# Sitemap

A list of all the posts and pages found on the site. For you robots out there is an XML version available for digesting as well.

## wUMCFC: a solver for wireless unsplittable multi-commodity flow routing with network coding

Published:

wUMCFC is a specialized branch-and-price (BP) based solver for unsplittable multi-commodity flow routing with network coding. Unsplittable multi-commodity flow is a fundamentel problem in network optimization. wUMCFC uses network coding to decrease the routing cost and increase the capacity usage for wireless networks. Github

## cflg: an algorithmic toolkit for continuous set covering on networks

Published:

Facility location is an important appication in operations research. Continuous set covering on networks generalizes the classical dicrete set covering problems in graphs, which allows both the demands and facilities continuously locating in edges. cflg contains several algorithms for solving continuous set covering on networks. cflg is written in Julia based on JuMP. Github

## cbp: branch-and-price algorithms for conic submodular binpacking

Published:

Binpacking is an important combinatorial problem in operations research. Conic submodular binpacking generalizes the classical binpacking problem to nonlinear setting, and it can formulate the chance-constrained binpacking, the distributionally robust binpacking etc. cbp implements several branch-and-price algorithms to solve the conic submodular binpacking problems. Github

## Traces.jl: A traces wrapper for graph canonical labeling and automorphism group computation

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A simple julia wrapper for traces. Github

## SymMIP.jl: Symmetry analysis for MIPs

Published:

Detect the formulation symmetry group of a MILP model, and display the orbits and the generators of this group. Github

## Optimal Location of Safety Landing Sites

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In urban air mobility probelm, Vertical Take Off and Landing (VTOLs) vehicles are used to move passengers between vertiports. Safety landing sites (SLSs) cover the trajectory of VTOLs for emergency landings. We study the optimal placement of SLSs in UAM network under budget constraints on SLS installation. slides

## Optimal Location of Safety Landing Sites

Published:

In urban air mobility probelm, Vertical Take Off and Landing (VTOLs) vehicles are used to move passengers between vertiports. Safety landing sites (SLSs) cover the trajectory of VTOLs for emergency landings. We study the optimal placement of SLSs in UAM network under budget constraints on SLS installation. slides report

## An algorithmic toolkit for continuous set-covering on networks

Published:

Covering problems are well-studied in the domain of Operations Research, and, in particular, Location Science. When the location space is a network, the most frequent assumption is to consider the candidate facility locations, the points to be covered, or both, to be discrete sets. In this talk, we study the set-covering location problem when both demand points and candidate locations are continuous sets on a network, and we propose several Mixed-Integer Linear Programming Formulations. CFLG.jl is an open-source software written in the Julia programming language for the continuous set cover problem, and these MILP formulations are implemented in CFLG.jl. CFLG.jl can be extended to model other covering problems on networks, such as discrete cover problems. We conduct the numerical experiment of CFLG.jl on several benchmarks and compare the performance of different MILP formulations. The results show that our formulations are more scalable than the existing formulation. slides

## (Three) Cutting Planes for Signomial Programming

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The generation of cutting planes is crucial in solving non-convex Mixed-Integer Nonlinear Programming problems to $\epsilon$-global optimality. In this work, we study the signomial-term set (the graph of a signomial term function) arising in the extended formulation of Signomial Programming, and we show that it suffices to consider the signomial-term set as the epigraph/hypograph of the associated signomial term function. We present a useful reformulation of the signomial-term set, written as the zero-sublevel set of the difference of two concave power functions. We propose three types of valid linear inequalities: intersection cuts and two types of outer approximation cuts. slides

## On a Concept of a Generic Intersection Cut Callback

Published:

Intersection cut framework can generate valid linear inequalities for a nonconvex set $S$. The framework requires a corner polyhedron relaxation of $S$, and a convex $S$-free set, which does not contain any point of $S$ in its interior. In this talk, I will review the recent development of intersection cuts in MINLPs (e.g quadratic/polynomial programming and signomial programming), featuring the construction of a variety of $S$-free sets. On the other hand, implementation of intersection cut requires much knowledge of a solver’s data structure and numerical stability. Software engineering can help here, as the solver can encapsulate cut separation procedures and provides an intersection cut callback without need for symbolic representation of $S$. Then, the users only need to provide defining-variables, zero- and first-order oracle access to the $S$-free set. I will also discuss some limitations of intersection cuts and open problems. slides

## Intersection cuts meet submodularity: the good and the bad

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Intersection cuts can tighten a polyhedral outer approximation of a non-convex set. We study intersection cuts for submodular and submodular-supermodular maximization problems. We construct corresponding S-free sets and propose a cut computation algorithm. We report our good and bad experiences with intersection cuts in max cut, maximization of Boolean multilinear functions, maximization of utility functions, and D-optimal design problems. We found experimentally and thus conjecture that intersection cuts hardly improve the polyhedral outer approximations of non-monotone submodular maximization problems and problems with convex MINLP problems. So, a new measure of cut efficiency in terms of the corner polyhedral relaxation is in need. This talk is based on a joint work with Leo Liberti. slides

## MILP formulations for continuous set-covering on networks

Published:

Covering problems are well-studied in the domain of Location Science. When the location space is a network, the most frequent assumption is to consider the candidate facility locations, the points to be covered, or both, to be finite sets. In this work, we study the set-covering location problem when both candidate locations and demand points are continuous on a network. This variant generalizes several problems, including set-covering, and uncapacitated facility location problems. However, this problem has received little attention, and the scarce existing approaches have focused on particular cases, such as tree networks and integer covering radius. Here we study the general problem through an integer programming approach, and propose two MILP formulations for the problem with several reduction techniques. We implement the existing and new MILP formulations in JuMP modeling language. Our computational experiments show the strengths and limitations of our exact approach to both real-world and random networks. Our formulations are also tested against an existing exact method. slides

## CSE201 - Object-oriented Programming in C++

Undergraduate course, École Polytechnique, DIX, 2021

The goal of CSE201 is to introduce students to the C++ programming language, and the object-based view of software design. C++ is one of the most widely-used programming languages in the world, especially for system-level programming. Much of its power derives from its use of objects, packets of data and functionality that model things and concepts in the real world.

## INF569 - Decision theory, with applications to energy systems

Master (M1) course, École Polytechnique, DIX, 2022

Management of energy systems is one of the biggest challenges of our time. The daily demand for energy increases constantly for many reasons, including the worldwide spreading of the electrification/decarbonization of vehicles used for public and private transportation. Moreover, the wide use of renewable energies, also aimed at limiting polluting emissions, can create instability in the networks and uncertainty in energy production. The current production sources and the current infrastructure for transmission and distribution are likely to soon become insufficient to cope with these changes. Decision makers will, thus, need efficient and effective tools aimed at helping them to optimize operational and strategic decisions to be taken in the short, medium, and long term. This course aims at providing the students with the background in mathematical optimization needed to play a fundamental role in the decision-making processes in energy systems. Mathematical optimization allows to formally state an extremely large variety of optimization problems as a so-called mathematical formulation. Once the problem is formalized, its optimal solution can be found by properly using mathematical optimization solvers or devising algorithms tailored for the specific problem. In this course, we will code the formulations and run solvers thanks to the modeling language AMPL. Each of the lectures will focus on a particular optimization aspect and one or more energy applications. The applications covered will be: production, transmission, distribution of energy; energy markets; renewable energies; smart grids. All these problems are challenging because they include technical, economic, political, and ethical issues.