David E. Bernal Neira

Purdue University West Lafayette | Purdue · Davidson School of Chemical Engineering

The healthcare industry frequently handles sensitive and proprietary data, and due to strict privacy regulations, it is often reluctant to share it directly. In today’s context, Federated Learning (FL) stands out as a crucial remedy, facilitating the rapid advancement of distributed machine learning while effectively managing critical concerns rega...

Dynamic optimization problems involving discrete decisions have several applications, yet lead to challenging optimization problems that must be addressed efficiently. Combining discrete variables with potentially nonlinear constraints stemming from dynamics within an optimization model results in mathematical programs for which off-the-shelf techn...

The widespread deployment of products powered by machine learning models is raising concerns around data privacy and information security worldwide. To address this issue, Federated Learning was first proposed as a privacy-preserving alternative to conventional methods that allow multiple learning clients to share model knowledge without disclosing...

Quantum Hamiltonian simulation is one of the most promising applications of quantum computing and forms the basis for many quantum algorithms. Benchmarking them is an important gauge of progress in quantum computing technology. We present a methodology and software framework to evaluate various facets of the performance of gate-based quantum comput...

Quantum approximate optimization is one of the promising candidates for useful quantum computation, particularly in the context of finding approximate solutions to Quadratic Unconstrained Binary Optimization (QUBO) problems. However, the existing quantum processing units (QPUs) are relatively small, and canonical mappings of QUBO via the Ising mode...

The advancement of domain reduction techniques has significantly enhanced the performance of solvers in mathematical programming. This paper delves into the impact of integrating convexification and domain reduction techniques within the Outer- Approximation method. We propose a refined convexification-based Outer-Approximation method alongside a B...

Generalized disjunctive programming (GDP) models with bilinear and concave constraints, often seen in water network design, are challenging optimization problems. This work proposes quadratic and piecewise linear approximations for nonlinear terms to reformulate GDP models into quadratic GDP (QGDP) models that suitable solvers may solve more effici...

Phthalates are the most widely used plasticizers in the polymers industry; however, their toxicity and environmental impacts have led to their ban in various applications. This has driven the search for more sustainable alternatives, including biobased citrate esters, especially tributyl citrate (TBC) and its acetylated form. TBC is typically produ...

Combinatorial optimization is anticipated to be one of the primary use cases for quantum computation in the coming years. The Quantum Approximate Optimization Algorithm (QAOA) and Quantum Annealing (QA) can potentially demonstrate significant run-time performance benefits over current state-of-the-art solutions. Inspired by existing methods to char...

Variational Quantum Eigensolvers (VQEs) represent a promising approach to computing molecular ground states and energies on modern quantum computers. These approaches use a classical computer to optimize the parameters of a trial wave function, while the quantum computer simulates the energy by preparing and measuring a set of bitstring observation...

Reverse electrodialysis (RED) is a nascent renewable technology that generates clean, baseload electricity from salinity differences between two water streams, a renewable source known as salinity gradient energy (SGE). Full-scale RED progress calls for robust techno-economic and environmental assessments. Using generalized disjunctive programming...

This work studied an alternative intensification approach for the downstream recovery of citric acid (CA) and its further transformation into tributyl citrate (TBC) bio-plasticizer. Avoiding several purification steps required to obtain citric acid, solid calcium citrate (CaCiH) was directly used in the production of the citrates. A set of experime...

Quantum computing is one of the most enticing computational paradigms with the potential to revolutionize diverse areas of future-generation computational systems. While quantum computing hardware has advanced rapidly, from tiny laboratory experiments to quantum chips that can outperform even the largest supercomputers on specialized computational...

Quantum computers currently rely on a hybrid quantum-classical approach known as Variational Quantum Algorithms (VQAs) to solve problems. Still, there are several challenges with VQAs on the classical computing side: it corresponds to a black-box optimization problem that is generally non-convex, the observations from the quantum hardware are noisy...

Model-based design of experiments (MBDoE) is a powerful framework for selecting and calibrating science-based mathematical models from data. This work extends popular MBDoE workflows by proposing a convex mixed integer (non)linear programming (MINLP) problem to optimize the selection of measurements. The solver MindtPy is modified to support calcul...

We propose the formulation of convex Generalized Disjunctive Programming (GDP) problems using conic inequalities leading to conic GDP problems. We then show the reformulation of conic GDPs into Mixed-Integer Conic Programming (MICP) problems through both the big-M and hull reformulations. These reformulations have the advantage that they are repres...

We present two algorithms in the quantum CONGEST-CLIQUE model of distributed computation that succeed with high probability: one for producing an approximately optimal Steiner tree, and one for producing an exact directed minimum spanning tree, each of which uses O˜(n1/4) rounds of communication and O˜(n9/4) messages, achieving a lower asymptotic r...

We present QUBO.jl, an end-to-end Julia package for working with QUBO (Quadratic Unconstrained Binary Optimization) instances. This tool aims to convert a broad range of JuMP problems for straightforward application in many physics and physics-inspired solution methods whose standard optimization form is equivalent to the QUBO. These methods includ...

In order to characterize and benchmark computational hardware, software, and algorithms, it is essential to have many problem instances on-hand. This is no less true for quantum computation, where a large collection of real-world problem instances would allow for benchmarking studies that in turn help to improve both algorithms and hardware designs...

The CONGEST and CONGEST-CLIQUE models have been carefully studied to represent situations where the communication bandwidth between processors in a network is severely limited. Messages of only $O(log(n))$ bits of information each may be sent between processors in each round. The quantum versions of these models allow the processors instead to comm...

Combinatorial optimization is anticipated to be one of the primary use cases for quantum computation in the coming years. The Quantum Approximate Optimization Algorithm (QAOA) and Quantum Annealing (QA) have the potential to demonstrate significant run-time performance benefits over current state-of-the-art solutions. Using existing methods for cha...

Recent years have seen significant advances in quantum/quantum-inspired technologies capable of approximately searching for the ground state of Ising spin Hamiltonians. The promise of leveraging such technologies to accelerate the solution of difficult optimization problems has spurred an increased interest in exploring methods to integrate Ising p...

In this work, we extend the regularization framework from Kronqvist et al. (Math Program 180(1):285–310, 2020) by incorporating several new regularization functions and develop a regularized single-tree search method for solving convex mixed-integer nonlinear programming (MINLP) problems. We propose a set of regularization functions based on distan...

Quantum computing has been attracting public attention recently. This interest is driven by the advancements in hardware, software, and algorithms required for its successful usage and the promise that it entails the potential acceleration of computational tasks compared to classical computing. This perspective article presents a short review on qu...

We present three core principles for engineering-oriented integrated modeling and optimization tool sets—intuitive modeling contexts, systematic computer-aided reformulations, and flexible solution strategies—and describe how new developments in Pyomo.GDP for Generalized Disjunctive Programming (GDP) advance this vision. We describe a new logical e...

Quantum devices can be used to solve constrained combinatorial optimization (COPT) problems thanks to the use of penalization methods to embed the COPT problem’s constraints in its objective to obtain a quadratic unconstrained binary optimization (QUBO) reformulation of the COPT. However, the particular way in which this penalization is carried out...

This manuscript presents the recent advances in Mixed-Integer Nonlinear Programming (MINLP) and Generalized Disjunctive Programming (GDP) with a particular scope for superstructure optimization within Process Systems Engineering (PSE). We present an environment of open-source software packages written in Python and based on the algebraic modeling l...

This manuscript introduces a Logic-based Discrete-Steepest Descent Algorithm (LD- SDA) to tackle problems arising from process superstructure optimization. These problems often appear in Process Systems Engineering and become challenging when addressing Process Intensification applications. The current algorithm considers a disjunctive interpretati...

We propose a novel iterative procedure to generate hybrid models (HMs) within an optimization framework to solve design problems. HMs are based on first principle and surrogate models (SMs) and they may represent potential plant units embedded within a superstructure. We generate initial SMs with simple algebraic regression models and refine them b...

We propose the formulation of convex Generalized Disjunctive Programming (GDP) problems using conic inequalities leading to conic GDP problems. We then show the reformulation of conic GDPs into Mixed-Integer Conic Programming (MICP) problems through both the Big-M and Hull Reformulations. These reformulations have the advantage that they are repres...

We propose a sample average approximation-based outer-approximation algorithm (SAAOA) that can address nonconvex two-stage stochastic programs (SP) with any continuous or discrete probability distributions. Previous work has considered this approach for convex two-stage SP (Wei and Realff in Comput Chem Eng 28(3):333–346, 2004). The SAAOA algorithm...

Quantum devices can be used to solve constrained combinatorial optimization (COPT) problems thanks to the use of penalization methods to embed the COPT problem's constraints in its objective to obtain a quadratic unconstrained binary optimization (QUBO) reformulation of the COPT. However, the particular way in which this penalization is carried out...

The determination of vehicle routes fulfilling connectivity, time, and operational constraints is a well-studied combinatorial optimization problem. The NP-hard complexity of vehicle routing problems has fostered the adoption of tailored exact approaches, matheuristics, and metaheuristics on classical computing devices. The ongoing evolution of qua...

This lecture series on Quantum Integer Programming (QuIP) -- created by Professor Sridhar Tayur, David E. Bernal, and Dr. Davide Venturelli, a collaboration between CMU and USRA, with the support from Amazon Braket during Fall 2020 -- is intended for students and researchers interested in Integer Programming and the potential of near term quantum a...

This work presents the optimal synthesis and design of a rigorous catalytic distillation (CD) column that explicitly considers the multiscale and multiphase nature of this intensification process. A rate-based model that couples micro and macroscale events taking place inside the CD column is explicitly considered. The direct solution of such inten...

A major limitation of current generations of quantum annealers is the sparse connectivity of manufactured qubits in the hardware graph. This technological limitation has generated considerable interest, motivating efforts to design efficient and adroit minor-embedding procedures that bypass sparsity constraints. In this paper, starting from a previ...

Engineering systems are typically maintained during planned, or unplanned, downtimes in between operation periods. If the duration of the downtime or the budget of the maintenance is an active constraint, all desired maintenance actions cannot be conducted. Seeking of the optimal subset of maintenance actions is referred to as selective maintenance...

This work addresses the optimal design of catalytic distillation (CD) columns taking into account discrete design variables, i.e., the number of stages and location of feed stages and reactive stages. This optimization problem is challenging due to the combinatorial complexity introduced by these discrete decisions. In this work, the binary variabl...

A new approach for the optimal design of superstructures in chemical engineering is proposed in this study. Contrary to most of the optimization techniques established in the literature, this approximation exploits the structure of a specific type of problem, i.e., the case where it is necessary to find the optimal location of a processing unit or...

In this work, a Mixed-Integer Nonlinear Programming (MINLP) modeling framework for integrating short-term Crude-oil Scheduling (CS) and mid-term Refinery Planning (RP) has been developed and effectively solved by a proposed Lagrangean Decomposition (LD) algorithm. The principles of this integration are based on the fact that both Crude-oil Scheduli...

A major limitation of current generations of quantum annealers is the sparse connectivity of manufactured qubits in the hardware graph. This technological limitation generated considerable interest, motivating efforts to design efficient and adroit minor-embedding procedures that bypass sparsity constraints. In this paper, starting from a previous...

The solver DICOPT is based on the outer-approximation algorithm used for solving mixed-integer nonlinear programming (MINLP) problems. This algorithm is very effective for solving some types of convex MINLPs. However, it has been observed that DICOPT has difficulties solving instances in which some of the nonlinear constraints are so restrictive th...

In this paper, we present a review of deterministic software for solving convex MINLP problems as well as a comprehensive comparison of a large selection of commonly available solvers. As a test set, we have used all MINLP instances classified as convex in the problem library MINLPLib, resulting in a test set of 335 convex MINLP instances. A summar...

This paper addresses the design and planning of manufacturing networks considering the option of centralized and distributed facilities, taking into account the potential trade-offs between investments and transportation. The problem is formulated as an extension of the Capacitated Multi-facility Weber Problem, which involves the selection of which...

In this paper, we present two new methods for solving convex mixed-integer nonlinear programming problems based on the outer approximation method. The first method is inspired by the level method and uses a regularization technique to reduce the step size when choosing new integer combinations. The second method combines ideas from both the level m...

Here we present a center-cut algorithm for convex mixed-integer nonlinear programming (MINLP) that can either be used as a primal heuristic or as a deterministic solution technique. Like several other algorithms for convex MINLP, the center-cut algorithm constructs a linear approximation of the original problem. The main idea of the algorithm is to...

This work addressed the rigorous modeling of catalytic distillation columns by simultaneously considering relevant phenomena such as pressure drop across the column, tray capacity constraints, non-ideal behavior of both liquid and vapor, and the column’s hydrodynamics, yet to be considered in earlier modeling studies for catalytic distillation. The...

In this paper, we present a new software framework developed in Pyomo, MindtPy (Mixed-Integer Nonlinear Decomposition Toolbox for Pyomo), which implements several decomposition methods for solving Mixed-Integer Nonlinear Programs (MINLP). These methods decompose the MINLP into a Mixed-integer Linear Program (MILP) and a Nonlinear Program (NLP). The...

This paper addresses the integration of scheduling of on-line blending and distribution for refinery oil products, which needs to determine simultaneously the blending recipes and the distribution times of oil products in every oil pipeline, satisfying the time-varying demand and product properties specifications for each oil product. We formulate...

This paper presents scaled quadratic cuts based on scaling the second-order Taylor expansion terms for the decomposition methods Outer Approximation and Partial Surrogate Cuts for solving convex Mixed Integer Nonlinear Programing problems. The scaled quadratic cut is proved to be a stricter and tighter underestimation for convex nonlinear functions...

We present a sample of 115 very low optical surface brightness, highly extended, HI-rich galaxies carefully selected from the ALFALFA survey that have similar optical absolute magnitudes, surface brightnesses, and radii to recently discovered "ultra-diffuse" galaxies (UDGs). However, these systems are bluer and have more irregular morphologies than...