A Probabilistic Beam Search Approach to the Shortest Common Supersequence Problem

Abstract

The Shortest Common Supersequence Problem (SCSP) is a well-known hard combinatorial optimization problem that formalizes many real world problems. This paper presents a novel randomized search strategy, called probabilistic beam search (PBS), based on the hybridization between beam search and greedy constructive heuristics. PBS is competitive (and sometimes better than) previous state-of-the-art algorithms for solving the SCSP. The paper describes PBS and provides an experimental analysis (including comparisons with previous approaches) that demonstrate its usefulness.

Hybrid metaheuristics in combinatorial optimization: A survey

“…With both disadvantages in mind, a recent line of research promotes the incorporation of features from branch & bound derivatives such as beam search into construction-based metaheuristics. Examples are probabilistic beam search [91], incomplete and non-deterministic tree search (ANTS) procedures [92][93][94], and Beam-ACO algorithms [95][96][97]. Exemplary, the working of Beam-ACO is outlined in more detail in the following.…”

Evolutionary-based iterative local search algorithm for the shortest common supersequence problem

“…Each string was generated from the target sequence by removing symbols with probability p = 20%. This type of benchmark was used also in [9] and [4,6,1] and appeared to be the hardest one out of the test benchmarks used in these works.…”

“…String s is a supersequence of r if (1) r = (where is the empty string) or (2) if s = αs , r = αr and s is a supersequence of r or (3) if s = αs , r = βr and α = β and s is a supersequence of r (where α and β are symbols from Σ and s = αs represents such a string s that is obtained by appending the symbol α in front of string s .). In other words, s is said to be a supersequence of r (or r is embedded in s) if all symbols in r are present in s in the very same order (although not necessarily consecutive) [1].…”

“…The iterative process stops after a specified number of iterations. 1 In all of the POEMS implementations presented in this paper, the prototype represents the developed supersequence as a variable length ordered list of symbols from alphabet Σ.…”

“…At that moment, the (super)sequence fragment starting at position l = 6 of length W = 5 is being modified by the EA. The head part of each string si that is completely covered by the head part of the (super)sequence (the symbols up to the position l − 1, in this case this is the sequence s [1,5]) is calculated and the first position of the tail part of each string si, ti, is identified (here, t1 = 4, t2 = 4, t3 = 3, t4 = 5). Note, that the whole tail part of each string si might become affected by some modification made within the (super)sequence fragment.…”