FloTra: Flower-shape Trajectory Mining for Instance-specific Parameter Tuning

Meta-heuristic algorithms play an important role in solving Combinatorial Optimization Problems (COP) in many real-life applications. The caveat is that the performance of a meta-heuristic algorithm is highly dependent on its parameter configuration which controls the algorithm behavior. Furthermore, finding the optimal parameter configuration, especially instance-specific configuration, is often a difficult, tedious and frustrating task. Among the proposed approaches for automated parameter tuning, CluPaTra [3] and SufTra [4] address the requirements of generic instance-specific automated parameter tuning. It introduces the notion of search trajectory as a generic feature. Search Trajectory, modeled as a sequence, is a series of solutions discovered by meta-heuristic algorithm as it searches for the best solutions over its neighborhood search space. Although CluPaTra and SufTra have been proven to give a significant improvement over onesize-fits-all approach, it suffers from descriptiveness issue due to their sequence representation model. CluPaTra and SufTra may oversimplify the search trajectory and lose finer-granularity details in some structural patterns. For example, Fig. 1 shows the sequence and graph representation for three search trajectories of Quadratic Assignment Problem (QAP) instances. The three sequences have many similar subsequences (Fig. 1a) but the real search trajectories (as shown in Fig. 1b) are different; two search trajectories have a smoother search while the other one has many cycles. In this work, we introduce FloTra, a technique to uncover important patterns from search trajectory graph for generic instance-specific automated parameter tuning. FloTra is an extension of CluPaTra and SufTra that overcomes their limitation on descriptiveness. FloTra constructs a graph representation of search trajectory and conducts a graph pattern mining to discover specific and important patterns in search trajectory. Using these patterns, FloTra then clusters the instances and computes a corresponding optimal parameter configuration for each cluster. We have applied our approach on QAP and SCP and show that FloTra gives an encouraging improvement for the overall performance.