arXiv subjects

Leandro C. Coelho

Publications and source records attributed to Leandro C. Coelho.

4 recordsLinked to original sources

arXiv2026

A scenario-cluster-based and enhanced progressive hedging algorithm for the two-stage stochastic quadratic knapsack problem

This paper introduces the two-stage stochastic quadratic knapsack problem (TSSQKP) with uncertainty in profits and weights. To overcome the computational difficulties arising from the combined stochastic, binary, and quadratic structure, we propose a solution framework that integrates an adaptation of the progressive hedging algorithm with clustering-based scenario reduction. The enhanced progressive hedging algorithm (EPHA) incorporates a rounding procedure and a dynamic penalty update strategy driven by the detection of oscillation and stagnation patterns. In parallel, we propose a clustering framework based on opportunity-cost distances between scenarios, from which we derive the medoid lower bound (MLB), the cluster lower bound (CLB) and the cluster upper bound (CUB). To further improve computational efficiency, EPHA is also used to solve the cluster subproblems heuristically; in this case, the resulting upper bound is referred to as the estimated cluster upper bound (ECUB), and the corresponding gaps are interpreted as estimated optimality gaps. Computational experiments on 800 generated TSSQKP instances show that the proposed framework yields smaller gaps than CPLEX under comparable computational conditions. In the EPHA-based clustering framework, the average estimated gaps associated with the CLB, EPHA and MLB 1.65%, 1.88% and 2.41% respectively, compared with an average optimality gap of 35.86% for CPLEX. MLB is fastest to compute, with an average execution time of 420.88s, while EPHA provides a favourable compromise between solution quality and computational effort, reducing the average computational time associated with the cluster bounds by approximately 52.7%, while increasing the average estimated gap by only 0.23 percentage points.

math.OC↗

arXiv2026

An Exact Combinatorial Branch-and-Bound Algorithm for the Job Sequencing and Tool Switching Problem

The Job Sequencing and Tool Switching Problem (SSP) is a well-known combinatorial optimization problem arising in the context of flexible manufacturing. Since the seminal work of Tang and Denardo (1988), the SSP has received significant attention in the literature, leading to the development of numerous exact and heuristic approaches. Despite these efforts, several benchmark instances proposed decades ago and containing only 20 jobs have remained unsolved to proven optimality. In this work, we propose an exact algorithm for the SSP, namely the Combinatorial Branch-and-Bound (C-B\&B) algorithm, which combines two distinct branch-and-bound algorithms, each introducing novel features compared with the existing literature. The former relies on a new branching scheme designed to reduce the size of the implicit enumeration tree, together with a collection of new bounding functions. The latter builds on the branching scheme introduced by Laporte et al. (2004) and strengthens it with a new bounding function and two dominance rules. Within C-B\&B, these exact algorithms are complemented by a preprocessing phase that incorporates a new branch-and-bound-based heuristic capable of rapidly generating a high-quality initial incumbent solution. Extensive computational experiments show that C-B\&B represents a strong breakthrough over previously published approaches, proving optimality for more instances with significantly less computational effort and closing several benchmark instances that have remained open for decades.

math.OC↗

arXiv2026

Superadditivity-based valid inequalities and asymptotic bounds for the vehicle routing problem with stochastic demands

Over the past thirty years, the vehicle routing problem with stochastic demands (VRPSD) has emerged as a canonical application of the integer L-shaped method. Recently, the disaggregated integer L-shaped (DL-shaped) method, which decomposes the recourse function by customer rather than treating it as an aggregate cost, has been proposed for the VRPSD under the classical detour-to-depot policy. However, its generalizability to other recourse policies has not been investigated. In this work, we identify the property that characterizes the validity of the DL-shaped reformulation: the superadditivity of the recourse function under path concatenation. We show that superadditivity holds under the optimal restocking policy, and rectify an incorrect argument from the original paper on the DL-shaped method, rigorously establishing its validity under the detour-to-depot policy. We then introduce a new family of valid inequalities, the edge-set cuts, which generalize the original DL-shaped cuts and are analytically shown to provide structural advantages over existing inequalities. Building on these results, we develop a DL-shaped algorithm for the VRPSD with optimal restocking. Our algorithm outperforms existing methods in the high customer-to-vehicle ratio regime and solves 14 open single-route instances. We further derive asymptotic bounds on the optimal value of the VRPSD in a Euclidean setting with i.i.d. customers. This analysis reveals an asymptotic equivalence between the VRPSD and the split-delivery vehicle routing problem. It also yields tight bounds on the cost of requiring the total expected demand on each route not to exceed the vehicle capacity, resolving an open question in our asymptotic setting.

math.OC↗

arXiv2019

Benchmark Instances and Branch-and-Cut Algorithm for the Hashiwokakero Puzzle

Hashiwokakero, or simply Hashi, is a Japanese single-player puzzle played on a rectangular grid with no standard size. Some cells of the grid contain a circle, called island, with a number inside it ranging from one to eight. The remaining positions of the grid are empty. The player must connect all of the islands by drawing a series of horizontal or vertical bridges between them, respecting a series of rules: the number of bridges incident to an island equals the number indicated in the circle, at most two bridges are incident to any side of an island, bridges cannot cross each other or pass through islands, and each island must eventually be reachable from any other island. In this paper, we present some complexity results and relationships between Hashi and well-known graph theory problems. We give a formulation of the problem by means of an integer linear mathematical programming model, and apply a branch-and-cut algorithm to solve the model in which connectivity constraints are dynamically generated. We also develop a puzzle generator. Our experiments on 1440 Hashi puzzles show that the algorithm can consistently solve hard puzzles with up to 400 islands.

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