Effectiveness of evaluation function and permutation GA in multimodal consecutive meals planning

The consecutive meals planning is a combinatorial optimization problem that determines a meals plan on a long period consisting of consecutive days. A meal is characterized in different characteristics such as food style, ingredient, and cooking method. For the problem, this paper proposes an evaluation function using information entropies on moving intervals. The function measures the appearance order of meal's characteristics on the plan. In addition, we design a specific genotype of a permutation GA and apply it to this problem. In the numerical experiments, we show that the consecutive meals planning employing our function can be viewed as a multimodal problem and then show that our meals plan obtained by the permutation GA is a good solution with large variation of appearance order of meal's characteristics.