**4. Experimental Assessment**

Due to the fact that the same constraints and courses database used in [3] is applied in this work, the results obtained by ILS-MOEA/D were compared, in terms of the meal plan cost, with those attained by the single-objective MA proposed in [3], which will be referred to as MA in the rest of the paper. Moreover, the level of repetition of the solutions provided by MA was also computed to properly evaluate the difference between the two approaches.

Regarding the courses database, a total of 64 different courses were available, grouped into three different categories: *lf c*: 18 starters, *lsc*: 33 main courses, *lds*: 13 desserts. Moreover, for every course available, the following information was obtained: name of the course, cost of the course, amount of nutrients in the course and the particular food groups the course belongs to.

Standard configurations for MA and ILS-MOEA/D were applied to different instances of the MPP. Specifically, plans for *n* = 20, *n* = 40 and *n* = 60 days were considered. All the experiments were performed using the elapsed time as the stopping criterion, which was different depending on the instance size. For *n* = 20 days, the stopping criterion was set to one hour, and it was increased to two and a half hours and five hours for *n* = 40 and *n* = 60 days, respectively.

Regarding the parameterisation of ILS-MOEA/D, the population size was set to *N* = 15 individuals, the neighbourhood size was fixed to *L* = 5 individuals and the crossover rate was set to *CR* = 1.0. The set of weight vectors *λ* was generated using the method described in [9]. We note that the same parameterisation was used to apply the single-objective MA, which means that the population size was set to *N* = 15 individuals and the crossover rate *CR* = 1.0. None of the algorithms applied a mutation operator. Finally, the number of iterations of the ILS was set to 100 in both cases.

The Metaheuristic-based Extensible Tool for Cooperative Optimisation (METCO) (Available at: https://github.com/PAL-ULL/software-metco), described in [39], was used to implement ILS-MOEA/D and the multi-objective constrained formulation of the MPP discussed here, as well as to perform the entire experimental assessment.Experiments were run on a server belonging to the "Laboratorio de Supercómputo del Bajío", which is maintained by the "Centro de Investigación en Matemáticas" (CIMAT), Mexico. The server provides two Intel Xeon E5-2620 v2 processors with 6 cores each at 2.1 GHz with 32 GB RAM. Since we are dealing with stochastic approaches, every execution was repeated 30 times. In order to statistically support the conclusions, the following statistical testing procedure, which was formerly used in previous work by the authors [40], was applied to conduct comparisons between experiments. First, a Shapiro–Wilk test was performed to check whether the values of the results followed a normal (Gaussian) distribution. If so, the Levene test checked for the homogeneity of the variances. If the samples had equal variances, an ANOVA test was done; if not, a Welch test was performed. For non-Gaussian distributions, the non-parametric Kruskal–Wallis test was used. For every test, a significance level *α* = 0.05 was considered.

The hypervolume (*HV*) [41], normalised in the range [0, 1], was selected as the metric to measure the performance of ILS-MOEA/D. To compute the normalised *HV*, the resulting Pareto Fronts of ILS-MOEA/D were normalised using the worst and best values achieved for each objective function, which defines the lower and upper bounds among all the executions performed. We should note that since the *HV* metric has to be maximised, the higher its value, the better the performance.
