American Institute of Mathematical Sciences

A painful lesson got from pandemic COVID-19 is that preventive healthcare service is of utmost importance to governments since it can make massive savings on healthcare expenditure and promote the welfare of the society. Recognizing the importance of preventive healthcare, this research aims to present a methodology for designing a network of preventive healthcare facilities in order to prevent diseases early. The problem is formulated as a bilevel non-linear integer programming model. The upper level is a facility location and capacity planning problem under a limited budget, while the lower level is a user choice problem that determines the allocation of clients to facilities. A genetic algorithm (GA) is developed to solve the upper level problem and a method of successive averages (MSA) is adopted to solve the lower level problem. The model and algorithm is applied to analyze an illustrative case in the Sioux Falls transport network and a number of interesting results and managerial insights are provided. It shows that solutions to medium-scale instances can be obtained in a reasonable time and the marginal benefit of investment is decreasing.

This paper describes the optimal fish-feeding in a three-dimensional calm freshwater pond based on the concentrations of seven water quality variables. A certain number of baby fishes are inserted into the pond simultaneously. They are then taken out of the pond simultaneously for harvest after having gone through a feeding program. This feeding program creates additional loads of water quality variables in the pond, which becomes pollutants. Thus, an optimal fish-feeding problem is formulated to maximize the final weight of the fishes, subject to the restrictions that the fishes are not under-fed and over-fed and the concentrations of the pollutants created by the fish-feeding program are not too large. A computational scheme using the finite element Galerkin scheme for the three-dimensional cubic domain and the control parameterization method is developed for solving the problem. Finally, a numerical example is solved.

This paper investigates the mean-field stochastic linear quadratic optimal control problem of Markov regime switching system (M-MF-SLQ, for short). The representation of the cost functional for the M-MF-SLQ is derived using the technique of operators. It is shown that the convexity of the cost functional is necessary for the finiteness of the M-MF-SLQ problem, whereas uniform convexity of the cost functional is sufficient for the open-loop solvability of the problem. By considering a family of uniformly convex cost functionals, a characterization of the finiteness of the problem is derived and a minimizing sequence, whose convergence is equivalent to the open-loop solvability of the problem, is constructed. We demonstrate with a few examples that our results can be employed for tackling some financial problems such as mean-variance portfolio selection problem.

This paper considers an optimal investment problem under CRRA utility with a borrowing constraint. We formulate it into a free boundary problem consisting of a fully nonlinear equation and a linear equation. We prove the existence and uniqueness of the classical solution and present the condition for the existence of the free boundary under a linear constraint on a borrowing rate. Furthermore, we prove that the free boundary is continuous and smooth when the relative risk aversion coefficient is sufficiently small.

The spectral norm and the nuclear norm of a third order tensor play an important role in the tensor completion and recovery problem. We show that the spectral norm of a third order tensor is equal to the square root of the spectral norm of three positive semi-definite biquadratic tensors, and the square roots of the nuclear norms of those three positive semi-definite biquadratic tensors are lower bounds of the nuclear norm of that third order tensor. This provides a way to estimate and to evaluate the spectral norm and the nuclear norm of that third order tensor. Some upper and lower bounds for the spectral norm and nuclear norm of a third order tensor, by spectral radii and nuclear norms of some symmetric matrices, are presented.

We consider integrated scheduling of production and distribution operations associated with two customers (agents). Each customer has a set of orders to be processed on the single production line at a supplier on a competitive basis. The finished orders of the same customer are then packed and delivered to the customer by a third-party logistics (3PL) provider with a limited number of delivery transporters. The number of orders carried in a delivery transporter cannot exceed its delivery capacity. Each transporter incurs a fixed delivery cost regardless of the number of orders it carries, and departs from the 3PL provider to a customer at fixed times. Each customer desires to minimise a certain optimality criterion involving simultaneously the customer service level and the total delivery cost for its orders only. The customer service level for a customer is related to the times when its orders are delivered to it. The problem is to determine a joint schedule of production and distribution to minimise the objective of one customer, while keeping the objective of the other customer at or below a predefined level. Using several optimality criteria to measure the customer service level, we obtain different scenarios that depend on optimality criterion of each customer. For each scenario, we either devise an efficient solution procedure to solve it or demonstrate that such a solution procedure is impossible to exist.

We develop a power penalty approach to a finite-dimensional double obstacle problem. This problem is first approximated by a system of nonlinear equations containing two penalty terms. We show that the solution to this penalized equation converges to that of the original obstacle problem at an exponential rate when the coefficient matrices are \begin{document}$ M $\end{document}-matrices. Numerical examples are presented to confirm the theoretical findings and illustrate the efficiency and effectiveness of the new method.

In this paper, we consider the new online scheduling model with linear lookahead intervals, which has the character that at any time \begin{document}$ t $\end{document}, one can foresee the jobs that will coming in the time interval \begin{document}$ (t, \lambda t+\beta ] $\end{document} with \begin{document}$ \lambda\geq1, \beta\geq 0 $\end{document}. We consider online scheduling of unit length jobs on \begin{document}$ m $\end{document} identical parallel-batch machines under this new lookahead model to minimize the maximum flowtime and the makespan, respectively. We give some lower bounds for these problems with the batch capacity \begin{document}$ b = \infty $\end{document} and \begin{document}$ b<\infty $\end{document}, respectively. And for the bounded model to minimize makespan, we give an online algorithm with competitive ratio \begin{document}$ 1+\alpha $\end{document} for \begin{document}$ 1\leq \lambda <4/3, 0\leq \beta\leq \frac{4-3\lambda}{6} $\end{document} and \begin{document}$ \frac{3}{2} $\end{document} for \begin{document}$ \lambda\geq1, 0\leq\beta<1 $\end{document}, where \begin{document}$ \alpha $\end{document} is the positive root of \begin{document}$ \lambda\alpha^2+(\lambda+\beta)\alpha+\beta-1 = 0 $\end{document}. The online algorithm is best possible when \begin{document}$ 1\leq \lambda <4/3, 0\leq \beta\leq \frac{4-3\lambda}{6} $\end{document}.

We present an effective hybrid metaheuristic of integrating reinforcement learning with a tabu-search (RLTS) algorithm for solving the max–mean dispersion problem. The innovative element is to design using a knowledge strategy from the \begin{document}$ Q $\end{document}-learning mechanism to locate promising regions when the tabu search is stuck in a local optimum. Computational experiments on extensive benchmarks show that the RLTS performs much better than state-of-the-art algorithms in the literature. From a total of 100 benchmark instances, in 60 of them, which ranged from 500 to 1, 000, our proposed algorithm matched the currently best lower bounds for all instances. For the remaining 40 instances, the algorithm matched or outperformed. Furthermore, additional support was applied to present the effectiveness of the combined RL technique. The analysis sheds light on the effectiveness of the proposed RLTS algorithm.

Heating, Ventilation, and Air-Condition (HVAC) systems are considered to be one of the essential applications for modern human life comfort. Due to global warming and population growth, the demand for such HVAC applications will continue to increase, especially in arid areas countries like the Arabian Gulf region. HVAC systems' energy consumption is very high and accounts for up to 70% of the total load consumption in some rapidly growing GCC countries such as Qatar. Additionally, the local extremely hot weather conditions usually lead to typical power demand peak issues that require adequate mitigation measures to ensure grid stability. In this paper, a novel control scheme for a combined group of Air-Conditioners is proposed as a peak-shaving strategy to address high power demand issues for Photo-Voltaic(PV)-integrated micro-grid applications. Using the local daily ambient temperature as input, the AC group control optimization is formulated as a Mixed-Integer Quadratic Programming (MIQP) problem. Under an acceptable range of indoor temperatures, the units in the same AC group are coordinately controlled to generate desired power consumption performance that is capable of shaving load peaks for both power consumption and PV generation. Finally, various simulations are performed that demonstrate the effectiveness of the proposed control strategy.

Considering the parameter uncertainty and actuator failure of hypersonic vehicle during maneuvering, this paper proposes a state observer-based hypersonic vehicle fault-tolerant control (FTC) system design method. Because hypersonic vehicles are prone to failure during maneuvering, the state quantity cannot be measured. First, a state observer-based FTC control method is designed for the linear parameter-varying (LPV) model with parameter uncertainty and partial failure of the actuator. Then, the Lyapunov function is used to demonstrate the asymptotic stability of the closed-loop system. The performance index function proved that the system has robust stability under the disturbance condition. Subsequently, the linear matrix inequality (LMI) was used to solve the observer parameters and the corresponding gain matrix in the control system. The simulation results indicated that the designed controller can track the flight command signal stably and has strong robustness, which verified the effectiveness of the design controller.