A p-step formulation for the capacitated vehicle routing problem

We introduce a _p_-step formulation for the capacitated vehicle routing problem (CVRP). The parameter _p_ indicates the length of partial paths corresponding to the used variables. This provides a family of formulations including both the traditional arc-based and path-based formulations. Hence, it is a generalization which unifies arc-based and path-based formulations, while also providing new formulations. We show that the LP bound of the _p_-step formulation is increasing in _p_, although not monotonically. Furthermore, we prove that computing the set partitioning bound is NP-hard. This is a meaningful result in itself, but combined with the _p_-step formulation this also allows us to show that there does not exist a strongest compact formulation for the CVRP, if _P ≠ NP_. While ending the search for a strongest compact formulation, we propose th

Using the primal-dual interior point algorithm within the branch-price-and-cut method

AbstractBranch-price-and-cut has proven to be a powerful method for solving integer programming problems. It combines decomposition techniques with the generation of both columns and valid inequalities and relies on strong bounds to guide the search in the branch-and-bound tree. In this paper, we present how to improve the performance of a branch-price-and-cut method by using the primal-dual interior point algorithm. We discuss in detail how to deal with the challenges of using the interior point algorithm with the core components of the branch-price-and-cut method. The effort to overcome the difficulties pays off in a number of advantageous features offered by the new approach. We present the computational results of solving well-known instances of the vehicle routing problem with time windows, a challenging integer programming problem. The results indicate that the proposed approach delivers the best overall performance when compared with a similar branch-price-and-cut method which is based on the simplex algorithm

Climate determines transmission hotspots of Polycystic Echinococcosis, a life-threatening zoonotic disease, across Pan-Amazonia

Polycystic Echinococcosis (PE), a neglected life-threatening zoonotic disease caused by the cestode is endemic in the Amazon. Despite being treatable, PE reaches a case fatality rate of around 29% due to late or missed diagnosis. PE is sustained in Pan-Amazonia by a complex sylvatic cycle. The hunting of its infected intermediate hosts (especially the lowland paca ) enables the disease to further transmit to humans, when their viscera are improperly handled. In this study, we compiled a unique dataset of host occurrences (~86000 records) and disease infections (~400 cases) covering the entire Pan-Amazonia and employed different modeling and statistical tools to unveil the spatial distribution of PE's key animal hosts. Subsequently, we derived a set of ecological, environmental, climatic, and hunting covariates that potentially act as transmission risk factors and used them as predictors of two independent Maximum Entropy models, one for animal infections and one for human infections. Our findings indicate that temperature stability promotes the sylvatic circulation of the disease. Additionally, we show how El Niño-Southern Oscillation (ENSO) extreme events disrupt hunting patterns throughout Pan-Amazonia, ultimately affecting the probability of spillover. In a scenario where climate extremes are projected to intensify, climate change at regional level appears to be indirectly driving the spillover of . These results hold substantial implications for a wide range of zoonoses acquired at the wildlife-human interface for which transmission is related to the manipulation and consumption of wild meat, underscoring the pressing need for enhanced awareness and intervention strategies

Large-scale optimization with the primal-dual column generation method

The primal-dual column generation method (PDCGM) is a general-purpose column generation technique that relies on the primal-dual interior point method to solve the restricted master problems. The use of this interior point method variant allows to obtain suboptimal and well-centered dual solutions which naturally stabilizes the column generation. As recently presented in the literature, reductions in the number of calls to the oracle and in the CPU times are typically observed when compared to the standard column generation, which relies on extreme optimal dual solutions. However, these results are based on relatively small problems obtained from linear relaxations of combinatorial applications. In this paper, we investigate the behaviour of the PDCGM in a broader context, namely when solving large-scale convex optimization problems. We have selected applications that arise in important real-life contexts such as data analysis (multiple kernel learning problem), decision-making under uncertainty (two-stage stochastic programming problems) and telecommunication and transportation networks (multicommodity network flow problem). In the numerical experiments, we use publicly available benchmark instances to compare the performance of the PDCGM against recent results for different methods presented in the literature, which were the best available results to date. The analysis of these results suggests that the PDCGM offers an attractive alternative over specialized methods since it remains competitive in terms of number of iterations and CPU times even for large-scale optimization problems.Comment: 28 pages, 1 figure, minor revision, scaled CPU time