A Hybrid Genetic Algorithm for Constrained Combinatorial Problems: An Application to Promotion Planning Problems
We propose a Hybrid Genetic Algorithm (HGA) for a combinatorial optimization problem, motivated by, and a simplification of, a TV Self-promotion Assignment Problem. Given the weekly self-promotion space (a set of TV breaks with known duration) and a set of products to promote, the problem consists of assigning the products to the breaks in the “best” possible way. The objective is to maximize contacts in the target audience for each product, whist satisfying all constraints. The HGA developed incorporates a greedy heuristic to initialize part of the population and uses a repair routine to guarantee feasibility of each member of the population. The HGA works on a simplified version of the problem that, nevertheless, maintains its essential features. The proposed simplified problem is a binary programming problem that has similarities with other known combinatorial optimization problems, such as the assignment problem or the multiple knapsack problem, but has some distinctive features that characterize it as a new problem. Although we are mainly interested in solving problems of large dimension (of about 200 breaks and 50 spots), the quality of the solution has been tested on smaller dimension problems for which we are able to find an exact global minimum using a branch-and-bound algorithm. For these smaller dimension problems we have obtained solutions, on average, within 1% of the optimal solution value.
keywordsGenetic Algorithms Combinatorial Optimization TV Self-Promotion Assignment Problem
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- 1.J.E. Baker. Reducing bias and inefficiency in the selection algorithms. In Proceedings of the Second International Conference on Genetic Algorithms, pages 14–21. Lawrence Erlbaum Associates Inc., USA, 1987.Google Scholar
- 3.E.Y.H. Lin. A biblographical survey on some well-known non-standard knapsack problems. INFOR, 36(4): 274–317, 1998.Google Scholar
- 4.P.A. Pereira, F.A.C.C. Fontes, and D.B.M.M. Fontes. A Decision Support System for Planning Promotion Time Slots. In Operations Research Proceedings 2007: Selected Papers of the Annual International Conference of the German Operations Research Society (GOR), page 147. Springer, 2008.Google Scholar
- 5.Paulo A. Pereira. Um Sistema de Apoio à Decisáo Baseado em Optimizaçáo para o Planea-mento de Auto-promoçáo de uma Estaçáo de Televisáo. PhD thesis, Departamento de Matemática para a Ciência e Tecnologia, Universidade do Minho, Guimaráes, Portugal, 2009.Google Scholar