On Solving the Multiple Variable Gapped Longest Common Subsequence Problem

This study addresses the Variable Gapped Longest Common Subsequence Problem (VGLCSP), a variant of the classical longest common subsequence problem with additional gap constraints and applications in sequence alignment and time-series analysis. While the two-sequence version has been widely studied using dynamic programming, the generalized multi-sequence form is usually solved with beam search-based heuristics, whose hand-crafted designs often lack robustness. To overcome this limitation, we propose a learning-based approach for automatically designing more effective data-driven heuristics. The heuristics are represented by a neural network with predefined architecture, whose weights are optimized by a genetic algorithm within a neuro-evolutionary framework. The learning process alternates between weight optimization and evaluation within an iterative multi-source beam search procedure, a state-of-the-art method for the problem. Rather than constructing solutions directly, the neural network learns to guide the search process, producing a neuro-evolved heuristic. We further introduce an ensemble heuristic that combines the scores of learned and the best-performing hand-crafted heuristic. Integrated into the iterative multi-source beam search framework, the resulting hybrid approach outperforms existing methods on both synthetic benchmark instances and newly introduced real-world instances with data-driven gap constraints.

Bidirectional heuristic search can potentially reduce search effort for problems amenable to backward search. Therein, it is well-known that front-to-front heuristics can reduce the number of node expansions, but their overhead is so high that overall runtime almost always increases. We propose BiXDFBnB, a bidirectional depth-first branch-and-bound algorithm that adapts the Single-Frontier Bidirectional Search (SFBDS) framework - originally developed for shortest-path (MIN) problems - to the Generalized Longest Simple Path (GLSP) setting. Because SFBDS inherently operates on paired states, front-to-front (F2F) heuristic evaluation arises naturally and avoids the overhead typically associated with bidirectional frontier management. We show that this adaptation can be successfully applied to maximization (MAX) problems while efficiently handling overlapping constraints. BiXDFBnB is applied to several types of longest-path problems: Longest Simple Path (LSP), Snakes, and Coil-in-the-Box (CIB). Empirical evaluation shows that the new algorithm frequently reduces the number of node expansions and, in some cases, also improves overall runtime.

Low autocorrelation binary sequences problem (LABS) is a hard combinatorial optimization challenge with important applications in communications, signal processing, and satellite navigation. This paper proposes a hybrid search framework that combines Thompson sampling with parallel self-avoiding walks to adaptively allocate computational effort across restriction classes of the LABS search space. By modeling partitions as arms in a multi-armed bandit setting, the proposed method dynamically shifts search resources toward partitions that empirically produce higher merit factors while maintaining exploration of less-sampled regions. The approach is further accelerated through GPU-parallel execution, shared posterior updates, efficient neighborhood evaluation, and a Bloom filter for cycle prevention. In addition, we use a two-stage optimization strategy that first searches constrained partitioned skew-symmetric spaces and then refines the best candidates in the unrestricted space. Experiments on long binary sequences show that the proposed method improves the previously best-known results for 35 sequence lengths in the range $450 \le L \le 527$ and for $L=573$. In particular, we report a new longest sequence with merit factor exceeding $8.0$, obtained for $L=451$. The results also show that Thompson sampling effectively prioritizes partitions with better observed performance, confirming the value of online, data-driven resource allocation in LABS optimization. Overall, the proposed framework provides a scalable and effective strategy for high-performance merit factor maximization.