Nonlinear projection equations (NPEs) provide a unified framework for addressing various constrained nonlinear optimization and engineering problems. However, when it comes to solving multiple NPEs, traditional numerical integration methods are not efficient enough. This is because traditional methods solve each NPE iteratively and independently. In this article, we propose a novel approach based on multitask learning (MTL) for solving multiple NPEs. The solution procedure is outlined as follows. First, we model each NPE as a system of ordinary differential equations (ODEs) using neurodynamic optimization. Second, for each ODE system, we use a physics-informed neural network (PINN) as the solution. Third, we use a multibranch MTL framework, where each branch corresponds to a PINN model. This allows us to solve multiple NPEs in parallel by training a single neural network model. Experimental results show that our approach has superior computational performance, especially when the number of NPEs to be solved is large.

This paper introduces a new neurodynamic duplex approach to address distributionally robust joint chanceconstrained optimization problems. We assume that the constraints' row vectors are independent, and their probability distributions belong to a specific distributional uncertainty set that is not known beforehand. Within our study, we examine two uncertainty sets for these unknown distributions. Our framework's key feature is the use of a neural network-based method to solve distributionally robust joint chance-constrained optimization problems, achieving an almost sure convergence to the optimum without relying on standard state-of-the-art solving methods. In the numerical section, we apply our proposed approach to solve a profit maximization problem, demonstrating its performance and comparing it against existing state-of-the-art methods.

We address radio resource allocation for the transport of extreme Ultra Reliable Low Latency and Reliability (URLLC) traffic. One illustrative use case is factory automation using 6G networks. In this context, extreme URLLC has very stringent Quality of Service (QoS) requirements: 0.1 ms for the delay and $10^{-7}$ for the reliability. Reliability can be even higher for other use cases. We model QoS in terms of outage probability, that is the likelihood of failing to serve at least one packet due to insufficient resources, and derive the minimal resource reservation that would meet such requirement. We formulate the problem as chance-constrained optimization and solve it assuming partial knowledge of arriving traffic distribution. We treat the case where traffic is described through its mean and variance, and make use of three approaches to find the optimal solution: distributionally robust using worst-case value at risk approach, distribution-based approximation and bounds from large deviation theory. We also solve the optimization problem using a data driven approach and propose a sliding window mechanism to perform it online. We compare the performance of the aforementioned approaches numerically and show the effectiveness of the data driven approach, accounting for user radio condition heterogeneity and thus different Modulation and Coding Schemes.

We propose a new performance model for transport of time-critical Ultra Reliable Low Latency Communications (URLLC) traffic in 5G networks and Beyond and apply it to dimensioning of such systems. The Quality of Service (QoS) requirement is formulated in terms of an outage probability which is defined as the probability that the latency exceeds a maximal allowed budget, and which should be kept very low. We develop a generic queuing model to compute this outage probability and adapt it to integrate the specificity of the 5G radio interface, taking into account the heterogeneity of users radio conditions and thus their Modulation and Coding Schemes (MCS) as well as retransmissions due to errors on the radio link. We also propose a low complexity method to calculate it using a geometric tail approach to approximate the tail distribution of the queue, for relevant arrival distributions: Poisson and Binomial. We show numerically the performance of our exact model and approximation and that they yield very accurate performance against simulations, and in comparison with other models from the state of the art. We also show the system dimensioning in terms of required resources to satisfy the outage constraint.

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In this article, we investigate the stochastic maximum weight forest problem. We present two mathematical formulations for the problem: a polynomial sized one based on the characterization of forests in graphs and a formulation with an exponential number of constraints. We give a proof of the correctness of the new formulation and present a polynomial reduction from the set cover problem to give some insight about the complexity of this problem. We introduce an L‐shaped decomposition approach for the polynomial formulation, thus allowing the optimal solution of large scale instances with up to 90 nodes. Finally, we propose a Kruskal based variable neighborhood search (VNS) metaheuristic to compute near optimal solutions with significantly less computational effort. Our numerical results show that the VNS approach provides tight near optimal solutions with a gap less than 1% for most of the instances. © 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 65(4), 289–305 2015

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We consider a workforce management problem arising in call centers, namely a staffing and shift-scheduling problem. It consists in determining the minimum-cost number of agents to be assigned to each shift of the scheduling horizon so as to reach the required customer quality of service. We assume that the mean call arrival rate in each period of the horizon is a random variable following a continuous distribution. We model the resulting optimization problem as a stochastic program involving joint probabilistic constraints. This allows to manage the risk of not reaching the required quality of service at the horizon level rather than on a period by period basis. We propose a solution approach based on linear approximations to provide heuristic solutions of the problem. We finally give numerical results carried out on a real-life instance. These results show that the proposed approach compares well with previously published approaches both in terms of risk management and cost minimization.

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Abstract This paper proposes two binary quadratically constrained quadratic programs for minimizing power subject to bit rate and subcarrier allocation constraints over wireless orthogonal frequency division multiple access. The first model represents a restricted case in which users are allowed to use only one modulation size in each subcarrier while the second, a more flexible real case in which they can use any size. We propose two semidefinite programming relaxations and compare with the linear programs obtained by applying Fortet linearization method. Numerical results show a total average tightness gain of 42.78 and 97.17% for the first and second quadratic model, respectively. Moreover, we get in average, near optimal lower bounds of 0.5 and 1% for the second model over random and realistic data, respectively. © 2011 Wiley Periodicals, Inc. NETWORKS, 2012

Abstract In this article, a mixed integer bilevel problem having a probabilistic knapsack constraint in the first level is proposed. The problem formulation is mainly motivated by practical pricing and service provision problems as it can be interpreted as a model for the interaction between a service provider and customers. A discrete probability space is assumed which allows a reformulation of the problem as an equivalent deterministic bilevel problem. The problem is further transformed into a linear bilevel problem, which in turn yields a quadratic optimization problem, namely the global linear complementarity problem. Based on this quadratic problem, a procedure to compute upper bounds on the initial problem by using a Lagrangian relaxation and an iterative linear minmax scheme is proposed. Numerical experiments confirm that the scheme practically converges.© 2011 Wiley Periodicals, Inc. NETWORKS, 2012

Abstract In this article, a detection strategy based on variable neighborhood search (VNS) and semidefinite relaxation of the multiuser model maximum likelihood (ML) is investigated. The VNS method provides a good method for solving the ML problem while keeping the integer constraints. A SDP relaxation is used as an efficient way to generate an initial solution in a limited amount of time, in particular using early termination. The SDP resolution tool used is the spectral bundle method developed by Helmberg. We show that using VNS can result in a better error rate, but at a cost of calculation time. © 2009 Wiley Periodicals, Inc. NETWORKS, 2010