Constraint-based pattern mining is at the core of numerous data mining tasks. Usually, pattern mining problems are handled as constraint-solving tasks. However, in practice, the resulting patterns are often large, and selecting appropriate thresholds for these constraints can be challenging. This paper addresses these issues by expanding data mining algorithms into the realm of optimization, treating the task as one of identifying the best patterns according to a set of objective functions. We explore a multi-objective optimization approach, where several potentially conflicting objectives are optimized simultaneously. In the absence of preferences, Pareto dominance is commonly used to identify optimal compromise solutions. We present a novel Constraint Programming model designed to efficiently mine Pareto optimal patterns. Our model leverages condensed pattern representations to reduce computational effort and introduces a new global constraint to enforce the closure of patterns across multiple measures. We demonstrate the application of our approach to derive high-quality frequent and (rare) non-redundant association rules without relying on threshold values. The effectiveness of our approach is validated using both UCI datasets and a case study involving gene expression analysis, integrating multiple external gene annotations.

Constraint-based pattern mining is at the core of numerous data mining tasks. Unfortunately, thresholds which are involved in these constraints cannot be easily chosen. This paper investigates a Multi-objective Optimization approach where several (often conflicting) functions need to be optimized at the same time. We introduce a new model for efficiently mining Pareto optimal patterns with constraint programming. Our model exploits condensed pattern representations to reduce the mining effort. To this end, we design a new global constraint for ensuring the closeness of patterns over a set of measures. We show how our approach can be applied to derive high-quality non redundant association rules without the use of thresholds whose added-value is studied on both UCI datasets and case study related to the analysis of genes expression data integrating multiple external genes annotations.