A Mixed Integer Linear Programming Formulation and Heuristics for Delay-Aware Neural Network Placement Problem in In-Network Learning

In this paper, we seek to jointly minimize the network power consumption and the user transmission delays in green wireless access networks. We recently studied the case of a WLAN, where we evaluated the tradeoffs between these two minimization objectives using a Mixed Integer Linear Programming (MILP) formulation. However, the MILP formulation could not deliver solutions in a reasonable amount of time due to computational complexity issues. As a result, we propose here a heuristic algorithm for the power-delay minimization problem. The proposed heuristic aims to compute the transmit power level of the Access Points (APs) deployed in the network and associate users with these APs in a way that jointly minimizes the total network power and the total network delay. The simulation results show that the proposed algorithm has a low computational complexity, which makes it advantageous compared with the optimal scheme, particularly in dense networks. Moreover, the heuristic algorithm performs close to optimally and provides power savings of up to 45% compared with legacy networks.

In the literature, e.g. [10], one can find the so-called basic UAV mission target assignment in which m UAVs each with a capacity limit q visit n targets in a cooperative manner (and return to their departure points) such that the cost incurred by each UAV’s travel is minimized. In [10], we proposed a mixed integer linear program (MILP) formulation which exactly solves the problem, as well as four alternative MILP formulations which are computationally less intensive (and therefore suited for real-time purposes) yet yield a theoretically guaranteed sub-optimal solution. In this chapter, we further consider timing constraints imposed on some p of the targets, so-called prime targets. This consideration is often required for scenarios in which prime targets must be visited in a pre-defined time interval, and mathematically results in the addition of several integer linear constraints to the previous MILP formulation making the problem computationally intractable. We propose a novel procedure of adding these cumbersome timing constraints to the previous MILP formulation, in order to avoid increasing too much computational cost under practically valid assumptions. We first show that the proposed procedure still guarantees the previously claimed theoretical solution quality associated with the basic mission. We then show through extensive numerical simulations that under certain conditions, our algorithms return solutions which are still computationally manageable.

One of the main obstacles in using mixed integer linear programming (MILP) formulations for large-scale open pit production scheduling is the size of the problem. The objective of this work is to develop, implement, and verify deterministic MILP formulations for long-term large-scale open pit production scheduling problems. The objective of the model is to maximize the net present value, while meeting grade blending, mining and processing capacities, and the precedence of block extraction constraints. We present four MILP formulations; the first two models are modifications of available models; we also propose, test and validate two new MILP formulations. To reduce the number of binary integer variables in the formulation, we aggregate blocks into larger units referred to as mining-cuts. We compare the performances of the proposed models based on net present value generated, practical mining production constraints, size of the mathematical programming formulations, the number of integer variables required in formulation, and the computational time required for convergence. An iron ore mine case study is represented to illustrate the practicality of the models as well.

Optimal operation of water-energy microgrids; a mixed integer linear programming formulation

The redundancy allocation problem (RAP) aims to find an allocation of redundant components that maximizes system reliability under resource constraints. In this paper, we consider the RAP for complex systems with heterogeneous components, which may have bridges or interconnecting subsystems and are generally more complicated in structure than commonly studied series-parallel systems. A major challenge of the RAP is that the reliability function is nonlinear. To tackle this, we develop six exact mixed integer linear programming (MILP) formulations, which, to our knowledge, are the first of such formulations for the problem. The key idea is to use binary variables and big-M constraints to successively linearize each product term in the reliability function. In addition, we propose a novel tree representation of the reliability function to establish the interconnections between different product terms, which is then used to reduce the number of decision variables and constraints needed in the linearization. We also propose an alternative form of the reliability function that only involves the failure probabilities of subsystems, and leverage this to derive better variable bounds, smaller big-M constants, and simpler formulations. We compare the six MILP formulations by solving them directly using an MILP solver based on three sets of test instances of varying complexity. Results indicate that all formulations achieve optimal solutions quickly for the first set and within reasonable computation times for the second set. For the third set, two formulations can always be solved within a given time limit. Overall, the MILP formulation derived based on the alternative form of the reliability function and a specific type of tree representation scheme performs the best. We also demonstrate that our approach is more robust and scalable than a benchmark branch-and-bound method. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This work was supported by National Natural Science Foundation of China [Grants 72310107003, 72471189, 71901176]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0842 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0842 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Joint scheduling and power control schemes have previously been proposed to reduce power dissipation in wireless ad hoc networks. However, instead of power consumption, throughput is a more important performance concern for some emerging multihop wireless networks, such as wireless mesh networks. This paper examines joint link scheduling and power control with the objective of throughput improvement. The MAximum THroughput link Scheduling with Power Control (MATH-SPC) problem is first formulated and then a mixed integer linear programming (MILP) formulation is presented to provide optimal solutions. However, simply maximizing the throughput may lead to a severe bias on bandwidth allocation among links. To achieve a good tradeoff between throughput and fairness, a new parameter called the demand satisfaction factor (DSF) to characterize the fairness of bandwidth allocation and formulate the MAximum Throughput fAir link Scheduling with Power Control (MATA-SPC) problem is defined. An MILP formulation and an effective polynomial-time heuristic algorithm, namely, the serial linear programming rounding (SLPR) heuristic, to solve the MATA-SPC problem are also presented. Numerical results show that bandwidth can be fairly allocated among all links/flows by solving the MILP formulation or by using the heuristic algorithm at the cost of a minor reduction of network throughput. In addition, extensions to end-to-end throughput and fairness and multiradio wireless multihop networks are discussed.

An MILP formulation for optimizing detailed schedules of a multiproduct pipeline network

An elastic optical network (EON) plays an important role in transport technology for virtualization of networks. A key aspect of EONs is to establish lightpaths (virtual links) with exactly the amount of spectrum that is needed and with the possibility of grooming, the process of grouping many small traffic flows into larger units, creating a super-lightpath. Grooming eliminates the need for many guard bands between lightpaths and also saves transceivers; however, it often leads to the need to perform optical–electrical–optical conversions to multiple-data-rate optical signals at intermediate nodes. The aim of this paper is to provide a mixed-integer linear programming (MILP) formulation, as well as heuristic and meta-heuristic approaches, for the design of multiple virtual optical networks (VONs) in an elastic optical substrate network with bandwidth-variable lightpaths, modulation format constraints, and virtual elastic regenerator placement. Traffic grooming is allowed inside each VON, and a distance-adaptive modulation format technique is employed to guarantee efficiency in terms of bandwidth for a physical substrate, subject to several virtual topologies. A reduced MILP formulation without grooming capability is also proposed for comparison. The complete MILP formulation jointly solves the virtual topology design, regenerator placement, and grooming problems, as well as the routing, modulation, and spectrum assignment (RMSA) problem. The reduced MILP formulation, heuristics, and meta-heuristic, on the other hand, separate the virtual topology design problem from the RMSA problem. It is shown that the grooming approach can provide good results, since it solves the problem for a complete design when compared to the approach without grooming. Furthermore, heuristic solutions for large networks are proposed, which present good performance (in terms of saving spectrum) for the design with large instances.

Autonomous vehicles have emerged as transformative technologies with vast implications across various domains, including surveillance. However, they are constrained by battery limitations, which can hinder their usability and efficiency. Designing algorithms to efficiently utilize them optimizing their battery usage, is crucial to unlocking their full potential. This paper addresses this challenge by studying an extension of the rural postman problem with multiple depots and rechargeable and reusable vehicles that can make multiple trips but have limited battery capacity. It presents a new Mixed Integer Linear Programming (MILP) formulation to find optimal solutions to the problem and proposes a new heuristic called the multi-trip (MT) algorithm. The paper describes the results of a study that tested the MT algorithm, other heuristics, and the MILP formulation on both benchmark instances and larger, real-world instances generated from road maps. Our results show that the MT algorithm found feasible solutions for every instance and produced better solutions than heuristics from the literature on 38 of the 39 instances that were tested. Due to its requirements for memory and computing time, the Gurobi optimizer used for solving the MILP formulation could not find optimal solutions for the largest instances that we tested. This research contributes to enhancing the efficiency and effectiveness of battery-operated unmanned by developing new heuristics to address the challenge of battery limitations.

Throughput is an important performance consideration for multihop wireless networks. In this paper, we study the joint link scheduling and power control problem, focusing on maximizing the network throughput. We formulate the maximum throughput link scheduling with power control (MATH-SPC) problem, and present a mixed integer linear programming (MILP) formulation to provide optimal solutions. However, simply maximizing the throughput leads to a severe bias on bandwidth allocation among all links. In order to enhance both throughput and fairness, we define a new parameter, the demand satisfaction factor (DSF), to characterize the fairness of bandwidth allocation. We formulate the maximum throughput fair link scheduling with power control (MATA-SPC) problem and present an MILP formulation for this problem. We also present an effective polynomial time heuristic algorithm, namely, the serial LP rounding (SLPR) heuristic. Our numerical results show that bandwidth can be fairly allocated among all links/flows by solving our MATA-SPC formulation or using our heuristic algorithm at the cost of a minor reduction of network throughput

Mixed integer linear programming for the design of solar thermal energy systems with short-term storage

The purpose of this research is to solve a general job shop problem with alternative machine routings. We consider four performance measures: mean flow time, makespan, maximum lateness, and total absolute deviation from the due dates. We first develop mixed-integer linear programming (MILP) formulations for the problems. The MILP formulations can be used either to compute optimal solutions for small-sized problems or to test the performance of existing heuristic algorithms. In addition, we have developed a genetic algorithm that can be used to generate relatively good solutions quickly. Further, computational experiments have been performed to compare the solution of the MILP formulations with that of existing algorithms.

A fundamental knowledge of the trade-off between sensor cooperation and autonomous vehicles' (AV) trajectory planning is pivotal towards characterizing the sensing capabilities of wireless sensor networks that employ AV for collecting the data and to ensure their successful integration in large scale sensor deployments. We formulate the problem of efficient data gathering as a mixed integer linear programming (MILP) problem that provides a joint optimization of AV trajectory and data-routing. Since MILP formulations are not scalable, we propose an approach to develop heuristics where the joint optimization is decoupled into three sub-problems. The first is to determine clusters of sensors with communication range limitations. The second is to efficiently connect the clusters. The third is to design the route inside the cluster that will minimize the cost of data collection. We characterize performance of the proposed heuristics through Monte-Carlo simulations. Performance is measured in terms of (a) the joint energy cost for cooperation and AV movement for different number of sensor nodes and communication ranges of these sensors, and (b) computational effort of the various heuristics. For small deployments, we compare the heuristics to the MILP global optimization and show that the gap between them can be lower than 2% for deployments as large as 18 nodes and typically below 25% for a wide range of scenarios.

This paper studies the problem of computing an input vector for a given pair of Artificial Neural Network (ANN) and output vector, which is a kind of inverse problem. This problem has potential applications in design of new objects, especially in design of new chemical compounds. This paper focuses on ANNs in which activation functions are represented as continuous piece-wise linear functions, which can exactly represent ReLU functions and well approximate sigmoid functions. It is shown that this inverse problem can be formulated as a Mixed Integer Linear Programming Problem (MILP) with O(|V | + nb) variables and constraints, where V is a set of neurons in a given ANN and nb denotes the total number of break points over all activation functions fv, v ϵ V.

MILP and MINLP models for the optimal scheduling of multi-energy systems accounting for delivery temperature of units, topology and non-isothermal mixing