This paper introduces a variant of the dynamic Facility Location Problem with modular capacities. Inspired by the challenges faced by cellular telecommunication networks, the problem seeks to optimize the placement and equipment of facilities to meet the fluctuating demand of clients while minimizing installation and operational costs. Selected facilities must provide coverage to the whole considered area. In addition, clients must be served by the active facility that provides the best quality of service. We propose two integer linear programming formulations and analyze their theoretical properties in terms of lower bound. Furthermore, we propose a reinforcement for one formulation and valid inequalities. To evaluate the performance of the proposed formulations, we performed computational experiments with a commercial solver on instances with up to 20 candidate sites and 60 clients. The formulations proved to be very sensitive to the size of the instances. The analysis, both theoretical and numerical, provides meaningful insights on the formulations performance, and it constitutes a key starting point for developing further approaches, either exact methods or heuristics.

Healthcare services are usually delivered by teams, each one composed of individuals working together sharing knowledge, experiences and skills. The staffing problem consists in finding an optimal set of teams with respect to a given performance metrics in such a way to meet a forecasted service demand, which determines the workload level. Various metrics can be used to measure the efficiency of one individual, and to evaluate the overall team performance. The random nature of the problem requires the introduction of random variables, and the characterisation of the overall team behaviour with a stochastic process. We propose hybrid algorithms based on generalised stochastic petri nets (GSPN) and optimisation. The basic idea is to exploit the GSPN model as a black box to evaluate a solution computed by an optimisation algorithm, that is the team performance under several demand scenarios. We test the proposed algorithms on a case study arising from an Italian Emergency Medical Services. The insights from the computational analysis confirm the validity of the proposed algorithms.

Federated learning (FL), particularly when data is distributed across multiple clients, helps reducing the learning time by avoiding training on a massive pile-up of data. Nonetheless, low computation capacities or poor network conditions can worsen the convergence time, therefore decreasing accuracy and learning performance. In this paper, we propose a framework to deploy FL clients in a network, while compensating end-to-end time variation due to heterogeneous network setting. We present a new distributed learning control scheme, named In-network Federated Learning Control (IFLC), to support the operations of distributed federated learning functions in geographically distributed networks, and designed to mitigate the stragglers with lower deployment costs.IFLC adapts the allocation of distributed hardware accelerators to modulate the importance of local training latency in the end-to-end delay of federated learning applications, considering both deterministic and stochastic delay scenarios. By extensive simulation on realistic instances of an in-network anomaly detection application, we show that the absence of hardware accelerators can strongly impair the learning efficiency. Additionally, we show that providing hardware accelerators at only 50% of the nodes, can reduce the number of stragglers by at least 50% and up to 100% with respect to a baseline FIRST-FIT algorithm, while also lowering the deployment cost by up to 30% with respect to the case without hardware accelerators. Finally, we explore the effect of topology changes on IFLC across both hierarchical and flat topologies.

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Managing uncertainty in surgery times presents a critical challenge in operating room (OR) scheduling, as it can have a significant impact on patient care and hospital efficiency. Objectives: By incorporating robustness into the decision-making process, we can provide a more reliable and adaptive solution compared to traditional deterministic approaches. Materials and methods: In this paper, we consider a cardinality-constrained robust optimization model for OR scheduling, addressing uncertain surgery durations. By accounting for patient waiting times, urgency levels and delay penalties in the objective function, our model aims to optimise patient-centred outcomes while ensuring operational resilience. However, to achieve an appropriate balance between resilience and robustness cost, the robustness level must be carefully tuned. In this paper, we conduct a comprehensive analysis of the model’s performance, assessing its sensitivity to robustness levels and its ability to handle different uncertainty scenarios. Results: Our results show significant improvements in patient outcomes, including reduced waiting times, fewer missed surgeries and improved prioritisation of urgent cases. Key contributions of this research include an evaluation of the representativeness and performance of the patient-centred objective function, a comprehensive analysis of the impact of robustness parameters on OR scheduling performance, and insights into the impact of different robustness levels. Conclusions: This research offers healthcare providers a pathway to increase operational efficiency, improve patient satisfaction, and mitigate the negative effects of uncertainty in OR scheduling.

This paper proposes a new hybrid strategy to optimally design membrane separation problems. We formulate the problem as a Non-Linear Programming (NLP) model. A common approach to represent the physical behavior of the membrane is to discretize the system of differential equations that govern the separation process. Instead, we represent the input/output behavior of the single membrane by an artificial neural network (ANN) predictor. The ANN is trained on a dataset obtained through the MEMSIC simulator. The equation form of the trained predictor (shape and weights) is then inserted in the NLP model at the place of the discretized system of differential equations. To improve the ANN accuracy without an excessive computational burden, we propose data augmentation strategies to target the regions where densify the dataset. We compare a data augmentation strategy from the literature with a novel one that densifies the dataset around the stationary points visited by a global optimization algorithm. Our approach was validated using a relevant industrial case study: hydrogen purification. Validation by simulation is performed on the obtained solutions. The computational results show that a data augmentation smartly coupled with optimization can produce a robust and reliable design tool.

The Network Function Virtualization (NFV) service chaining problem, which involves locating Virtual Network Functions (VNFs) in an NFV-enabled network and routing network demands through their required VNFs, is key to the success of NFV. Solving the chaining problem can efficiently reduce required network resources, and thus reducing capital expenditures (CAPEX) and operational expenditures (OPEX). Previous works mainly focus on finding heuristic solutions, rather than investigating the intrinsic features of the problem. In this paper, we investigate the features of the problem from both theoretical and numerical points of view, by shrinking the NFV service chaining problem into a particular version and conducting tests to study what makes the NFV service chaining problem fundamentally difficult to solve. Results reveal that the demand routing part of the problem has a significant impact on solving the mathematical formulated problem, i.e., finding a feasible routing can be time-consuming. We further propose constructive methods that improve upon the mathematical formulation, which make the time of finding the optimal solution be reduced in most cases.

Edge intelligence combined with federated learning is considered as a way to distributed learning and inference tasks in a scalable way, by analyzing data close to where it is generated, unlike traditional cloud computing where data is offloaded to remote servers.In this paper, we address the placement of Artificial Intelligence Functions (AIF) making use of federated learning and hardware acceleration.We model the behavior of federated learning and related inference point to guide the placement decision, taking into consideration the specific constraint and the empirical behavior of a virtualized infrastructure anomaly detection use-case.Besides hardware acceleration, we consider the specific training time trend when distributing training over a network, by using empirical piece-wise linear distributions.We model the placement problem as a MILP and we propose a variant of the problem.Simulation results show the impact that hardware acceleration can have in the decision of the number of AIF to enable, while dividing by a relevant factor the distributed training time.We also show how our approach exacerbates the importance of monitoring an end-to-end learning system delay budget composed of link propagation delay and distributed training time in the location of AIFs.

Thanks to the increased availability of computing capabilities in data centers, the recently proposed virtual network function paradigm can be used to keep up with the increasing demand for network services as internet and its applications grow. The problem arises then of managing the virtual network functions, that is, to decide where to instantiate the functions and how to route the demands to reach them. While it arises in an application field, the Virtual Network Function placement and routing problem combines location and routing aspects in an interesting, challenging problem. In this paper, we propose several ILP‐based heuristics and compare them on a dataset that includes instances with different sizes, network topologies, and service capacity. The heuristics prove effective in tackling even large size instances, with up to 50 nodes and more than 80 arcs.

Membrane separation is a key technology for biogas purification. Multistaged processes based on either cellulose acetate (CA) or polyimide (PI) materials are classically used for this application. In this study, a systematic process synthesis optimization is performed in order to identify the most cost effective solution for three different membrane materials (CA, PI and zeolite) and three different outlet pressure levels (5, 10 and 15 Bar). It is shown that a costly (i.e. 2000 EUR per square meter vs 50 for CA and PI) but high performance membrane material such a zeolite offers the best cost effective solution compared to commercially available polymeric membranes. Increasing the outlet pressure increases the purification cost. Two stages processes with recycling loops offer the best balance between purity, recovery, complexity and cost, whatever the outlet pressure level. The use of vacuum pumping is shown to improve the process economy, while expander and extra feed compression do not show an interest.

The mass diffusion of internet applications, both from computers and mobiles, has yielded to an increasing demand for network services with which the expensive and not flexible hardware appliances cannot keep up. On the other hand, computational capability has become available on the network nodes connected with computing servers and the cloud. This has suggested the network functions virtualization paradigm: services are provided on a software basis thus giving a flexible and cost effective response to the request for services. The network functions virtualization proposes challenging optimization problems such as the virtual network functions (VNFs) chaining problem, where service instances must be located on some network nodes and each demand must be routed through the services it requires. Most of the literature is currently focused on heuristic solutions, rather than on studying the problem properties or comparing approaches. With the aim of investigating the problem properties and comparing existing formulations, both from the theoretical and the numerical points of view, we consider a single service VNFs chaining problem, with different link and service capacities and the objective of minimizing the number of installed VNF instances.

Nitrogen production from air by membrane gas separation processes is a mature technology which is applied in numerous industrial sectors (chemical, food, aeronautics, space..). Depending on the nitrogen purity requirements (typically between 90 and 99.9%), single stage or multistage membrane process configurations are used. A very large number of advanced membrane materials have been recently reported, showing increasing permeability and/or selectivity for air separation applications (i.e. trade-off limits of dense polymeric materials for the O2/N2 gas pair) compared to the commercially available membranes. The interest of these new materials in terms of nitrogen production cost and their impact in terms of process configuration are reported through a process synthesis study. Based on a tailor made optimization methodology and program, the production cost and associated optimal process configuration are first identified for two standard O2/N2 separation membranes at four different levels of N2 purity (90, 95, 99, 99.9%). The same strategy is then performed with advanced trade-off membrane materials, with the possibility to combine different materials in multistaged systems. The impact in terms of nitrogen production cost for the different purities and the corresponding optimal membrane materials and process configurations are discussed. Surprisingly, a medium membrane selectivity combined to a high permeability is shown to systematically offer the best set of performances, for mono or multistaged systems. Vacuum operation and recycling loops are shown to generate lower N2 production costs.

The demand for network services, such as proxy or firewall, is ever increasing due to the massive diffusion of applications, both on computers and mobile devices. Virtual Network Functions allow to instantiate network services on clouds in a software based manner, thus allowing to dynamically provide services at a reasonable cost. In this work we consider the problem of placing Virtual Network Function instances (services) and routing the demands so as to guarantee that demands can reach the requested services. We discuss the complexity of a particular version of the Virtual Network Function placement and routing problem and the impact of the network topology on the problem complexity.

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. A journey through optimization: from global to discrete optimization and back. Bernardetta Addis

A Global Optimization approach of membrane gas separation processes, based on a general process superstructure including a wide array of possible configurations, and solved by a Nonlinear Programming formulation is presented. The capacity of the proposed approach to provide optimal configurations at minimum separation cost is first validated by comparing the obtained solutions with those of a reference study in the domain. The optimization approach is then applied to the optimization of CO2 capture from blast furnace gas considering multistage processes with up to four membrane stages. The optimal process configuration and main process variables, upstream and downstream pressure and membrane area, are determined for processes with CO2 recoveries of 90%, 95% and 99% and N2 residual contents of 1%, 0.5% and 0.1%. The resulting separation cost is in the range of 29–45 EUR/ton CO2 based on a NETL type cost model. Two stage permeate cascades (enrichers) with retentate recycle are shown to be the optimal configuration for N2 residual contents down to 1% at any recovery and down to 0.5% at 90% recovery. For larger recovery or purity levels, three stage processes offered the lowest separation cost. Four stage processes offered no marked improvement over three stage processes.