Motivation: The Multiple Longest Common Subsequence (MLCS) problem for an arbitrary number of sequences is an NP-hard problem in sequence analysis. Existing exact algorithms based on dynamic programming or MLCS-DAG pruning rapidly exhaust memory as sequence lengths and set sizes grow, while heuristic and hyper-heuristic approaches compromise solution quality and require heavy parameter tuning, respectively. Results: This paper presents the ARP heuristic that, for a given primary sequence, performs three key actions: (i) Adding-$Δ$s, which incrementally builds a solution by adding subsequences, called $Δ$s, of the primary sequence to an initial solution; (ii) Replacing-Subsequences, which enhances the diversity of the solution set via targeted replacement of subsequences common to all solutions; and (iii) Prioritizing groups of characters from the primary sequence that are likely to appear together in longer common subsequences. ARP allows the user to configure the degree of Replacements and Prioritization actions for carrying out quality-runtime tradeoff. Empirical evaluations on both synthetic and biological sequence sets demonstrate that ARP's fastest configuration AOnly finds significantly longer common subsequences than the BNMAS classical heuristic and its aggressive configuration attains solution quality comparable to state-of-the-art hyper-heuristic (UB-HH) while running 1.1$\times$-1.7$\times$ faster.

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