A derivative-free approach for a simulation-based optimization problem in healthcare

Hospitals have been challenged in recent years to deliver high quality care with limited resources. Given the pressure to contain costs,developing procedures for optimal resource allocation becomes more and more critical in this context. Indeed, under/overutilization of emergency room and ward resources can either compromise a hospital's ability to provide the best possible care, or result in precious funding going toward underutilized resources. Simulation--based optimization tools then help facilitating the planning and management of hospital services, by maximizing/minimizing some specific indices (e.g. net profit) subject to given clinical and economical constraints. In this work, we develop a simulation--based optimization approach for the resource planning of a specific hospital ward. At each step, we first consider a suitably chosen resource setting and evaluate both efficiency and satisfaction of the restrictions by means of a discrete--event simulation model. Then, taking into account the information obtained by the simulation process, we use a derivative--free optimization algorithm to modify the given setting. We report results for a real--world problem coming from the obstetrics ward of an Italian hospital showing both the effectiveness and the efficiency of the proposed approach

A Linesearch-based Derivative-free Approach for Nonsmooth Optimization

In this paper, we propose new linesearch-based methods for nonsmooth optimization problems when first-order information on the problem functions is not available. In the first part, we describe a general framework for bound-constrained problems and analyze its convergence towards stationary points, using the Clarke-Jahn directional derivative. In the second part, we consider inequality constrained optimization problems where both objective function and constraints can possibly be nonsmooth. In this case, we first split the constraints into two subsets: difficult general nonlinear constraints and simple bound constraints on the variables. Then, we use an exact penalty function to tackle the difficult constraints and we prove that the original problem can be reformulated as the bound-constrained minimization of the proposed exact penalty function. Finally, we use the framework developed for the bound-constrained case to solve the penalized problem, and we prove that every accumulation point of the generated sequence of points is a stationary points of the original constrained problem. In the last part of the paper, we report extended numerical results on both bound-constrained and nonlinearly constrained problems, showing the effectiveness of our approach when compared to some state-of-the-art codes from the literature

BFO, a trainable derivative-free Brute Force Optimizer for nonlinear bound-constrained optimization and equilibrium computations with continuous and discrete variables

A direct-search derivative-free Matlab optimizer for bound-constrained problems is described, whose remarkable features are its ability to handle a mix of continuous and discrete variables, a versatile interface as well as a novel self-training option. Its performance compares favorably with that of NOMAD (Nonsmooth Optimization by Mesh Adaptive Direct Search), a well-known derivative-free optimization package. It is also applicable to multilevel equilibrium- or constrained-type problems. Its easy-to-use interface provides a number of user-oriented features, such as checkpointing and restart, variable scaling, and early termination tools

A Linesearch-based Derivative-free Approach for Nonsmooth Constrained Optimization

In this paper, we propose new linesearch-based methods for nonsmooth constrained optimization problems when first-order information on the problem functions is not available. In the first part, we describe a general framework for bound-constrained problems and analyze its convergence toward stationary points, using the Clarke-Jahn directional derivative. In the second part, we consider inequality constrained optimization problems where both objective function and constraints can possibly be nonsmooth. In this case, we first split the constraints into two subsets: difficult general nonlinear constraints and simple bound constraints on the variables. Then, we use an exact penalty function to tackle the difficult constraints and we prove that the original problem can be reformulated as the bound-constrained minimization of the proposed exact penalty function. Finally, we use the framework developed for the bound-constrained case to solve the penalized problem. Moreover, we prove that every accumulation point, under standard assumptions on the search directions, of the generated sequence of iterates is a stationary point of the original constrained problem. In the last part of the paper, we report extended numerical results on both bound-constrained and nonlinearly constrained problems, showing that our approach is promising when compared to some state-of-the-art codes from the literature

DERIVATIVE-FREE METHODS FOR BOUND CONSTRAINED MIXED-INTEGER OPTIMIZATION

We consider the problem of minimizing a continuously differentiable function of several variables subject to simple bound constraints where some of the variables are restricted to take integer values. We assume that the first order derivatives of the objective function can be neither calculated nor approximated explicitly. This class of mixed integer nonlinear optimization problems arises frequently in many industrial and scientific applications and this motivates the increasing interest in the study of derivative-free methods for their solution. The continuous variables are handled by a linesearch strategy whereas to tackle the discrete ones we employ a local search-type approach. We propose different algorithms which are characterized by the way the current iterate is updated and by the stationarity conditions satisfied by the limit points of the sequences they produce

Trajectory-based methods for solving nonlinear and mixed integer nonlinear programming problems

A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, 2015.I would like to acknowledge a number of people who contributed towards the completion of this thesis. Firstly, I thank my supervisor Professor Montaz Ali for his patience, enthusiasm, guidance and teachings. The skills I have acquired during this process have infiltrated every aspect of my life. I remain forever grateful. Secondly, I would like to say a special thank you to Professor Jan Snyman for his assistance, which contributed immensely towards this thesis. I would also like to thank Professor Dominque Orban for his willingness to assist me for countless hours with the installation of CUTEr, as well as Professor Jose Mario Martinez for his email correspondence. A heartfelt thanks goes out to my family and friends at large, for their prayers, support and faith in me when I had little faith in myself. Thank you also to my colleagues who kept me sane and motivated, as well as all the support staff who played a pivotal roll in this process. Above all, I would like to thank God, without whom none of this would have been possible

Data-Driven Mixed-Integer Optimization for Modular Process Intensification

High-fidelity computer simulations provide accurate information on complex physical systems. These often involve proprietary codes, if-then operators, or numerical integrators to describe phenomena that cannot be explicitly captured by physics-based algebraic equations. Consequently, the derivatives of the model are either absent or too complicated to compute; thus, the system cannot be directly optimized using derivative-based optimization solvers. Such problems are known as “black-box” systems since the constraints and the objective of the problem cannot be obtained as closed-form equations. One promising approach to optimize black-box systems is surrogate-based optimization. Surrogate-based optimization uses simulation data to construct low-fidelity approximation models. These models are optimized to find an optimal solution. We study several strategies for surrogate-based optimization for nonlinear and mixed-integer nonlinear black-box problems. First, we explore several types of surrogate models, ranging from simple subset selection for regression models to highly complex machine learning models. Second, we propose a novel surrogate-based optimization algorithm for black-box mixed-integer nonlinear programming problems. The algorithm systematically employs data-preprocessing techniques, surrogate model fitting, and optimization-based adaptive sampling to efficiently locate the optimal solution. Finally, a case study on modular carbon capture is presented. Simultaneous process optimization and adsorbent selection are performed to determine the optimal module design. An economic analysis is presented to determine the feasibility of a proposed modular facility.Ph.D