[Paper Review] When data mining meets optimization: A case study on the quadratic assignment problem

Yangming Zhou, Jin‐Kao Hao+1 more|arXiv (Cornell University)|Aug 17, 2017

Data Mining Algorithms and Applications39 references3 citations

TL;DR

This paper proposes a hybrid optimization approach called Frequent Pattern Based Search (FPBS) that integrates data mining with metaheuristics to solve the quadratic assignment problem (QAP). By mining frequent patterns from elite solutions and using them to construct new starting solutions, FPBS achieves state-of-the-art performance, finding the best-known solution on 19 out of 21 benchmark instances within 2 hours.

ABSTRACT

This paper presents a hybrid approach called frequent pattern based search that combines data mining and optimization. The proposed method uses a data mining procedure to mine frequent patterns from a set of high-quality solutions collected from previous search, and the mined frequent patterns are then employed to build starting solutions that are improved by an optimization procedure. After presenting the general approach and its composing ingredients, we illustrate its application to solve the well-known and challenging quadratic assignment problem. Computational results on the 21 hardest benchmark instances show that the proposed approach competes favorably with state-of-the-art algorithms both in terms of solution quality and computing time.

Motivation & Objective

• To address the challenge of balancing exploration and exploitation in metaheuristic search for NP-hard combinatorial problems.
• To investigate whether frequent patterns from high-quality solutions can guide the construction of effective starting solutions.
• To evaluate the performance of the proposed FPBS framework on the notoriously difficult QAP benchmark instances.
• To analyze the impact of key parameters such as the number of frequent patterns and mining thresholds on algorithm performance.

Proposed method

• The FPBS framework alternates between a data mining phase that extracts frequent patterns from a set of elite solutions and an optimization phase that uses these patterns to construct new starting solutions.
• Frequent patterns are mined using a maximal frequent itemset algorithm, with patterns representing recurring configurations in high-quality solutions.
• New solutions are constructed by fixing the positions of items in the most frequent patterns and then applying a local search procedure to optimize the remaining elements.
• The algorithm maintains an elite set of solutions and periodically updates it to include newly discovered high-quality solutions.
• A dynamic parameter update strategy controls the frequency of pattern mining and solution improvement, with parameters tuned via empirical analysis.
• The approach is applied to the QAP by modeling permutations as itemsets, where each position in the assignment corresponds to a transaction.

Experimental results

Research questions

• RQ1 Can frequent patterns extracted from elite solutions guide the construction of high-quality starting solutions in combinatorial optimization?
• RQ2 How does the number of mined frequent patterns influence the diversity and quality of the constructed solutions?
• RQ3 Does integrating data mining into the search process improve solution quality and convergence speed compared to standard metaheuristics?
• RQ4 What is the impact of parameter settings such as the minimum support threshold and the number of patterns on algorithm performance?

Key findings

• FPBS achieved the best-known objective value on 19 out of 21 QAPLIB benchmark instances within a 2-hour time limit, with only slight deviations on tai80a and tai100a.
• The average percentage deviation (PD) of FPBS from the best-known solution was 0.043%, significantly better than the 0.056% achieved by the baseline FPBS-QAP 0 variant.
• The algorithm outperformed state-of-the-art algorithms in both solution quality and computational efficiency, with an average runtime of 8.6 minutes across all instances.
• The optimal number of frequent patterns to use was found to be 11, as it maximized performance across multiple test instances, with performance degrading for smaller or larger values.
• The inclusion of a mutation-like procedure in FPBS-QAP (compared to FPBS-QAP 0) significantly improved solution quality, confirming the value of pattern-guided diversification.
• Parameter tuning, particularly for β=0.75 and max_no_update=15, was critical for balancing exploration and exploitation, with performance sensitive to these settings.