Multiobjective Evolutionary Algorithm with Double-level Archives for Nutritional Dietary Decision Problem

With the development of computational science, quantitative nutritional dietary study has received more and more attention. One important direction is the optimization of menu planning, i.e., to obtain a nutritional balanced menu while the expense is minimized. But existing studies only consider a small-scale food database and only a few nutrients, which cannot satisfy the requirements of nutritional balance. In this paper, we propose a specific model based on the multiobjective evolutionary algorithm with double-level archives (MOEA-DLA) for the nutritional dietary decision problem (NDDP). First, we collect nutrition data from the database with 1282 kinds of foods, and each food has the corresponding unit price and unit content of each nutrient. We also collect data of ideal daily nutrient intake. Based on the data, we formulate NDDP as a bi-objective optimization problem. Second, we adopt MOEA-DLA to solve NDDP and propose MOEA-NDD. MOEA-DLA takes the advantage of the double-archives strategy, which performs well in multiobjective optimization. To make MOEA-DLA adapt to NDDP, we encode decision variables as a matrix, which includes the information of food items and the corresponding quantity requirements. An improved crossover operator is proposed, which provides two options, one-point crossover or group-level crossover. Besides, a preprocessing rule is also proposed to tackle the encoding redundancy. To investigate the performance of MOEA-NDD, experiments are conducted on the real food database and MOEA-NDD is compared with other multiobjective evolutionary algorithms. The experimental results and a representative example verify the effectiveness of MOEA-NDD in dealing with NDDP.