The Second Annual JuMP-dev Workshop

June 27-29, 2018, at the Institut de Mathématiques de Bordeaux, University of Bordeaux.

The workshop was sponsored by the MIT Sloan school of management, IDEX Bordeaux, and Changhyun Kwon.

Group Photo

Purpose

This workshop is a follow-up to the first annual JuMP-dev workshop held in June 2017 at MIT. The purpose of the workshop is to bring together students, researchers, and practitioners with interests in the software aspects of JuMP and related packages. Interest areas of the workshop include:

The JuMP-dev workshop is a great opportunity to meet other people working on and around JuMP, as well as to provide feedback to the core JuMP team concerning its future direction. The workshop is scheduled to lead into ISMP.

Location

The workshop will be held at the Institut de Mathématiques de Bordeaux, University of Bordeaux. There are options to stay in Talence (walking distance to JuMP-dev), or the Bordeaux city centre (short tram ride).

The main entrance to the Institut is located here. The workshop will be held in the room “salle de conf”. It is the first room on the left as you enter through the main entrance. The main entrance looks like this.

A variety of information about Bordeaux, as well as how to get there, and possible accommodation options, is available on the ISMP conference website.

Call for participants

The workshop is open for anybody to attend. In particular, we invite new contributors and those who have not met the core development team.

The call for talks has now closed.

Travel support

Thanks to the generous support of MIT Sloan School of Management, the JuMP-dev committee has funds available to provide travel support to a limited number of attendees. The deadline for travel support requests was May 15.

Schedule

The workshop schedule is outlined below. The scheduled start of the workshop is at 13:30 on Wednesday, 27th June. This is to allow participants to arrive in Bordeaux on Wednesday morning.

Wednesday 27 June

13:30 - 14:00 Introduction Juan Pablo Vielma (MIT)

14:00 - 14:25 Systematically building mixed-integer programming formulations using JuMP and Julia Joey Huchette (MIT) [Slides]

Abstract Mixed-integer programming (MIP) has proven itself a valuable tool for practically solving difficult discrete or nonconvex optimization problems. However, the performance of these methods will typically depend significantly on the quality of the MIP formulation, or the way you choose to represent your problem in the specific format dictated by the MIP solver. This talk will overview what makes a good formulation, how to systematically build good formulations, and how JuMP and other Julia packages (e.g. Polyhedra.jl) are fantastic tools for building intuition, and also for constructing high-performing formulations that may not be "human-readable."

14:25 - 14:50 Modeling decomposable Mixed Integer Programs Guillaume Marques (Université de Bordeaux) [Slides]

Abstract BlockDecomposition.jl is a package that allows to model decomposable mathematical programs using either a Dantzig-Wolfe or a Benders decomposition paradigm. The package assumes a problem description as a compact mixed integer program written with JuMP. The user further produces a decomposition function that defines blocks of the mathematical program by specifying the associated variable and/or constraint indices. Extra-features have been added such as the dynamic instantiation of constraints and variables. As an example of specific implementation that can be built on top of BlockDecomposition.jl, we introduce an interface to model problems with resource constrained shortest paths subproblems. This interface can be used in particular to model routing problems which are then solved using our modern Branch-Cut-and-Price algorithm.

14:50 - 15:15 Coffee Break

15:15 - 15:40 Artelys Knitro 11.0, a new conic solver and other novelties Jean-hubert Hours (Artelys) [Slides]

Abstract The latest 11.0 release of the nonlinear solver Artelys Knitro will be presented. This new version introduces a novel solver for nonlinear optimization problems with conic constraints. It is a first of its kind because it is a specialized interior-point algorithm for second-order cone programs (SOCPs) which also allows including general nonlinear non-convex constraints. Knitro 11.0 also introduces a new C API, enabling users to build complex optimization models piece by piece and to provide structural information about their problems, such as linear, quadratic or conic constraints structures. Finally, several other numerical improvements on convex programs as well as ill-conditioned problems have been introduced with this release and will be presented during the talk.

15:40 - 16:05 Power and exponential Cones with Mosek Ulf Worsøe (MOSEK)

Abstract In the current alpha release of MOSEK we have added support for several new cones, specifically the primal and dual power cones and the primal and dual exponential cones. This allows integrating semidefinite and quadratic optimization with convex exponential terms and power terms, and fits well into the JuMP framework. We will show how to model with these new cones and present a few models to illustrate their usefulness. MOSEK is a commercial solver. Free licenses for academic use are available.

16:05 - 16:30 ProxSDP.jl: A semidefinite programming solver written in Julia Joaquim Dias Garcia & Mario Souto (PUC-Rio) [Slides]

Abstract In contrast with most convex optimization classes, state-of-the-art semidefinite programming solvers are yet unable to efficiently solve large scale instances. This work aims to reduce this scalability gap by proposing a novel proximal algorithm for solving general semidefinite programming problems. This algorithm, based on the primal-dual hybrid gradient operator splitting method, allows the presence of linear inequalities without the need of adding extra slack variables and avoids solving a linear system at each iteration. More importantly, the algorithm simultaneously computes the dual variables associated with the linear constraints. The second contribution of this work is to achieve a substantial speedup by effectively adjusting the proposed algorithm in order to exploit the low-rank property of semidefinite programming problems. Additionally, an open source semidefinite programming solver written in Julia language, called ProxSDP.jl, is made available and implementation details are discussed.

16:30 Finish

Thursday 28 June

10:00 - 10:25 Stochastic Programming for Hydropower Operations: Modeling and Algorithms Martin Biel (KTH - The Royal Institute of Technology) [Slides]

Abstract The aim of this talk is to present three JuMP related Julia packages that I have developed during my research. The first package, StochasticPrograms.jl, is a JuMP extension for formulating two-stage stochastic recourse models. It is similar in idea to StructJuMP, but implemented with a different approach that allows for extended features. It provides classical constructs from the stochastic programming field, such as EVPI and VSS. Like StructJuMP, it also has parallel capabilities. However, the parallel features in StochasticPrograms.jl are implemented using the standard library for distributed computations in Julia, instead of using MPI. The second package, LShapedSolvers.jl, is a collection of structured optimization algorithms for stochastic programming problems, that interfaces to StochasticPrograms.jl. All algorithms are variants of the L-shaped method, each with a distributed version that runs in parallel. Finally, HydroModels.jl is a modeling framework for hydropower operations. It provides modeling templates for defining deterministic and stochastic (in terms of StochasticPrograms.jl) planning problems for hydropower operations. In addition, it provides some predefined models: ShortTerm, for production planning over a fixed horizon, and DayAhead, for optimal order strategies on a day-ahead electricity market. Common to both StochasticPrograms.jl and HydroModels.jl is the idea of deferred model creation through anonymous functions. The idea is that JuMP models are created when they are required. This gives a lot of flexibility such as effective model re-initialization and effective distribution of scenario problems on worker processes.

10:25 - 10:50 Optimal energy management and stochastic decomposition François Pacaud (CERMICS, ENPC) [Slides]

Abstract We consider a microgrid management problem where multiple units are interacting together via a network. Each unit is represented as a (small) controlled stochastic dynamic system, located at a node. Each unit state evolution is affected by uncertainties and by controls from the neighbor units. Further, static constraints couple all units at each time. We aim at developing resolution methods based on (stochastic) Dynamic Programming, and compare two solvers to compute Bellman value functions. i) The first solver --- global SDDP --- uses the well-known Stochastic Dual Dynamic Programming algorithm, on top of the StochDynamicProgramming package. ii) The second solver --- nodal SDDP --- uses a novel method based on stochastic decomposition, that splits the problem node by node to solve them afterward independently by SDDP. We will present our implementation of the nodal SDDP method, which deeply relies on the JuliaOpt ecosystem --- from Gurobi.jl to solve the inner subproblems up to Ipopt.jl to coordinate the decomposition scheme.

10:50 - 11:20 Coffee Break

11:20 - 11:45 A Julia JuMP-based module for polynomial optimization with complex variables applied to Optimal Power Flow Julie Sliwak (RTE) [Slides]

Abstract Integrating variable renewable generation technologies raises more and more issues in mathematical programming for power systems. In particular, there is a need for tools to model Polynomial Optimization Problems with Complex variables (POP-C) as resistive losses computation is only possible with Alternating Current (AC) modelling. To this purpose, RTE (the French transmission system operator) presents a JuMP-based module for POP-C applied to Optimal Power Flow (OPF). Computational results are presented on Preventive Security Constrained OPF (PSCOPF) datasets of the Grid Optimization Competition organized by ARPA-E. This work demonstrates the convenience of a module for POP-C to rapidly test several local or global methods.

11:45 - 12:10 Topology Optimization and JuMP Mohamed Tarek (UNSW Canberra) [Slides]

Abstract Topology optimization is a field that combines computational mechanics with optimization theory to come up with new shapes for mechanical designs that mechanical engineers are unable to come up with due to the complexity of the design problem. While topology optimization requires the integration of an optimization solver and a finite element solver, a clear interface can be successfully made separating the 2 parts of the program. In this talk, I will highlight my experience in writing an unpublished topology optimization package in Julia that abstracts away the finite element analysis and linear algebra and only exposes objectives and constraints to the optimization solver.

12:10 - 12:35 Developing new optimization methods with packages from the JuliaSmoothOptimizers organization. Abel Soares Siqueira (Federal University of Paraná) [Slides]

Abstract We present the packages in JuliaSmoothOptimizers (JSO). Aimed at nonlinear optimization in Julia, we develop tools to help create, test, and compare optimization solvers. Among other things, we have trust-region and line-search methods for subproblems, well-known collections of problems, like the CUTEst collection (Gould et al., 2014), the ability to easily create new problems, and tools for benchmarking the solvers, such as the performance profile. We show that, while sharing many common goals with other optimization packages and groups, JSO works on an underexplored area, and integrates well with other packages - specially JuMP.

12:35 - 14:00 Lunch

14:00 - 14:35 The Gravity modeling language Hassan Hijazi (LANL)

14:35 - 15:00 POD, A Global Solver for Nonconvex MINLPs Harsha Nagarajan (LANL)

Abstract MINLPs arise in practical applications such as synthesis of process and water networks, energy infrastructure networks, to name a few. Efficient algorithms to solve such optimization problems to global optimality is a key to addressing these applications. State-of-the-art techniques go by the philosophy of sub-dividing down the original problem into a large number of "easy-to-solve" sub-problems which will in turn be used to find the globally optimal solution. To this end, there has been development of MILP-based approaches, that leverage commercial solvers like Gurobi/Cplex, to solve a MINLP by applying piecewise polyhedral relaxations iteratively by partitioning the variable domains. However, the two major bottlenecks for this approach are (a) The tightness of the lower-bounding MILPs (with min. objective) and (b) The efficiency of the iterative algorithm. To address the former, we present tight MILP formulations of piecewise, polyhedral relaxations of multilinear functions. To address the latter, we discuss an algorithm based on adaptive, multivariate partitioning with non-uniform variable partitions combined with optimality-based bound tightening to speed up the convergence to global optimum.  Finally, we present a framework unifying Piecewise relaxations (P), Outer-approximations (O) and Dynamic Discretizations (D), underlying the open-source solver, “POD.jl”, written in Julia/JuMP, based on the proposed algorithms and show extensive results on standard benchmarks. POD.jl has generally faster solution times compared to the global open-source solvers (SCIP, Couenne) and very comparable to commercial solvers (Baron).

15:00 - 15:20 Coffee Break

15:20 - 16:20 MathOptInterface and JuMP 0.19 Miles Lubin (Google) [Slides]

16:20 onwards Discussion and unstructured collaboration time

19:30 - late Workshop Dinner

The workshop dinner will be held at Mama Shelter, 19 rue Poquelin Molière, beginning at 19:30. To travel there from the workshop, take the B tram to the stop Gambetta - MADD. The restaurant is a 200m walk from the stop.

Friday 29 June

10:00 - 10:25 Juniper: An Open-Source Nonlinear Branch-and-Bound Solver in Julia Ole Kröger (Uni Heidelberg)

Abstract Non-convex mixed-integer nonlinear programs (MINLPs) represent a challenging class of optimization problems that often arise in engineering and scientific applications. Because of non-convexities, these programs are typically solved with global optimization algorithms, which have limited scalability. However, nonlinear branch-and-bound has recently been shown to be an effective heuristic for quickly finding high-quality solutions to large-scale non-convex MINLPs, such as those arising in infrastructure network optimization. This work proposes Juniper, a Julia-based open-source solver for nonlinear branch-and-bound. Leveraging the high-level Julia programming language makes it easy to modify Juniper's algorithm and explore extensions, such as branching heuristics, feasibility pumps, and parallelization. Detailed numerical experiments demonstrate that the initial release of Juniper is comparable with other nonlinear branch-and-bound solvers, such as Bonmin, Minotaur, and Knitro, illustrating that Juniper provides a strong foundation for further exploration in utilizing nonlinear branch-and-bound algorithms as heuristics for non-convex MINLPs.

10:25 - 10:50 NEOS.jl: A Julia interface to the NEOS Server Oscar Dowson (University of Auckland) [Slides]

Abstract The NEOS Server (neos-server.org/neos) is a is a free internet-based service for solving numerical optimization problems. In this talk, we present NEOS.jl, a Julia interface for the NEOS Server. In addition to wrapping the XML-RPC API exposed by NEOS, NEOS.jl also implements the MathProgBase interface. This enables JuMP models to be solved via NEOS in a seamless fashion.

10:50 - 11:20 Coffee Break

11:20 - 11:45 Automatic reformulation using constraint bridges Benoît Legat (UCLouvain) [Slides]

Abstract A same mathematical optimization problem often possess different equivalent formulations but a given solver may only support one of them. Writing this solver specific formulation is inconvenient when the solver is not familiar to the user and it is not an option when writing solver independent code. This motivates the need of a mechanism that, given a model and a solver, automatically rewrites the model into an equivalent one supported by the solver. To make this rewritting transparent, the solver result also need to be automatically transformed into the original problem formulation. We introduce the MathOptInterfaceBridges package implementing constraint bridges for MathOptInterface. When applied to a solver, the bridge automatically rewrites each constraint of the corresponding type into an equivalent form while keeping the necessary information to translate the result back to the user. In MathOptInterface, each solver declares the constraint types supported. This information is used by the AutomaticBridger to algorithmically determine a reformulation of a given model into one supported by a given solver. As the reformulation is done constraint-wise, it never uses the full model information hence does not need to maintain a copy of the model. When different reformulations are available, heuristics are used to determine the formulation that will incur the lower computational cost to the solver.

11:45 - 12:10 EAGO: A Deterministic Nonconvex Optimization Package for Julia Matthew Wilhelm (University of Connecticut) [Slides]

Abstract Nonconvex optimization problems arise naturally in process systems engineering applications. Most physical models and trivial unit operations lead to significant nonconvexity (mixing, chemical reactions, separations, etc.). One emergent approach to solving these nonconvex problems is via the use of a generalized McCormick relaxations within a Branch-and-Bound algorithm. This approach operates in a reduced-dimension space in comparison to other global solvers such as BARON and COUENNE. Preliminary results in this area have demonstrated dramatic performance benefits that can be attained for some classes of problems with a natural formulation into the reduced space, as in model-based systems engineering applications. EAGO.jl provides an implementation of these relaxations in conjunction with a nonconvex global solver. This is the first widely-available global solver that makes use of McCormick relaxations in Julia. The McCormick library includes implementations of the most up-to-date theoretical developments while being significantly faster than comparable C++ libraries. In addition, the EAGO solver can be configured flexibly in a manner not previously possible with high performance code. We intend that this mixture of flexibility, speed, and user-accessibility (though JuMP) will allow EAGO to serve as an effective toolkit for developing and evaluating future low-level global optimization algorithms.

12:10 - 12:35 EMP.jl, a package for modelling Extended Mathematical Programming Olivier Huber (UW Madison) [Slides]

Abstract Extended Mathematical Programming (EMP) aims at enable the modelling of mathematical problems that do not fit into the classical structure of minimization problems. Example of such problems include Variational Inequalities (VI), instances from game theory (Multiple Objectives Problem with Equilibrium Constraints [MOPEC]), optimal value function. Solving an instance of an EMP problem usually involves reformulations or transformations. In this talk, we present a package that enables the user to model EMP problems and to solve them by using the SELKIE solver.

12:35 - 15:00 Lunch and unstructured collaboration time

15:00 - 17:00 JuMP Tutorial

The tutorial will cover how to use the new version of JuMP with MathOptInterface. The tutorial will be open to anyone, even if they have not attended the workshop. No JuMP experience is required.

17:00 Finish

Committee

Contact o.dowson at auckland.ac.nz or jump-dev-committee at googlegroups.com for more information.