arXiv subjects

Ricardo Fukasawa

Publications and source records attributed to Ricardo Fukasawa.

9 recordsLinked to original sources

arXiv2026

On vehicle routing problems with stochastic demands -- Scenario-optimal recourse policies

Two-Stage Vehicle Routing Problems with Stochastic Demands (VRPSDs) form a class of stochastic combinatorial optimization problems where routes are planned in advance, demands are revealed upon vehicle arrival, and recourse actions are triggered whenever capacity is exceeded. Following recent works, we consider VRPSDs where demands are given by an empirical probability distribution of scenarios. Existing approaches rely on integer L-shaped (ILS) cuts, whose coefficients are tailored for specific recourse policies. In contrast, we propose a framework that casts recourse policies as solutions of a higher-dimensional mixed-integer program, and we characterize its convex hull in the original lower-dimensional space via a new class of inequalities called scenario recourse inequalities (SRIs). We show that SRIs are valid for any recourse policy satisfying mild assumptions and are sufficient for formulating the VRPSD under a scenario-optimal recourse policy, where the recourse actions are chosen optimally for each scenario. Under this latter policy, we also demonstrate that SRIs dominate several known classes of ILS cuts. We conduct computational experiments on the VRPSD with scenarios under both the classical and the scenario-optimal recourse policies. By using the SRIs, our algorithm solves 329 more instances to optimality than the previous state-of-the-art ILS algorithm.

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arXiv2026

On vehicle routing problems with stochastic demands -- Generic disaggregated integer L-shaped formulations

We study the vehicle routing problem with stochastic demands (VRPSD), an important variant of the classical capacitated vehicle routing problem in which customer demands are modeled as random variables. We develop the first algorithm for the VRPSD in the case where the demands are given by an empirical probability distribution of scenarios -- a data-driven variant that tackles a significant challenge identified in the literature: dealing with correlations. Indeed, most previous exact algorithms for this problem relied on independence of the random variables. To address the VRPSD with scenarios, we introduce a unifying framework that generalizes existing integer L-shaped (ILS) formulations developed for other variants of the problem. This framework and subsequent analysis allow us to generalize previous ILS cuts and pinpoint which assumptions are needed to apply those generalizations. In particular, our results enable, for the first time, the combination of two previous types of inequalities: partial route and set cuts, which leads to significant computational improvements.

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arXiv2025

The Branch-and-Bound Tree Closure

This paper investigates the a-posteriori analysis of Branch-and-Bound~(BB) trees to extract structural information about the feasible region of mixed-binary linear programs. We introduce three novel outer approximations of the feasible region, systematically constructed from a BB tree. These are: a tight formulation based on disjunctive programming, a branching-based formulation derived from the tree's branching logic, and a mixing-set formulation derived from the on-off properties inside the tree. We establish an inclusion hierarchy, which ranks the approximations by their theoretical strength \wrt to the original feasible region. The analysis is extended to the generation of valid inequalities, revealing a separation-time hierarchy that mirrors the inclusion hierarchy in reverse. This highlights a trade-off between the tightness of an approximation and the computational cost of generating cuts from it. Motivated by the computational expense of the stronger approximations, we introduce a new family of valid inequalities called star tree inequalities. Although their closure forms the weakest of the proposed approximations, their practical appeal lies in an efficient, polynomial-time combinatorial separation algorithm. A computational study on multi-dimensional knapsack and set-covering problems empirically validates the theoretical findings. Moreover, these experiments confirm that computationally useful valid inequalities can be generated from BB trees obtained by solving optimization problems considered in practice.

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arXiv2025

Approximating value functions via corner Benders' cuts

We introduce a novel technique to generate Benders' cuts from a conic relaxation ("corner") derived from a basis of a higher-dimensional polyhedron that we aim to outer approximate in a lower-dimensional space. To generate facet-defining inequalities for the epigraph associated to this corner, we develop a computationally-efficient algorithm based on a compact reverse polar formulation and a row generation scheme that handles the redundant inequalities. Via a known connection between arc-flow and path-flow formulations, we show that our method can recover the linear programming bound of a Dantzig-Wolfe formulation using multiple cuts in the projected space. In computational experiments, our generic technique enhances the performance of a problem-specific state-of-the-art algorithm for the vehicle routing problem with stochastic demands, a well-studied variant of the classic capacitated vehicle routing problem that accounts for customer demand uncertainty.

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arXiv2024

Trained Random Forests Completely Reveal your Dataset

We introduce an optimization-based reconstruction attack capable of completely or near-completely reconstructing a dataset utilized for training a random forest. Notably, our approach relies solely on information readily available in commonly used libraries such as scikit-learn. To achieve this, we formulate the reconstruction problem as a combinatorial problem under a maximum likelihood objective. We demonstrate that this problem is NP-hard, though solvable at scale using constraint programming -- an approach rooted in constraint propagation and solution-domain reduction. Through an extensive computational investigation, we demonstrate that random forests trained without bootstrap aggregation but with feature randomization are susceptible to a complete reconstruction. This holds true even with a small number of trees. Even with bootstrap aggregation, the majority of the data can also be reconstructed. These findings underscore a critical vulnerability inherent in widely adopted ensemble methods, warranting attention and mitigation. Although the potential for such reconstruction attacks has been discussed in privacy research, our study provides clear empirical evidence of their practicability.

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arXiv2024

Interdiction of minimum spanning trees and other matroid bases

In the minimum spanning tree (MST) interdiction problem, we are given a graph $G=(V,E)$ with edge weights, and want to find some $X\subseteq E$ satisfying a knapsack constraint such that the MST weight in $(V,E\setminus X)$ is maximized. Since MSTs of $G$ are the minimum weight bases in the graphic matroid of $G$, this problem is a special case of matroid interdiction on a matroid $M=(E,\mathcal{I})$, in which the objective is instead to maximize the minimum weight of a basis of $M$ which is disjoint from $X$. By reduction from 0-1 knapsack, matroid interdiction is NP-complete, even for uniform matroids. We develop a new exact algorithm to solve the matroid interdiction problem. One of the key components of our algorithm is a dynamic programming upper bound which only requires that a simpler discrete derivative problem can be calculated/approximated for the given matroid. Our exact algorithm then uses this bound within a custom branch-and-bound algorithm. For different matroids, we show how this discrete derivative can be calculated/approximated. In particular, for partition matroids, this yields a pseudopolynomial time algorithm. For graphic matroids, an approximation can be obtained by solving a sequence of minimum cut problems, which we apply to the MST interdiction problem. The running time of our algorithm is asymptotically faster than the best known MST interdiction algorithm, up to polylog factors. Furthermore, our algorithm achieves state-of-the-art computational performance: we solved all available instances from the literature, and in many cases reduced the best running time from hours to seconds.

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arXiv2021

Optimized Cranial Bandeau Remodeling

Craniosynostosis, a condition affecting 1 in 2000 infants, is caused by premature fusing of cranial vault sutures, and manifests itself in abnormal skull growth patterns. Left untreated, the condition may lead to severe developmental impairment. Standard practice is to apply corrective cranial bandeau remodeling surgery in the first year of the infant's life. The most frequent type of surgery involves the removal of the so-called fronto-orbital bar from the patient's forehead and the cutting of well-placed incisions to reshape the skull in order to obtain the desired result. In this paper, we propose a precise optimization model for the above cranial bandeau remodeling problem and its variants. We have developed efficient algorithms that solve best incision placement, and show hardness for more general cases in the class. To the best of our knowledge this paper is the first to introduce optimization models for craniofacial surgery applications.

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arXiv2017

A joint routing and speed optimization problem

Fuel cost contributes to a significant portion of operating cost in cargo transportation. Though classic routing models usually treat fuel cost as input data, fuel consumption heavily depends on the travel speed, which has led to the study of optimizing speeds over a given fixed route. In this paper, we propose a joint routing and speed optimization problem to minimize the total cost, which includes the fuel consumption cost. The only assumption made on the dependence between the fuel cost and travel speed is that it is a strictly convex differentiable function. This problem is very challenging, with medium-sized instances already difficult for a general mixed-integer convex optimization solver. We propose a novel set partitioning formulation and a branch-cut-and-price algorithm to solve this problem. Our algorithm clearly outperforms the off-the-shelf optimization solver, and is able to solve some benchmark instances to optimality for the first time.

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arXiv2012

On the mixing set with a knapsack constraint

The mixing set with a knapsack constraint arises as a substructure in mixed-integer programming reformulations of chance-constrained programs with stochastic right-hand-sides over a finite discrete distribution. Recently, Luedtke et al. (2010) and Küçükyavuz (2012) studied valid inequalities for such sets. However, most of their results were focused on the equal probabilities case (equivalently when the knapsack reduces to a cardinality constraint), with only minor results in the general case. In this paper, we focus on the general probabilities case (general knapsack constraint). We characterize the valid inequalities that do not come from the knapsack polytope and use this characterization to generalize the inequalities previously derived for the equal probabilities case. We also show that one can separate over a large class of inequalities in polynomial time.

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