Modified Deterministic Parameter Controlled Harmony Search Algorithm to Solve 4-Color Mapping Problem

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Bnar Faisal A. Daham
Mohammed Nasseh Mohammed
Kanar Shukr Mohammed


Optimization, 4-Color Mapping Problem, Harmony Search Algorithm, Map Coloring, Parameter Control


Harmony Search Algorithm (HSA) is one of the optimization algorithms which is imitating the behavior of musicians when composing melodies. This algorithm which consists of three phases; initialization, improvisation, and selection has been applied in this paper with some variations to solve the 4-Color Mapping Problem.

In this study, two approaches have been applied together and introduced to enhance the performance of HSA, in solving the 4-Color Mapping Problem. The first modification has been applied to the initialization section of the algorithm. And the second approach included using a number of deterministic parameter control rules to fine-tune these parameters individually and dynamically, turning harmony search into a more dynamic algorithm.

Hence, by applying both of them, better results were obtained in terms of higher performance of  the improvisation process,  and  consequently,  reducing  the time  and  number  of  cycles taken to solve  the 4-color mapping problem compared to the original HSA. In this paper, maps with different numbers of regions have been taken as case studies, using HSA, Modified Harmony Search Algorithm (MHSA), Deterministic Parameter Controlled Harmony Search Algorithm (PCHSA), and Modified Deterministic Parameter Controlled Harmony Search Algorithm (MPCHSA). The experimental results revealed that MPCHSA has better outcomes compared to HSA, MHSA, and PCHSA.

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