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Margarita Castro

Publications and source records attributed to Margarita Castro.

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DD-suite: A cross-platform package to build Decision Diagrams for optimization purposes

Decision diagrams (DDs) have become a powerful tool for discrete optimization, supporting a wide range of algorithms that span cut-generation procedures, decomposition methods, and specialized branch-and-bound searches. Despite this growth, their adoption remains limited, partly because most existing DD code is tailored to a specific algorithm or application and is therefore hard to reuse. We introduce DD-suite, a cross-platform, open-source software package for building and manipulating DDs for discrete optimization. DD-suite is available in both Python and C++ through a shared modeling interface, and lets users construct exact, restricted, and relaxed DDs for any discrete optimization problem expressed in recursive form. The package implements the DD reduction procedure, shortest-path routines for obtaining primal and dual bounds, a visualization tool, and an extensive automated test suite. Furthermore, it includes extensive documentation, a support webpage, and ready-to-use examples for four combinatorial problems. Rather than a closed solver, DD-suite is designed as an extensible building block: users can add new construction mechanisms or run custom algorithms on top of the resulting diagram, as we illustrate with a DD-based cutting plane procedure embedded in a state-of-the-art mixed-integer programming solver. Our numerical experiments show that the C++ implementation is 5-6 times faster than the Python one while producing identical diagrams, and remains within a small constant factor of ddo, a specialized Rust framework, confirming that DD-suite combines an accessible, extensible codebase with competitive performance.

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Beyond Hand-Derived Inequalities: Decision Diagrams for Cut Generation in Binary Polynomial Optimization

We study cutting-plane generation for binary polynomial optimization (BPO), whose feasible region is the multilinear set of a hypergraph. Strong inequalities for this set---such as two-links, flowers, and odd $\beta$-cycles---are classically hand-derived for fixed support patterns. Instead, we propose a decision-diagram (DD) approach: for any chosen support, it separates a facet-defining cut in the local multilinear polytope and lifts it back to the original problem. We utilize a novel compact DD encoding based on a recursive formulation that represents only the vertex variables and implicitly encodes the hyperedge variables inside the state representation. From this DD encoding, we also obtain: (i) an extended formulation of the multilinear polytope, (ii) a width characterization via valid antichains that uncovers a new polynomially solvable class of hypergraphs, and (iii) a certificate for the facetness of the generated cuts. We explore three different support strategies for cut generation that reuse, expand, or partition local structures into section hypergraphs. Our empirical results show that our DD-based methodologies achieve a larger gap closure at the root node with fewer cuts than existing procedures and, in turn, markedly accelerate branch-and-bound procedures.

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A Decision Diagram Approach for the Parallel Machine Scheduling Problem with Chance Constraints

The Chance-Constrained Parallel Machine Scheduling Problem (CC-PMSP) assigns jobs with uncertain processing times to machines, ensuring that each machine's availability constraints are met with a certain probability. We present a decomposition approach where the master problem assigns jobs to machines, and the subproblems schedule the jobs on each machine while verifying the solution's feasibility under the chance constraint. We propose two different Decision Diagram (DD) formulations to solve the subproblems and generate cuts. The first formulation employs DDs with a linear cost function, while the second uses a non-linear cost function to reduce the diagram's size. We show how to generate no-good and irreducible infeasible subsystem (IIS) cuts based on our DDs. Additionally, we extend the cuts proposed by Lozano & Smith (2018) to solve two-stage stochastic programming models. Our DD-based methodology outperforms traditional integer programming (IP) models designed to solve the CC-PMSP in several instances. Specifically, our best DD-based approach solves 55 more instances than the best IP alternative (from a total of 405) and typically achieves smaller gaps (50% vs. 120% gap on average).

math.OC