Consecutive Meals Planning by Using Permutation GA: The Case of Three Meal's Characteristics

Abstract

The consecutive meals planning is a combinatorial optimization problem that determines the meals plan on one period consisting of consecutive days. This paper designs two evaluation functions for the planning and applies a permutation GA to optimize it. The evaluation function measures the variation of appearance order of meals or meal's characteristics on the plan. In the numerical experiments, we show that our meals plan has a large variation of appearance order of meal's characteristics.

GAs with escape from stagnation of search for multiset iteration permutations problem – consecutive meals planning

“…In this paper, evaluation function is formulated using information entropy to maximize variation of meal's characteristics in meal classes, thus meeting requests by daycares and schools to avoid repetition of meal classes with same characteristics. With evaluation function proposed in previous research, 11,12 section is defined as a period containing as many time points as there are elements | J i | in characteristic i (i = 1, …, N ), and information entropy is calculated for appearance of each element of characteristic i in section moved by one time point; thus, rolling‐type information entropy is obtained to measure variation of appearance order of elements of meals characteristic i through all T time points.…”

“…. , Y [9]) and (Y [10], Y [11], Y [12]), but information entropy is not maximized for non-partial optimal sections containing time points where partial optimal solutions break up (in the diagram, two sections of Y [8], Y [9], Y [10] and Y [12], Y [11], Y [1]). In this case, arrangement of some sections often collapses, even though conventional crossover or mutation is executed; as a result, evaluation value of the entire solution declines, and search for good solutions stagnates.…”

“…The authors of this study have explored a permutation problem of consecutive meals planning 10–13 . There were many previous studies that used linear programming to formulate a combination of single‐meal menus, that is, to maximize one‐time nutrient intake under a calorie constraint 14–18 .…”

“…9 The authors of this study have explored a permutation problem of consecutive meals planning. [10][11][12][13] There were many previous studies that used linear programming to formulate a combination of single-meal menus, that is, to maximize one-time nutrient intake under a calorie constraint. [14][15][16][17][18] However, the research on consecutive meals planning to order in which meals are provided with regard to menu variability, when there is a need for longterm meals planning in day-cares or schools, is unique, as far as we are aware.…”

“…[14][15][16][17][18] However, the research on consecutive meals planning to order in which meals are provided with regard to menu variability, when there is a need for longterm meals planning in day-cares or schools, is unique, as far as we are aware. In previous studies, 11,12 information entropy was used to formulate an evaluation function for variability of meal's characteristics in consecutive meals planning, and optimization was performed by means of evolutionary computation, namely, a permutation genetic algorithm (below referred to as permutation GA). However, experimental results showed that solutions obtained with permutation representation might be greatly different from optimal solutions.…”