Papers by Johannes Royset
Structural Safety
Design and operation of complex engineering systems rely on reliability optimization. Such optimi... more Design and operation of complex engineering systems rely on reliability optimization. Such optimization requires us to account for uncertainties expressed in terms of complicated, high-dimensional probability distributions, for which only samples or data might be available. However, using data or samples often degrades the computational efficiency, particularly as the conventional failure probability is estimated using the indicator function whose gradient is not defined at zero. To address this issue, by leveraging the buffered failure probability, the paper develops the buffered optimization and reliability method (BORM) for efficient, data-driven optimization of reliability. The proposed formulations, algorithms, and strategies greatly improve the computational efficiency of the optimization and thereby address the needs of high-dimensional and nonlinear problems. In addition, an analytical formula is developed to estimate the reliability sensitivity, a subject fraught with difficulty when using the conventional failure probability. The buffered failure probability is thoroughly investigated in the context of many different distributions, leading to a novel measure of tail-heaviness called the buffered tail index. The efficiency and accuracy of the proposed optimization methodology are demonstrated by three numerical examples, which underline the unique advantages of the buffered failure probability for data-driven reliability analysis.
AIAA Journal, 2021
Reliable, risk-averse design of complex engineering systems with optimized performance requires d... more Reliable, risk-averse design of complex engineering systems with optimized performance requires dealing with uncertainties. A conventional approach is to add safety margins to a design that was obtained from deterministic optimization. Safer engineering designs require appropriate cost and constraint function definitions that capture the risk associated with unwanted system behavior in the presence of uncertainties. The paper proposes two notions of certifiability. The first is based on accounting for the magnitude of failure to ensure data-informed conservativeness. The second is the ability to provide optimization convergence guarantees by preserving convexity. Satisfying these notions leads to certifiable risk-based design optimization (CRiBDO). In the context of CRiBDO, risk measures based on superquantile (a.k.a. conditional value-at-risk) and buffered probability of failure are analyzed. CRiBDO is contrasted with reliability-based design optimization (RBDO), where uncertainties are accounted for via the probability of failure, through a structural and a thermal design problem. A reformulation of the short column structural design problem leading to a convex CRiBDO problem is presented. The CRiBDO formulations capture more information about the problem to assign the appropriate conservativeness, exhibit superior optimization convergence by preserving properties of underlying functions, and alleviate the adverse effects of choosing hard failure thresholds required in RBDO.
This paper focuses on a non-standard constrained nonlinear optimal control problem in which the o... more This paper focuses on a non-standard constrained nonlinear optimal control problem in which the objective functional involves an integration over a space of stochastic parameters aswell as an integration over the time domain. The research is inspired by the problem of optimizing the trajectories of multiple searchers attempting to detect non-evadingmoving targets. In this paper, we propose a framework based on the approximation of the integral in the parameter space for the considered uncertain optimal control problem. The framework is proved to produce a zeroth-order consistent approximation in the sense that accumulation points of a sequence of optimal solutions to the approximate problem are optimal solutions of the original problem. In addition, we demonstrate the convergence of the corresponding adjoint variables. The accumulation points of a sequence of optimal state-adjoint pairs for the approximate problem satisfy a necessary condition of PontryaginMinimumPrinciple type,whic...
OR Spectrum, 2020
This paper deals with the long term Military Flight and Maintenance Planning problem. In order to... more This paper deals with the long term Military Flight and Maintenance Planning problem. In order to solve this problem efficiently, we propose a new solution approach based on a new Mixed Integer Program and the use of both valid cuts generated on the basis of initial conditions and learned cuts based on the prediction of certain characteristics of optimal or near optimal solutions. These learned cuts are generated by training a Machine Learning model on the input data and results of 5000 instances. This approach helps to reduce the solution time with little losses in optimality and feasibility in comparison to alternative matheuristic methods. The obtained experimental results show the benefit of a new way of adding learned cuts to problems based on predicting specific characteristics of solutions.
Naval Research Logistics (NRL), 2018
This article provides a modeling framework for quantifying cost and optimizing motion plans in co... more This article provides a modeling framework for quantifying cost and optimizing motion plans in combat situations with rapid weapon fire, multiple agents, and attacker uncertainty characterized by uncertain parameters. Recent developments in numerical optimal control enable the efficient computation of numerical solutions for optimization problems with multiple agents, nonlinear dynamics, and a broad class of objectives. This facilitates the application of more realistic, equipment-based combat models, which track both more realistic models, which track both agent motion and dynamic equipment capabilities. We present such a framework, along with a described algorithm for finding numerical solutions, and a numerical example.
Journal of the Operational Research Society, 2018
An important task of operators in Norwegian vessel traffic services (VTS) centers is to cleverly ... more An important task of operators in Norwegian vessel traffic services (VTS) centers is to cleverly position tugboats before potential vessel distress calls. Here, we formulate a nonlinear binary-integer program, integrated in a receding horizon control algorithm, that minimizes the expected cost of grounding accidents by positioning tugboats optimally under uncertainty about vessel incidents and environmental conditions. Linearizations of the model lead to easy-to-compute bounds on the optimal value. Numerical experiments with real-world data demonstrate significant reduction in the expected cost, suggesting that the model can be used as a decision-support tool at VTS centers.
International law enforcement organizations around the world endeavor to combat high drug related... more International law enforcement organizations around the world endeavor to combat high drug related mortality rates by seizing illicit drugs in transit over international waters. This mission requires effective plans that route multiple aerial searchers and position surface interdictors through large expanses of geographical areas in the presence of highly uncertain estimates about drug smuggler whereabouts. This high uncertainty combined with the challenge of coordinating search and interdiction make it particularly difficult to conduct mission planning. We present optimal search and interdiction models that address these important challenges and demonstrate how planners can used these models by applying them to a realistic counterdrug operation scenario.
Applications of Statistics and Probability in Civil Engineering, 2011
The buffered failure probability is an alternative measure of reliability that offers several the... more The buffered failure probability is an alternative measure of reliability that offers several theoretical, practical, and computational advantages over the traditional failure probability. It is handled with relative ease in design optimization problems, accounts for the degree of violation of a performance threshold, and is more conservative than the failure probability. This paper examines the difference between the buffered failure probability and the failure probability in several examples and find that the buffered failure probability typically overestimates the failure probability of a structure with a factor of three. We examine the use of the buffered failure probability in reliability-based optimal design and present three algorithms for the solution of the resulting optimization problems. Computational results on six engineering design examples indicate that the problems are solvable in few seconds using standard optimization solvers.
Operations Research/Computer Science Interfaces Series
A "project manager" wishes to complete a project (e.g., a weaponsdevelopment program) as quickly ... more A "project manager" wishes to complete a project (e.g., a weaponsdevelopment program) as quickly as possible. Using a limited interdiction budget, an "interdictor" wishes to delay the project's overall completion time by interdicting and thereby delaying some of the project's component tasks. We explore a variety of PERT-based interdiction models for such problems and show that the resulting problem complexities run the gamut: polynomially solvable, weakly NP-complete, strongly NP-complete or NP-hard. We suggest methods for solving the problems that are easier than worst-case complexity implies.
Optimality functions define stationarity in nonlinear programming, semi-infinite optimization, an... more Optimality functions define stationarity in nonlinear programming, semi-infinite optimization, and optimal control in some sense. In this paper, we consider optimality functions for stochastic programs with nonlinear, possibly nonconvex, expected value objective and constraint functions. We show that an optimality function directly relates to the difference in function values at a candidate point and a local minimizer. We construct confidence intervals for the value of the optimality function at a candidate point and, hence, provide a quantitative measure of solution quality. Based on sample average approximations, we develop two algorithms for classes of stochastic programs that include CVaR-problems and utilize optimality functions to select sample sizes as well as "active" sample points in an active-set strategy. Numerical tests illustrate the procedures.
Automatica, 2014
This paper focuses on a non-standard constrained nonlinear optimal control problem in which the o... more This paper focuses on a non-standard constrained nonlinear optimal control problem in which the objective functional involves an integration over a space of stochastic parameters as well as an integration over the time domain. The research is inspired by the problem of optimizing the trajectories of multiple searchers attempting to detect non-evading moving targets. In this paper, we propose a framework based on the approximation of the integral in the parameter space for the considered uncertain optimal control problem. The framework is proved to produce a zeroth-order consistent approximation in the sense that accumulation points of a sequence of optimal solutions to the approximate problem are optimal solutions of the original problem. In addition, we demonstrate the convergence of the corresponding adjoint variables. The accumulation points of a sequence of optimal state-adjoint pairs for the approximate problem satisfy a necessary condition of Pontryagin Minimum Principle type, which facilitates assessment of the optimality of numerical solutions.
IFAC Proceedings Volumes, 2014
This paper explores the potential for applying newly available numerical methods in optimal contr... more This paper explores the potential for applying newly available numerical methods in optimal control to solve motion planning problems created by the search for targets with motion uncertainty characterized by constant but unknown parameters. These recent developments enable the efficient computation of numerical solutions for search problems with multiple searchers, nonlinear dynamics, and a broad class of objectives. We demonstrate the efficacy of these methods through implementing a multi-agent optimal search problem. We then derive an expansion of the optimal search modeling framework which facilitates the consideration of multi-agent searching problems with more general strategic objectives and utilize this expanded framework to implement an example combat defense scenario.
2012 IEEE 51st IEEE Conference on Decision and Control (CDC), 2012
This paper focuses on the problem of optimizing the trajectories of multiple searchers attempting... more This paper focuses on the problem of optimizing the trajectories of multiple searchers attempting to detect a non-evading moving target whose motion is conditionally deterministic. This problem is a parameter-distributed optimal control problem, as it involves an integration over a space of stochastic parameters as well as an integration over the time domain. In this paper, we consider a wide range of discretization schemes to approximate the integral in the parameter space by a finite summation, which results in a standard controlconstrained optimal control problem that can be solved using existing techniques in optimal control theory. We prove that when the sequence of solutions to the discretized problem has an accumulation point, it is guaranteed to be an optimal solution of the original search problem. We also provide a necessary condition that accumulation points of this sequence must satisfy.
52nd IEEE Conference on Decision and Control, 2013
This paper focuses on an optimal control problem in which the objective is to minimize the expect... more This paper focuses on an optimal control problem in which the objective is to minimize the expectation of a cost functional with stochastic parameters. The inclusion of the stochastic parameters in the objective raises new theoretical and computational challenges not present in a standard nonlinear optimal control problem. In this paper, we provide a numerical framework for the solution of this uncertain optimal control problem by taking a sample average approximation approach. An independent random sample is taken from the parameter space, and the expectation is approximated by the sample average. The result is a family of standard nonlinear optimal control problems which can be solved using existing techniques. We provide an optimality function for both the uncertain optimal control problem and its approximation, and show that the approximation based on the sample average approach is consistent in the sense of Polak. We illustrate the approach with a numerical example arising in optimal search for a moving target.
Reliability Engineering & System Safety, 2010
In reliability engineering focused on the design and optimization of structures, the typical meas... more In reliability engineering focused on the design and optimization of structures, the typical measure of reliability is the probability of failure of the structure or its individual components relative to specific limit states. However, the failure probability has troublesome properties that raise several theoretical, practical, and computational issues. This paper explains the seriousness of these issues in the context of design optimization and goes on to propose a new alternative measure, the buffered failure probability, which offers significant advantages. The buffered failure probability is handled with relative ease in design optimization problems, accounts for the degree of violation of a performance threshold, and is more conservative than the failure probability.
Operations Research, 2013
The sample average approximation approach to solving stochastic programs induces a sampling error... more The sample average approximation approach to solving stochastic programs induces a sampling error, caused by replacing an expectation by a sample average, as well as an optimization error due to approximating the solution of the resulting sample average problem. We obtain estimators of an optimal solution and the optimal value of the original stochastic program after executing a finite number of iterations of an optimization algorithm applied to the sample average problem. We examine the convergence rate of the estimators as the computing budget tends to infinity, and we characterize the allocation policies that maximize the convergence rate in the case of sublinear, linear, and superlinear convergence regimes for the optimization algorithm.
Naval Research Logistics (NRL), 2013
We introduce a generalized Orienteering Problem where, as usual, a vehicle is routed from a presc... more We introduce a generalized Orienteering Problem where, as usual, a vehicle is routed from a prescribed start node, through a directed network, to a prescribed destination node, collecting rewards at each node visited, in order to maximize the total reward along the path. In our generalization, transit on arcs in the network and reward collection at nodes both consume a variable amount of the same limited resource. We exploit this resource trade-off through a specialized branch-and-bound algorithm that relies upon partial path relaxation problems which often yield tight bounds and lead to substantial pruning in the enumeration tree. We present the Smuggler Search Problem as an important real-world application of our generalized Orienteering Problem. Numerical results show that our algorithm applied to the Smuggler Search Problem outperforms standard Mixed-Integer Nonlinear Programming solvers for moderate to large problem instances. We demonstrate model enhancements that allow practitioners to represent realistic search planning scenarios by accounting for multiple heterogeneous searchers and complex smuggler motion.
Naval Research Logistics (NRL), 2010
We consider a discrete time-and-space route-optimization problem across a finite time horizon in ... more We consider a discrete time-and-space route-optimization problem across a finite time horizon in which multiple searchers seek to detect one or more probabilistically moving targets. The paper formulates a novel convex mixed-integer nonlinear program for this problem that generalizes earlier models to situations with multiple targets, searcher deconfliction, and target-and location-dependent search effectiveness. We present two solution approaches, one based on the cutting-plane method and the other on linearization. These approaches result in the first practical exact algorithms for solving this important problem, which arises broadly in military, rescue, law enforcement, and border patrol operations. The cutting-plane approach solves many realistically sized problem instances in a few minutes, while existing branch-and-bound algorithms fail. A specialized cut improves solution time by 50% in difficult problem instances. The approach based on linearization, which is applicable in important special cases, may further reduce solution time with one or two orders of magnitude. The solution time for the cutting-plane approach tends to remain constant as the number of searchers grows. In part, then, we overcome the difficulty that earlier solution methods have with many searchers.
Naval Research Logistics, 2010
We formulate and solve a discrete-time path-optimization problem where a single searcher, operati... more We formulate and solve a discrete-time path-optimization problem where a single searcher, operating in a discretized 3-dimensional airspace, looks for a moving target in a finite set of cells. The searcher is constrained by maximum limits on the consumption of several resources such as time, fuel, and risk along any path. We develop a specialized branch-and-bound algorithm for this problem that utilizes several network reduction procedures as well as a new bounding technique based on Lagrangian relaxation and network expansion. The resulting algorithm outperforms a state-of-the-art algorithm for solving time-constrained problems and also is the first algorithm to solve multi-constrained problems.
Naval Research Logistics (NRL), 2011
Given a number of patrollers that are required to detect an intruder in a channel, the channel pa... more Given a number of patrollers that are required to detect an intruder in a channel, the channel patrol problem consists of determining the periodic trajectories that the patrollers must trace out so as to maximized the probability of detection of the intruder. We formulate this problem as an optimal control problem. We assume that the patrollers' sensors are imperfect and that their motions are subject to turn-rate constraints, and that the intruder travels straight down a channel with constant speed. Using discretization of time and space, we approximate the optimal control problem with a large-scale nonlinear programming problem which we solve to obtain an approximately stationary solution and a corresponding optimized trajectory for each patroller. In numerical tests for one, two, and three underwater patrollers, an underwater intruder, different trajectory constraints, several intruder speeds and other specific parameter choices, we obtain new insightnot easily obtained using simply geometric calculations-into efficient patrol trajectory design under certain conditions for multiple patrollers in a narrow channel where interaction between the patrollers is unavoidable due to their limited turn rate. 1 Quoting from Daily Mail Online, November 11th, 2007, "American military chiefs have been left dumbstruck by an undetected Chinese submarine popping up at the heart of a recent Pacific exercise and close to the vast U.S.S. Kitty Hawk-a 1,000 ft super carrier with 4,500 personnel on board. By the time it surfaced the 160 ft Song Class diesel-electric attack submarine is understood to have sailed within viable range for launching torpedoes or missiles at the carrier," by Matthew Hickley.
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Papers by Johannes Royset