Joey Huchette

Parallel algebraic modeling for stochastic optimization

We present scalable algebraic modeling software, StochJuMP, for stochastic optimization as applied to power grid economic dispatch. It enables the user to express the problem in a high-level algebraic format with minimal boiler-plate. StochJuMP allows efficient parallel model instantiation across nodes and efficient data localization. Computational results are presented showing that the model construction is efficient, requiring roughly one percent of solve time. StochJuMP is configured with the parallel interior-point solver PIPS-IPM but is sufficiently generic to allow straight forward adaptation to other solvers.

Strong mixed-integer formulations for the floor layout problem

Abstract The floor layout problem (FLP) tasks a designer with positioning a collection of rectangular boxes on a fixed floor in such a way that minimizes total communication costs between the components. While several mixed-integer programming (MIP) formulations for this problem have been developed, it remains extremely challenging from a computational perspective. This work takes a systematic approach to constructing MIP formulations and valid inequalities for the FLP that unifies and recovers all known formulations for it. In addition, the approach yields new formulations that can provide a significant computational advantage and can solve previously unsolved instances. While the construction approach focuses on the FLP, it also exemplifies generic formulation techniques that should prove useful for broader classes of problems.

Beating the SDP bound for the floor layout problem: a simple combinatorial idea

ABSTRACT For many mixed-integer programming (MIP) problems, high-quality dual bounds can be obtained either through advanced formulation techniques coupled with a state-of-the-art MIP solver, or through semi-definite programming (SDP) relaxation hierarchies. In this paper, we introduce an alternative bounding approach that exploits the ‘combinatorial implosion’ effect by solving portions of the original problem and aggregating this information to obtain a global dual bound. We apply this technique to the one-dimensional and two-dimensional floor layout problems and compare it with the bounds generated by both state-of-the-art MIP solvers and by SDP relaxations. Specifically, we prove that the bounds obtained through the proposed technique are at least as good as those obtained through SDP relaxations, and present computational results that these bounds can be significantly stronger and easier to compute than these alternative strategies, particularly for very difficult problem instances.

On efficient Hessian computation using the edge pushing algorithm in Julia

Evaluating the Hessian matrix of second-order derivatives at a sequence of points can be costly when applying second-order methods for nonlinear optimization. In this work, we discuss our experiences implementing the recently proposed Edge Pushing (EP) method in Julia as an experimental replacement for the current colouring-based methods used by JuMP, an open-source algebraic modelling language. We propose an alternative data structure for sparse Hessians to avoid the use of hash tables and analyse the space and time complexity of EP method. In our benchmarks, we find that EP is very competitive in terms of both preprocessing time and Hessian evaluation time. We identify cases where EP closes the performance gap between JuMPs previous implementation and the implementation in AMPL, a commercial software package with similar functionality.