On three soft rectangle packing problems with guillotine constraints

We investigate how to partition a rectangular region of length $L_1$ and height $L_2$ into $n$ rectangles of given areas $(a_1, \dots, a_n)$ using two-stage guillotine cuts, so as to minimize either (i) the sum of the perimeters, (ii) the largest perimeter, or (iii) the maximum aspect ratio of the rectangles. These problems play an important role in the ongoing Vietnamese land-allocation reform, as well as in the optimization of matrix multiplication algorithms. We show that the first problem can be solved to optimality in $\mathcal{O}(n \log n)$, while the two others are NP-hard. We propose mixed integer programming (MIP) formulations and a binary search-based approach for solving the NP-hard problems. Experimental analyses are conducted to compare the solution approaches in terms of computational efficiency and solution quality, for different objectives

The Vehicle Routing Problem with Service Level Constraints

We consider a vehicle routing problem which seeks to minimize cost subject to service level constraints on several groups of deliveries. This problem captures some essential challenges faced by a logistics provider which operates transportation services for a limited number of partners and should respect contractual obligations on service levels. The problem also generalizes several important classes of vehicle routing problems with profits. To solve it, we propose a compact mathematical formulation, a branch-and-price algorithm, and a hybrid genetic algorithm with population management, which relies on problem-tailored solution representation, crossover and local search operators, as well as an adaptive penalization mechanism establishing a good balance between service levels and costs. Our computational experiments show that the proposed heuristic returns very high-quality solutions for this difficult problem, matches all optimal solutions found for small and medium-scale benchmark instances, and improves upon existing algorithms for two important special cases: the vehicle routing problem with private fleet and common carrier, and the capacitated profitable tour problem. The branch-and-price algorithm also produces new optimal solutions for all three problems

A Hybrid Genetic Algorithm for the Traveling Salesman Problem with Drone

This paper addresses the Traveling Salesman Problem with Drone (TSP-D), in which a truck and drone are used to deliver parcels to customers. The objective of this problem is to either minimize the total operational cost (min-cost TSP-D) or minimize the completion time for the truck and drone (min-time TSP-D). This problem has gained a lot of attention in the last few years since it is matched with the recent trends in a new delivery method among logistics companies. To solve the TSP-D, we propose a hybrid genetic search with dynamic population management and adaptive diversity control based on a split algorithm, problem-tailored crossover and local search operators, a new restore method to advance the convergence and an adaptive penalization mechanism to dynamically balance the search between feasible/infeasible solutions. The computational results show that the proposed algorithm outperforms existing methods in terms of solution quality and improves best known solutions found in the literature. Moreover, various analyses on the impacts of crossover choice and heuristic components have been conducted to analysis further their sensitivity to the performance of our method.Comment: Technical Report. 34 pages, 5 figure

Vietnamese children’s play and parents’ prejudice, stereotypes and discrimination on the basis of gender and social classes: A quantitative study

Premio extraordinario de Trabajo Fin de Máster curso 2020/2021. Máster en Erasmus Mundus en Juego, Educación, Juguetes y Lenguas / Play, Education, Toys and Languages (PETaL)This study aims to explore parents’ prejudice, stereotypes and discrimination towards their children’s play on the basis of social classes and gender, applying a Likert scale ‘Parents’ prejudice, stereotypes, and discrimination towards their children’s play, based on gender and social classes’ (PPSD) with 760 Vietnamese parents inhabiting in the country. The Likert scale was built, applying the Delphi method and analysed with Cronbach alpha test and Factor Analysis in order to validate the measurement tool. After that, Descriptive Analysis, Kruskal-Wallis test and Man Whitney U test were utilised to analyse the impact of key factors such as gender, education, income, living areas on parents’ prejudice, stereotypes and discrimination towards their children’s play. Results show that parents somewhat disagreed with the statements expressing dislike to accents and dialects of children from other social groups. However, they did not show consistency in their dislike towards behaviours and ways of speaking of children from other social classes, in which while some parents agreed, others did not. Although parents were not quite sure if they could accept the values and thoughts of children from other social groups, they quite avoided negative stereotypes as well as discrimination against them. Regarding gender, the study found out that although parents were inconsistent in their affection of children’s cross-sex play and the fact that their children like playing with toys associated with the opposite gender, they were consistent in their thinking of solidifying their children’s gender attributes through gender-specific toys. Especially, they reached agreement in their action of orientating children’s gender through children’s play and toys which need to be gender-appropriate. In addition, the study also reported that gender, education, living areas and income affect parents’ prejudice, stereotypes and discrimination towards their children’s play, based on social class and gender

Symbolic Powers of Monomial Ideals

We investigate symbolic and regular powers of monomial ideals. For a square-free monomial ideal $I$ in $k[x_0, \ldots, x_n]$ we show $I^{t(m+e-1)-e+r)}$ is a subset of $M^{(t-1)(e-1)+r-1}(I^{(m)})^t$ for all positive integers $m$, $t$ and $r$, where $e$ is the big-height of $I$ and $M = (x_0, \ldots, x_n)$. This captures two conjectures ($r=1$ and $r=e$): one of Harbourne-Huneke and one of Bocci-Cooper-Harbourne. We also introduce the symbolic polyhedron of a monomial ideal and use this to explore symbolic powers of non-square-free monomial ideals.Comment: 15 pages. Fixed typ