ABSTRACT The generalized seniority scheme has long been proposed as a means of dramatically reduc... more ABSTRACT The generalized seniority scheme has long been proposed as a means of dramatically reducing the dimensionality of nuclear shell model calculations, when strong pairing correlations are present. However, systematic benchmark calculations, comparing results obtained in a model space truncated according to generalized seniority with those obtained in the full shell model space, are required to assess the viability of this scheme. Here, we extend recent calculations for semimagic nuclei, the Ca isotopes, to include nuclei with both valence protons and valence neutrons, namely, the Ti and Cr isotopes, taken in a full major shell and with realistic interactions.
This paper presents a stochastic optimization model for allocating and sharing a critical resourc... more This paper presents a stochastic optimization model for allocating and sharing a critical resource in the case of a pandemic. The demand for different entities peaks at different times, and an initial inventory from a central agency is to be allocated. The entities (states) may share the critical resource with a different state under a risk-averse condition. The model is applied to study the allocation of ventilator inventory in the COVID-19 pandemic by the Federal Emergency Management Agency of the US Department of Homeland Security (FEMA) to different states in the US. Findings suggest that if less than 60% of the ventilator inventory is available for non-COVID-19 patients, FEMA's stockpile of 20,000 ventilators (as of 03/23/2020) would be nearly adequate to meet the projected needs. However, when more than 75% of the available ventilator inventory must be reserved for non-COVID-19 patients, various degrees of shortfall are expected. In an extreme case, where the demand is ass...
In “A Repeated Route-then-Schedule Approach to Coordinated Vehicle Platooning: Algorithms, Valid ... more In “A Repeated Route-then-Schedule Approach to Coordinated Vehicle Platooning: Algorithms, Valid Inequalities and Computation,” Luo and Larson propose a novel repeated route-then-schedule algorithmic framework to efficiently solve a complex vehicle routing and scheduling problem arising in the intelligent transportation system. The goal is to maximize the collective savings of a set of vehicles (especially heavy-duty vehicles) by utilizing the fact that platooning vehicles save energy due to reduced aerodynamic drag. In the algorithm, the original simultaneous route-and-schedule approach is decomposed into the routing stage and scheduling stage with a sophisticated learning-like feedback mechanism to update the presumed fuel cost for each vehicle traversing through each road segment. This leads to an iterative change of objective function in the routing problem and thereby changes the routes that are fed to the scheduling problem. This approach helps identify high-quality solution. ...
Estimation of the $\phi$-divergence between two unknown probability distributions using empirical... more Estimation of the $\phi$-divergence between two unknown probability distributions using empirical data is a fundamental problem in information theory and statistical learning. We consider a multi-variate generalization of the data dependent partitioning method for estimating divergence between the two unknown distributions. Under the assumption that the distribution satisfies a power law of decay, we provide a convergence rate result for this method on the number of samples and hyper-rectangles required to ensure the estimation error is bounded by a given level with a given probability.
by Fengqiao Luo The limited capability of the traditional nuclear shell model in dealing with cal... more by Fengqiao Luo The limited capability of the traditional nuclear shell model in dealing with calculations for nuclei with large numbers of valence nucleons or with phenomena requiring multiple shells for their description motivated ongoing research on establishing an economical model space, one which still could reveal nuclear structural properties but in a lower dimensional space compared to the traditional shell model. Towards this goal, the generalized seniority shell model (GSSM) and the symplectic no-core shell model (Sp-NCSM) were developed. The GSSM is based on the BCS description of nucleon pairing. It is most effective for spherical and semimagic shell-configured nuclei. The Sp-NCSM is established on the SU(3) many-body basis motivated by the SU(3) symmetry structure of the harmonic oscillator many-nucleon basis states, embedded further with a higher Sp(3,R) symmetry, as an extension of SU(3) symmetry to multiple harmonic oscillator shells. We set up a recursive method to ...
This paper establishes and analyzes a service center location model with a simple but novel decis... more This paper establishes and analyzes a service center location model with a simple but novel decision-dependent demand induced from a maximum attraction principle. The model formulations are investigated in the distributionally-robust optimization framework for the capacitated and uncapacitated cases. A statistical model that is based on the maximum attraction principle for estimating customer demand and utility gain from service is established and analyzed. Novel valid (facet defining) inequalities for the deterministic problem are investigated for an independent interest. The numerical experiments show that the model admits high computational efficiency in solving midand large-size instances.
The generalized seniority approximation provides a truncation scheme for the nuclear shell model ... more The generalized seniority approximation provides a truncation scheme for the nuclear shell model based on building the states of the nucleus from nucleon pairs. We present a computer code to calculate matrix elements of one-body and two-body operators between generalized seniority states and overlaps of these states based on a set of recurrence relations.
We establish and analyze a service center location model with a simple but novel decision-depende... more We establish and analyze a service center location model with a simple but novel decision-dependent demand induced from a maximum attraction principle. The model formulations are investigated in the distributionally-robust optimization framework. A statistical model that is based on the maximum attraction principle for estimating customer demand and utility gain from service is established and analyzed. Combinatorial properties such as the submodularity and novel valid (facet defining) inequalities for the deterministic problem are investigated. The numerical experiments show that the model admits high computational efficiency in solving mid-size instances.
We study a service center location problem with ambiguous utility gains upon receiving service. T... more We study a service center location problem with ambiguous utility gains upon receiving service. The model is motivated by the problem of deciding medical clinic/service centers, possibly in rural communities, where residents need to visit the clinics to receive health services. A resident gains his utility based on travel distance, waiting time, and service features of the facility that depend on the clinic location. The elicited location-dependent utilities are assumed to be ambiguously described by an expected value and variance constraint. We show that despite a non-convex nonlinearity, given by a constraint specified by a maximum of two second-order conic functions, the model admits a mixed 0-1 second-order cone (MISOCP) formulation. We study the non-convex substructure of the problem, and present methods for developing its strengthened formulations by using valid tangent inequalities. Computational study shows the effectiveness of solving the strengthened formulations. Examples...
We develop a decomposition algorithm for distributionally-robust two-stage stochastic mixed-integ... more We develop a decomposition algorithm for distributionally-robust two-stage stochastic mixed-integer convex cone programs, and its important special case of distributionally-robust two-stage stochastic mixed-integer second order cone programs. This generalizes the algorithm proposed by Sen and Sherali~[Mathematical Programming 106(2): 203-223, 2006]. We show that the proposed algorithm is finitely convergent if the second-stage problems are solved to optimality at incumbent first stage solutions, and solution to an optimization problem to identify worst-case probability distribution is available. The second stage problems can be solved using a branch-and-cut algorithm. The decomposition algorithm is illustrated with an example. Computational results on a stochastic programming generalization of a facility location problem show significant solution time improvements from the proposed approach. Solutions for many models that are intractable for an extensive form formulation become poss...
We investigate robust optimization problems defined for maximizing convex functions. While the pr... more We investigate robust optimization problems defined for maximizing convex functions. While the problems arise in situations which are naturally modeled as minimization of concave functions, they also arise when a decision maker takes an optimistic approach to making decisions with convex functions. For finite uncertainty set, we develop a geometric branch-and-bound algorithmic approach to solve this problem. The geometric branch-and-bound algorithm performs sequential piecewise-linear approximations of the convex objective, and solves linear programs to determine lower and upper bounds at each node. Finite convergence of the algorithm to an $$\epsilon -$$ optimal solution is proved. Numerical results are used to discuss the performance of the developed algorithm. The algorithm developed in this paper can be used as an oracle in the cutting surface method for solving robust optimization problems with compact ambiguity sets.
ABSTRACT The generalized seniority scheme has long been proposed as a means of dramatically reduc... more ABSTRACT The generalized seniority scheme has long been proposed as a means of dramatically reducing the dimensionality of nuclear shell model calculations, when strong pairing correlations are present. However, systematic benchmark calculations, comparing results obtained in a model space truncated according to generalized seniority with those obtained in the full shell model space, are required to assess the viability of this scheme. Here, we extend recent calculations for semimagic nuclei, the Ca isotopes, to include nuclei with both valence protons and valence neutrons, namely, the Ti and Cr isotopes, taken in a full major shell and with realistic interactions.
This paper presents a stochastic optimization model for allocating and sharing a critical resourc... more This paper presents a stochastic optimization model for allocating and sharing a critical resource in the case of a pandemic. The demand for different entities peaks at different times, and an initial inventory from a central agency is to be allocated. The entities (states) may share the critical resource with a different state under a risk-averse condition. The model is applied to study the allocation of ventilator inventory in the COVID-19 pandemic by the Federal Emergency Management Agency of the US Department of Homeland Security (FEMA) to different states in the US. Findings suggest that if less than 60% of the ventilator inventory is available for non-COVID-19 patients, FEMA's stockpile of 20,000 ventilators (as of 03/23/2020) would be nearly adequate to meet the projected needs. However, when more than 75% of the available ventilator inventory must be reserved for non-COVID-19 patients, various degrees of shortfall are expected. In an extreme case, where the demand is ass...
In “A Repeated Route-then-Schedule Approach to Coordinated Vehicle Platooning: Algorithms, Valid ... more In “A Repeated Route-then-Schedule Approach to Coordinated Vehicle Platooning: Algorithms, Valid Inequalities and Computation,” Luo and Larson propose a novel repeated route-then-schedule algorithmic framework to efficiently solve a complex vehicle routing and scheduling problem arising in the intelligent transportation system. The goal is to maximize the collective savings of a set of vehicles (especially heavy-duty vehicles) by utilizing the fact that platooning vehicles save energy due to reduced aerodynamic drag. In the algorithm, the original simultaneous route-and-schedule approach is decomposed into the routing stage and scheduling stage with a sophisticated learning-like feedback mechanism to update the presumed fuel cost for each vehicle traversing through each road segment. This leads to an iterative change of objective function in the routing problem and thereby changes the routes that are fed to the scheduling problem. This approach helps identify high-quality solution. ...
Estimation of the $\phi$-divergence between two unknown probability distributions using empirical... more Estimation of the $\phi$-divergence between two unknown probability distributions using empirical data is a fundamental problem in information theory and statistical learning. We consider a multi-variate generalization of the data dependent partitioning method for estimating divergence between the two unknown distributions. Under the assumption that the distribution satisfies a power law of decay, we provide a convergence rate result for this method on the number of samples and hyper-rectangles required to ensure the estimation error is bounded by a given level with a given probability.
by Fengqiao Luo The limited capability of the traditional nuclear shell model in dealing with cal... more by Fengqiao Luo The limited capability of the traditional nuclear shell model in dealing with calculations for nuclei with large numbers of valence nucleons or with phenomena requiring multiple shells for their description motivated ongoing research on establishing an economical model space, one which still could reveal nuclear structural properties but in a lower dimensional space compared to the traditional shell model. Towards this goal, the generalized seniority shell model (GSSM) and the symplectic no-core shell model (Sp-NCSM) were developed. The GSSM is based on the BCS description of nucleon pairing. It is most effective for spherical and semimagic shell-configured nuclei. The Sp-NCSM is established on the SU(3) many-body basis motivated by the SU(3) symmetry structure of the harmonic oscillator many-nucleon basis states, embedded further with a higher Sp(3,R) symmetry, as an extension of SU(3) symmetry to multiple harmonic oscillator shells. We set up a recursive method to ...
This paper establishes and analyzes a service center location model with a simple but novel decis... more This paper establishes and analyzes a service center location model with a simple but novel decision-dependent demand induced from a maximum attraction principle. The model formulations are investigated in the distributionally-robust optimization framework for the capacitated and uncapacitated cases. A statistical model that is based on the maximum attraction principle for estimating customer demand and utility gain from service is established and analyzed. Novel valid (facet defining) inequalities for the deterministic problem are investigated for an independent interest. The numerical experiments show that the model admits high computational efficiency in solving midand large-size instances.
The generalized seniority approximation provides a truncation scheme for the nuclear shell model ... more The generalized seniority approximation provides a truncation scheme for the nuclear shell model based on building the states of the nucleus from nucleon pairs. We present a computer code to calculate matrix elements of one-body and two-body operators between generalized seniority states and overlaps of these states based on a set of recurrence relations.
We establish and analyze a service center location model with a simple but novel decision-depende... more We establish and analyze a service center location model with a simple but novel decision-dependent demand induced from a maximum attraction principle. The model formulations are investigated in the distributionally-robust optimization framework. A statistical model that is based on the maximum attraction principle for estimating customer demand and utility gain from service is established and analyzed. Combinatorial properties such as the submodularity and novel valid (facet defining) inequalities for the deterministic problem are investigated. The numerical experiments show that the model admits high computational efficiency in solving mid-size instances.
We study a service center location problem with ambiguous utility gains upon receiving service. T... more We study a service center location problem with ambiguous utility gains upon receiving service. The model is motivated by the problem of deciding medical clinic/service centers, possibly in rural communities, where residents need to visit the clinics to receive health services. A resident gains his utility based on travel distance, waiting time, and service features of the facility that depend on the clinic location. The elicited location-dependent utilities are assumed to be ambiguously described by an expected value and variance constraint. We show that despite a non-convex nonlinearity, given by a constraint specified by a maximum of two second-order conic functions, the model admits a mixed 0-1 second-order cone (MISOCP) formulation. We study the non-convex substructure of the problem, and present methods for developing its strengthened formulations by using valid tangent inequalities. Computational study shows the effectiveness of solving the strengthened formulations. Examples...
We develop a decomposition algorithm for distributionally-robust two-stage stochastic mixed-integ... more We develop a decomposition algorithm for distributionally-robust two-stage stochastic mixed-integer convex cone programs, and its important special case of distributionally-robust two-stage stochastic mixed-integer second order cone programs. This generalizes the algorithm proposed by Sen and Sherali~[Mathematical Programming 106(2): 203-223, 2006]. We show that the proposed algorithm is finitely convergent if the second-stage problems are solved to optimality at incumbent first stage solutions, and solution to an optimization problem to identify worst-case probability distribution is available. The second stage problems can be solved using a branch-and-cut algorithm. The decomposition algorithm is illustrated with an example. Computational results on a stochastic programming generalization of a facility location problem show significant solution time improvements from the proposed approach. Solutions for many models that are intractable for an extensive form formulation become poss...
We investigate robust optimization problems defined for maximizing convex functions. While the pr... more We investigate robust optimization problems defined for maximizing convex functions. While the problems arise in situations which are naturally modeled as minimization of concave functions, they also arise when a decision maker takes an optimistic approach to making decisions with convex functions. For finite uncertainty set, we develop a geometric branch-and-bound algorithmic approach to solve this problem. The geometric branch-and-bound algorithm performs sequential piecewise-linear approximations of the convex objective, and solves linear programs to determine lower and upper bounds at each node. Finite convergence of the algorithm to an $$\epsilon -$$ optimal solution is proved. Numerical results are used to discuss the performance of the developed algorithm. The algorithm developed in this paper can be used as an oracle in the cutting surface method for solving robust optimization problems with compact ambiguity sets.
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