Abstract
Encouraging healthy and balanced diet plans is one of the most important action points for governments around the world. Generating healthy, balanced and inexpensive menu plans that fulfil all the recommendations given by nutritionists is a complex and time-consuming task; because of this, computer science has an important role in this area. This paper deals with a novel constrained multi-objective formulation of the menu planning problem specially designed for school canteens that considers the minimisation of the cost and the minimisation of the level of repetition of the specific courses and food groups contained in the plans. Particularly, this paper proposes a multi-objective memetic approach based on the well-known multi-objective evolutionary algorithm based on decomposition (MOEA/D). A crossover operator specifically designed for this problem is included in the approach. Moreover, an ad-hoc iterated local search (ILS) is considered for the improvement phase. As a result, our proposal is referred to as ILS-MOEA/D. A wide experimental comparison against a recently proposed single-objective memetic scheme, which includes explicit mechanisms to promote diversity in the decision variable space, is provided. The experimental assessment shows that, even though the single-objective approach yields menu plans with lower costs, our multi-objective proposal offers menu plans with a significantly lower level of repetition of courses and food groups, with only a minor increase in cost. Furthermore, our studies demonstrate that the application of multi-objective optimisers can be used to implicitly promote diversity not only in the objective function space, but also in the decision variable space. Consequently, in contrast to the single-objective optimiser, there was no need to include an explicit strategy to manage the diversity in the decision space in the case of the multi-objective approach.
Highlights
Nowadays, due to unhealthy and sedentary lifestyles, a high percentage of the human population suffers from various diseases such as high cholesterol, diabetes and other conditions related to those habits which can cause other serious illnesses, including several types of cancer [1]
The reader should recall that the working hypothesis behind this comparison is that by applying iterated local search (ILS)-multi-objective evolutionary algorithm based on decomposition (MOEA/D) to a multi-objective formulation of the menu planning problem (MPP), which considers the cost of the plan and the level of repetition, it is possible to find solutions that are similar in terms of the cost to those provided by memetic algorithms (MAs), but significantly better with respect to the level of repetition of specific courses and food groups contained in the menu plan
This paper proposes a memetic multi-objective algorithm based on the well-known MOEA/D, which applies an ILS as the improvement phase, i.e., ILS-MOEA/D, to solve a novel multi-objective constrained formulation of the MPP
Summary
Due to unhealthy and sedentary lifestyles, a high percentage of the human population suffers from various diseases such as high cholesterol, diabetes and other conditions related to those habits which can cause other serious illnesses, including several types of cancer [1]. This work presents a novel constrained multi-objective formulation of the well-known menu planning problem (MPP) [2]. The working hypothesis is that by using our novel multi-objective constrained formulation of the MPP, which considers the cost of the plan and at the same time the level of repetition of the specific courses and food groups contained in the plan, it is possible to find solutions that are similar in terms of the cost to those provided by the aforementioned single-objective MA, but significantly better regarding the level of repetition.
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