enhance concurrent search in multi-tasking optimization. In this paper, we attempt to capture the underlying commonality across tasks in the context of permutation flowshop scheduling problem, one of the most intensively studied combinatorial optimization problems. Despite the belief that certain common structure exists among them, it has been long recognized that scheduling is a typical example of the weak theory domains where the similarity across tasks are not captured explicitly. It is hard to characterize the general difference in characteristics of their functional landscapes by the differences in pairs of fitness-solution due to curse of dimensionality. We answer the imposing theoretical and computational challenges in discrepancy between tasks. Precisely, first, a normalized inter-task distance is proposed and expressed as a closed-form analytical solution to a well-structured constrained quadratic programming problem. It has extremely low overhead and high accuracy to discern explicitly between tasks. It could be forms of domain knowledge to guide the transfer in multi-tasking optimization to minimize harmful interactions. Second, we showcase it is unrelated or faintly related between randomly paired instances from available single-task benchmarks. A large-scale multi-tasking benchmark is generated which covers from completely unrelated tasks to highly close ones, serving the purposes of validation of the inter-task distance metric.