Ant-Based Approaches for Solving Autocorrelation Problems Ilias S. Kotsireas 1 , Konstantinos E. Parsopoulos 2 , Grigoris S. Piperagkas 2 , and Michael N. Vrahatis 3 1 Department of Physics and Computer Science, Wilfrid Laurier University, Waterloo, Canada ikotsire@wlu.ca 2 Department of Computer Science, University of Ioannina, Greece {kostasp,gpiperag}@cs.uoi.gr 3 Department of Mathematics, University of Patras, Greece vrahatis@math.upatras.gr Abstract. We propose two ant–based formulations for solving autocor- relation problems. The formulations are combined with different ACO variants. Preliminary experiments of the derived approaches are con- ducted on two hard instances of the problem. Their performance is com- pared to an efficient Tabu Search algorithm, offering useful conclusions and motivation for further investigation. 1 Introduction Several difficult combinatorial problems can be defined in a succinct way via the concepts of periodic and non–periodic autocorrelation functions (PAF and NPAF, respectively) associated with a finite binary or ternary sequence. Vari- ous metaheuristics have been previously employed in the search for solutions of similar combinatorial problems, with varying degrees of success. The present paper aims at triggering the interest of the Ant Colony Opti- mization (ACO) research community in solving such combinatorial problems through ant–based approaches. For this purpose, we propose two ant–based for- mulations. To the best of our knowledge, this is the first attempt of formulating such problems in the specific algorithmic framework. As case study, we use our formulations to find Hadamard matrices with two circulant cores, a problem that can be defined via the PAF associated to two binary sequences. Nevertheless, the proposed ant–based formulations can be applied with minor modifications to any combinatorial problem defined via PAF and NPAF. The sequences that arise as solutions to these problems are useful in a wide va- riety of applications, ranging from code–division multiple–access (CDMA) com- munication systems to pulse compression of radar signals. The reader is referred to [6] and [8] for further details and application areas. Additional applications in Coding Theory can be found in [3]. The rest of the paper is organized as follows: Section 2 offers brief descriptions of the problems while Section 3 introduces our ant–based formulations. Experimental results are presented in Section 4. The paper concludes with Section 5. M. Dorigo et al. (Eds.): ANTS 2012, LNCS 7461, pp. 220–227, 2012. c  Springer-Verlag Berlin Heidelberg 2012