MPC

MPC 2018, ISSUE 2



Mathematical Programming Computation, Volume 10, Issue 2, June 2018

Detecting almost symmetries of graphs

Ben Knueven, Jim Ostrowski, Sebastian Pokutta

We present a branch-and-bound framework to solve the following problem: Given a graph G and an integer k, find a subgraph of G formed by removing no more than k edges that minimizes the number of vertex orbits. We call the symmetries on such a subgraph “almost symmetries” of G. We implement our branch-and-bound framework in PEBBL to allow for parallel enumeration and demonstrate good scaling up to 16 cores. We show that the presented branching strategy is much better than a random branching strategy on the tested graphs. Finally, we consider the presented strategy as a heuristic for quickly finding almost symmetries of a graph G. The software that was reviewed as part of this submission has been issued the Digital Object Identifier DOI:10.5281/zenodo.840558.

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Mathematical Programming Computation, Volume 10, Issue 2, June 2018

pyomo.dae: a modeling and automatic discretization framework for optimization with differential and algebraic equations

Bethany Nicholson, John D. Siirola, Jean-Paul Watson, Victor M. Zavala, Lorenz T. Biegler

We describe pyomo.dae, an open source Python-based modeling framework that enables high-level abstract specification of optimization problems with differential and algebraic equations. The pyomo.dae framework is integrated with the Pyomo open source algebraic modeling language, and is available at http://www. pyomo.org. One key feature of pyomo.dae is that it does not restrict users to stan- dard, predefined forms of differential equations, providing a high degree of modeling flexibility and the ability to express constraints that cannot be easily specified in other modeling frameworks. Other key features of pyomo.dae are the ability to specify optimization problems with high-order differential equations and partial differential equations, defined on restricted domain types, and the ability to automatically trans- form high-level abstract models into finite-dimensional algebraic problems that can be solved with off-the-shelf solvers. Moreover, pyomo.dae users can leverage existing capabilities of Pyomo to embed differential equation models within stochastic and integer programming models and mathematical programs with equilibrium constraint formulations. Collectively, these features enable the exploration of new modeling con- cepts, discretization schemes, and the benchmarking of state-of-the-art optimization solvers.

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Mathematical Programming Computation, Volume 10, Issue 2, June 2018

Algorithmic innovations and software for the dual decomposition method applied to stochastic mixed-integer programs

Kibaek Kim, Victor M. Zavala

We present algorithmic innovations for the dual decomposition method to address two-stage stochastic programs with mixed-integer recourse and provide an open-source software implementation that we call DSP. Our innovations include the incorporation of Benders-like cuts in a dual decomposition framework to tighten Lagrangian subproblems and aid the exclusion of infeasible first-stage solutions for problems without (relative) complete recourse. We also use an interior-point cutting- plane method with new termination criteria for solving the Lagrangian master problem. We prove that the algorithm converges to an optimal solution of the Lagrangian dual problem in a finite number of iterations, and we also prove that convergence can be achieved even if the master problem is solved suboptimally. DSP can solve instances specified in C code, SMPS files, and Julia script. DSP also implements a standard Benders decomposition method and a dual decomposition method based on subgradi- ent dual updates that we use to perform benchmarks. We present extensive numerical results using SIPLIB instances and a large unit commitment problem to demonstrate that the proposed innovations provide significant improvements in the number of iter- ations and solution times. The software reviewed as part of this submission has been given the Digital Object Identifier (DOI) https://doi.org/10.5281/zenodo.998971.

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Mathematical Programming Computation, Volume 10, Issue 2, June 2018

mplrs: A scalable parallel vertex/facet enumeration code

David Avis, Charles Jordan

We describe a new parallel implementation, mplrs, of the vertex enumer- ation code lrs that uses the MPI parallel environment and can be run on a network of computers. The implementation makes use of a C wrapper that essentially uses the existing lrs code with only minor modifications. mplrs was derived from the earlier parallel implementation plrs, written by G. Roumanis in C++ which runs on a shared memory machine. By improving load balancing we are able to greatly improve performance for medium to large scale parallelization of lrs. We report computational results comparing parallel and sequential codes for vertex/facet enu- meration problems for convex polyhedra. The problems chosen span the range from simple to highly degenerate polytopes. For most problems tested, the results clearly show the advantage of using the parallel implementation mplrs of the reverse search based code lrs, even when as few as 8 cores are available. For some problems almost linear speedup was observed up to 1200 cores, the largest number of cores tested. The software that was reviewed as part of this submission is included in lrslib-062.tar.gz which has MD5 hash be5da7b3b90cc2be628dcade90c5d 1b9.

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