This paper deals with the construction of binary sequences with low autocorrelation, a very hard problem with many practical applications. The paper analyzes several metaheuristic approaches to tackle this kind of sequences. More specifically, the paper provides an analysis of different local search strategies, used as standalone techniques and embedded within memetic algorithms. One of our proposals, namely a memetic algorithm endowed with a Tabu Search local searcher, performs at the state-of-the-art, as it consistently finds optimal sequences in considerably less time than previous approaches reported in the literature. Moreover, this algorithm is also able to provide new best-known solutions for large instances of the problem. In addition, a variant of this algorithm that explores only a promising subset of the whole search space (known as skew-symmetric sequences) is also analyzed. Experimental results show that this new algorithm provides new best-known solutions for very large instances of the problem.
Branch-and-Bound and memetic algorithms represent two very different approaches for tackling combinatorial optimization problems. These approaches are not incompatible however. In this paper, we consider a hybrid model that combines these two techniques. To be precise, it is based on the interleaved execution of both approaches. Since the requirements of time and memory in branch-and-bound techniques are generally conflicting, we have opted for carrying out a truncated exact search, namely, beam search. The resulting hybrid algorithm has therefore a heuristic nature. The multidimensional 0-1 knapsack problem and the shortest common supersequence problem have been chosen as benchmarks. As will be shown, the hybrid algorithm can produce better results in both problems at the same computational cost, specially for large problem instances.
Abstract. The Golomb Ruler Problem is a very hard combinatorial optimization problem that has been tackled with many different approaches, such as Constraint Programming (CP), Local Search (LS), Evolutionary Algorithms (EAs), and hybrid LS and CP, among others. This paper describes several local search-based hybrid algorithms to find optimal or near-optimal Golomb rulers. These algorithms are based on both stochastic methods and systematic techniques. More specifically, the algorithms combine ideas from greedy randomized adaptive search procedures (GRASP), scatter search (SS), tabu search (TS), clustering techniques, and constraint programming (CP). Each new algorithm is, in essence, born from the conclusions extracted after the observation of the previous one. With these algorithms we are capable of solving large rulers with a reasonable efficiency. In particular, we can now find optimal Golomb rulers for up to 16 marks.In addition, the paper also provides an empirical study of the fitness landscape of the problem with the aim of shedding some light about the question of what makes the Golomb ruler problem hard for certain classes of algorithm.
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.
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