Abstract
In this paper, we introduce a new combinatorial optimization problem entitled the color mix problem (CMP), which is a more general case of the grey pattern quadratic assignment problem (GP-QAP). Also, we propose an original hybrid genetic-iterated tabu search algorithm for heuristically solving the CMP. In addition, we present both analytical solutions and graphical visualizations of the obtained solutions, which clearly demonstrate the excellent performance of the proposed heuristic algorithm.
Highlights
We have introduced a new combinatorial optimization problem entitled the color mix problem, which has practical potential applications in modern computer graphics, multimedia, as well as the visual arts
We have proposed the hybrid genetic-iterated tabu search algorithm for heuristically solving the color mix problem
The most important feature of the algorithm used is that the genetic algorithm operators are hybridized with the hierarchical iterated tabu search procedure, which, in turn, incorporates the efficient tabu search algorithm combined with mutations of solutions and fast greedy adaptive search procedure
Summary
The values of the analytical solution, where the black points are elements scattered of as the regularly as possible oni.e., the permutation rectangle. The values of the elements of the analytical solution, i.e., permutation p are related to the corresponding coordinates (r, s) of the sites (locations) on the grid through the (). Note that the first m elements in the permutation determine the sites on the grid where the red squares are placed in. For the solution of the color mix problem, (meta)heuristic optimization algorithms can be applied. Single solution-based local search and simulated annealing algorithms were examined in [9] for solving the grey pattern problem [2], which is the “sibling” of the CMP. For the solution of this problem, a hybrid genetic-hierarchical iterated tabu search (HITS) algorithm is proposed.
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