ABSTRACT Irregular strip packing problems are present in a wide variety of industrial sectors, such as the garment, footwear, furniture and metal industry. The goal is to find a layout in which an object will be cut into small pieces with minimum raw-material waste. Once a layout is obtained, it is necessary to determine the path that the cutting tool has to follow to cut the pieces from the layout. In the latter, the goal is to minimize the cutting distance (or time). Although industries frequently use this solution sequence, the trade-off between the packing and the cutting path problems can significantly impact the production cost and productivity. A layout with minimum raw-material waste, obtained through the packing problem resolution, can imply a longer cutting path compared to another layout with more material waste but a shorter cutting path, obtained through an integrated strategy. Layouts with shorter cutting path are worthy of consideration because they may improve the cutting process productivity. In this paper, both problems are solved together using a biobjective matheuristic based on the Biased Random-Key Genetic Algorithm. Our approach uses this algorithm to select a subset of the no-fit polygons edges to feed the mathematical model, which will compute the layout waste and cutting path length. Solving both strip packing and cutting path problems simultaneously allows the decision-maker to analyze the compromise between the material waste and the cutting path distance. As expected, the computational results showed the trade-off’s relevance between these problems and presented a set of solutions for each instance solved.

ABSTRACT Vehicle Routing Problems (VRP) have been widely researched throughout history as a way of optimising routes by minimising distances and planning deliveries efficiently, but the issue of risk in VRP has received less attention over time. This is essential to increasing transport safety to avoid interruptions in supply chains and improve delivery reliability. Therefore, this study aims to support decision makers to plan routes for road freight transportation considering not only the logistics cost, but also travel safety due to road hazards. An analytical approach based on statistics was developed in which data of vehicle accidents and road features were used to estimate the risk cost by using the Monte Carlo simulation. A bi-objective approach based on PROMETHEE II and ε-constrained methods was used in the Capacitated Vehicle Routing Problem (CVRP) to analyse the conflict between the logistic cost and accident risk. Key contributions of this study are an analytical approach based on statistics, Monte Carlo simulation and multicriteria methods in a CVRP model to explore the trade-off between logistic costs and accident risk expressed by a risk cost. The outcomes of this study show to be useful in practice to analyse transportation decisions in the VRP model involving route planning considering accident risk.

ABSTRACT The problem of finding the shortest path between a source and a destination node, commonly represented by graphs, has several computational algorithms as an attempt to find what is called the minimum path. Depending on the number of nodes in-between the source and destination, the process of finding the shortest path can demand a high computational cost (with polynomial complexity). A solution to reduce the computational cost is the use of the concept of parallelism, which divides the algorithm tasks between the processing cores. This article presents a comparative analysis of the main algorithms of the shortest path class: Dijkstra, Bellman-Ford, Floyd-Warshall and Johnson. The performance of each algorithm was evaluated considering different parallelization approaches and they were applied on general and open-pit mining databases present in the literature. The experimental results showed an improvement in performance of about 55% on the execution time depending on the chosen parallelization point.

ABSTRACT This paper studies the bandwidth reduction problem for large-scale sparse matrices in serial computations. A heuristic for bandwidth reduction reorders the rows and columns of a given sparse matrix, placing entries with a non-null value as close to the main diagonal as possible. Recently, a paper proposed the FNCHC+ heuristic. The heuristic method is a variant of the Fast Node Centroid Hill-Climbing algorithm. The FNCHC+ heuristic presented better results than the other existing heuristics in the literature when applied to reduce the bandwidth of large-scale graphs (of the underline matrices) with sizes up to 18.6 million vertices and up to 57.2 million edges. The present paper provides new experiments with even larger graphs. Specifically, the present study performs experiments with test problems containing up to 24 million vertices and 130 million edges. The results confirm that the FNCHC+ algorithm is the state-of-the-art metaheuristic algorithm for reducing the bandwidth of large-scale matrices.

ABSTRACT The Least Cost Influence Problem is a combinatorial optimization problem that appears in the context of social networks. The objective is to give incentives to individuals of a network, such that some information spreads to a desired fraction of the network at minimum cost. We introduce a problem-dependent algorithm in a branch-and-bound scheme to compute a dual bound for this problem. The idea is to exploit the connectivity properties of sub-graphs of the input graph associated with each node of the branch-and-bound tree and use it to increase each sub-problem’s lower bound. Our algorithm works well and finds a lower bound tighter than the LP-relaxation in linear time in the size of the graph. Computational experiments with synthetic graphs and real-world social networks show improvements in using our proposed bounds. The improvements are gains in running time or gap reduction for exact solutions to the problem.