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. The problem consists of, given the weekly self-promotion space (a set of TV breaks with known duration) and a set of products to promote, to assign the products to the breaks in the “best” possible way. The objective is to maximize contacts in the target audience for each product, while 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 were mainly interested in solving problems of large dimension (of about 200 breaks and 50 spots), the quality of the solution was tested on smaller dimension problems for which we could find the 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. keywords Genetic Algorithms, Combinatorial Optimization, TV Self-Promotion Assignment Problem. Paulo A. Pereira CMAT and Dept. of Mathematics and Applications, Universidade do Minho, 4800-058 Guimarães, Portugal, [email protected] Fernando A. C. C. Fontes ISR and Faculdade de Engenharia, Universidade do Porto, 4200-465 Porto, Portugal, [email protected] Dalila B. M. M. Fontes LIAAD-INESC Porto L.A. and Faculdade de Economia, Universidade do Porto, 4200-464 Porto, Portugal, [email protected]