An extensive search algorithm to find feasible healthy menus for humans.

Promoting healthy lifestyles is nowadays a public priority among most public entities. The ability to design an array of nutritious and appealing diets is very valuable. Menu Planning still presents a challenge which complexity derives from the problems’ many dimensions and the idiosyncrasies of human behavior towards eating. Among the difficulties encountered by researchers when facing the Menu Planning Problem, being able of finding a rich feasible region stands out. We consider it as a system of inequalities to which we try to find solutions. We have developed and implemented a two-phase algorithm -that mainly stems from the Randomized Search and the Genetic- that is capable of rapidly finding an pool of solutions to the system with the aim of properly identifying the feasible region of the underlying problem and proceed to its densification. It consists of a hybrid algorithm inspired on a GRASP metaheuristic and a later recombination. First, it generates initial seeds, identifying best candidates and guiding the search to create solutions to the system, thus attempting to verify every inequality. Afterwards, the recombination of different promising candidates helps in the densification of the feasible region with new solutions. This methodology is an adaptation of other previously used in literature, and that we apply to the MPP. For this, we generated a database of a 227 recipes and 272 ingredients. Applying this methodology to the database, we are able to obtain a pool of feasible (healthy and nutritious) complete menus for a given D number of days.