Nonconvex Mixed-integer Nonlinear Programming Research Articles

Federated Learning Over Multihop Wireless Networks With In-Network Aggregation

Communication limitation at the edge is widely recognized as a major bottleneck for federated learning (FL). Multi-hop wireless networking provides a cost-effective solution to enhance service coverage and spectrum efficiency at the edge, which could facilitate large-scale and efficient machine learning (ML) model aggregation. However, FL over multi-hop wireless networks has rarely been investigated. In this paper, we optimize FL over wireless mesh networks by taking into account the heterogeneity in communication and computing resources at mesh routers and clients. We present a framework that each intermediate router performs <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in-network</i> model aggregation before sending the data to the next hop, so as to reduce the outgoing data traffic and hence aggregate more models under limited communication resources. To accelerate model training, we formulate our optimization problem by jointly considering model aggregation, routing, and spectrum allocation. Although the problem is a non-convex mixed-integer nonlinear programming, we transform it into a mixed-integer linear programming (MILP), and develop a coarse-grained fixing procedure to solve it efficiently. Simulation results demonstrate the effectiveness of the solution approach, and the superiority of the in-network aggregation scheme over the counterpart without in-network aggregation.

Reinforcement Learning-Based Near-Optimal Load Balancing for Heterogeneous LiFi WiFi Network

Owing to the nonoverlapping spectrum, light fidelity (LiFi) and WiFi technologies can coexist and form a heterogeneous LiFi WiFi network (HLWN). The performance of HLWN significantly depends upon the load balancing strategies. Since load balancing of HLWN is a nonconvex mixed-integer nonlinear programming optimization problem, it is mathematically intractable, and therefore, the conventional optimization methods fail to provide an optimal global solution. Although an optimal solution can be obtained using the exhaustive search method, it would be computationally complex. Therefore, in this article, a reinforcement learning (RL)-based algorithm is explored for solving the load balancing problem for the downlink HLWN at reasonably low complexity and near optimal performance. We have proposed three different reward functions for RL; the first and second reward functions work toward maximizing average network throughput and user satisfaction, respectively. The third reward function is designed to maximize the long-term system throughput and ensure at least 50% user’s satisfaction for all users. In order to study the effects of link aggregation on the system performance, this article considers two different types of receiver schemes, namely, single access point (SAP) and link aggregation (LA) scheme. While the SAP allows the user to receive data only from an SAP, the LA scheme allows the user to receive data simultaneously from both LiFi and WiFi AP. This article also includes effect of random orientation of the receiver device and handover overhead. Furthermore, concepts of domain knowledge have been included in this article to reduce the computational complexity of the algorithm. The proposed system performance is compared with the the following two benchmarks: received signal strength (RSS) and exhaustive search based on the computational complexity, average system throughput, and user satisfaction. It is shown that the proposed RL scheme outperforms the RSS scheme in average system throughput and user satisfaction. The RL scheme with an appropriate reward function provides a matching performance to the exhaustive search at reasonably low complexity.

Nuclear Accident Emergency Response System: Radiation Field Estimation and Evacuation

In this paper, a nuclear accident emergency response system based on unmanned aerial vehicles (UAVs) and bus collaboration is designed for radiation field estimation and evacuation. When a nuclear accident occurs, the radiation field is estimated firstly using the measurements acquired by UAVs. Based on the Cramer–Rao Lower Bound (CRLB), the coordinate optimization combined with UAV routing is formulated as a nonconvex mixed integer nonlinear programming (MINLP) problem to maximize the estimation accuracy. Further, a two-stage solution procedure based on genetic algorithm (GA) is proposed to solve the above problem. Then, taking the predicted radiation field as input, personnel in the emergency planning zone (EPZ) are evacuated to shelters by buses. The evacuation routing problem for minimizing both the total radiation exposure and evacuation time is formulated as a mixed integer linear programming (MILP) problem, which is solvable with efficient commercial solvers, such as Gurobi and CPLEX. The simulation results indicate that the system can provide effective help for emergency management under the nuclear accident scenarios.

Joint Clustering and Power Allocation in Coordinated Multipoint Assisted C-NOMA Cellular Networks

We consider a wireless network consisting of two adjacent cells, where the joint transmission (JT) coordinated multipoint (CoMP) is established to assist the user equipments (UEs) located at the edge of each cell. In addition, full-duplex (FD) cooperative non-orthogonal-multiple-access (C-NOMA) is invoked within each cell to improve the data rates of the UEs and to assist those at the cell edge. The UEs are categorized into two groups, namely, cell-center UEs (<inline-formula> <tex-math notation="LaTeX">$CUs$ </tex-math></inline-formula>) and cell-edge UEs (<inline-formula> <tex-math notation="LaTeX">$EUs$ </tex-math></inline-formula>). The <inline-formula> <tex-math notation="LaTeX">$CUs$ </tex-math></inline-formula> are the UEs located around the center of each cell. Meanwhile, the <inline-formula> <tex-math notation="LaTeX">$EUs$ </tex-math></inline-formula> are the UEs located at the edge of each cell, where the JT-CoMP is applied since they have less distinctive received power from two cells. In this paper, a framework to jointly optimize the power control and the UEs clustering of CoMP-assisted FD C-NOMA system is formulated as an optimization problem to maximize the network sum-rate while guaranteeing the required quality-of-service of UEs. The formulated problem is a non-convex mixed-integer non-linear program that cannot be solved in a straightforward manner. To tackle this issue, the formulated problem is decomposed into an inner power allocation problem and an outer UEs clustering problem. For the inner problem, a computational-efficient solution is obtained. Meanwhile, the outer problem is reformulated as a one-to-one three-sided matching game. Then, a low-complexity near-optimal clustering algorithm is proposed. The simulation results demonstrate that 1) the optimality of the power control solution; 2) the CoMP-assisted FD C-NOMA has a superior performance compared to CoMP-assisted half-duplex (HD) C-NOMA and CoMP NOMA schemes for moderate values of self-interference. It has been also shown that the proposed solution achieves around 96.5&#x0025; of the average achievable network sum-rate of the optimal solution.

Resource allocation for cellular device‐to‐device‐aided vehicle‐to‐everything networks with partial channel state information

AbstractIn Vehicle‐to‐Everything (V2X), cellular Device‐to‐Device (D2D) communication can not only enhance system capacity and spectral utilization but also reduce the traffic load and communication delay. However, due to the fast variations of the channel state information (CSI) caused by high mobility of vehicles, the accurate CSI is difficult to be obtained in real‐time. In this paper, different from other previous researches that are subject to the perfect CSI, a more realistic channel state model is adopted that only the partial CSI of the communication links is available. Then we study the joint power allocation and spectrum sharing problem to maximize the total weighted ergodic capacity of all vehicular links, namely, Vehicle‐to‐Infrastructure (V2I) links and Vehicle‐to‐Vehicle (V2V) links. Meanwhile, the transmission reliability guarantees the quality of service (QoS) requirements of V2I and V2V. Since the formulated problem is a nonconvex mixed integer nonlinear programming (MINLP) problem, we first derive the strategy for obtaining the optimal solution of power allocation under arbitrary weighted factor and quantify different cases of feasible regions. Then we propose a two‐stage algorithm to complete the optimal resource allocation in polynomial time. Moreover, we further propose a low‐complexity spectrum sharing method based on the principles of Gale‐Shapley mechanism. The simulation results show that the proposed algorithms outperform the other baseline schemes significantly, and the low‐complexity scheme can effectively achieve a tradeoff between performance and complexity.

ESN Reinforcement Learning for Spectrum and Flight Control in THz-Enabled Drone Networks

Terahertz (THz)-band communications have been envisioned as a key technology to support ultra-high-data-rate applications in 5G-beyond (or 6G) wireless networks. Compared to the microwave and mmWave bands, the main challenges with the THz band are in its i) large path loss hence limited network coverage and ii) visible-light-like propagation characteristics hence poor support of mobility in blockage-rich environments. This paper studies quantitatively the applicability of THz-band communications in blockage-rich mobile environments, focusing on a new network scenario called FlyTera. In FlyTera, a set of hotspots mounted on flying drones collaboratively provide data streaming services to ground users, in the microwave, mmWave and THz bands. We first provide a mathematical formulation of the FlyTera control problem, where the objective is to maximize the network spectral efficiency by jointly controlling the flight of the drone hotspots, their association to the ground users, and the spectrum bands used by the users. To solve the resulting problem, which is shown to be a mixed integer nonlinear nonconvex programming (MINLP) problem, we design distributed solution algorithms based on a combination of echo state learning and reinforcement learning. An extensive simulation campaign is then conducted with SimBAG, a newly developed Simulator of Broadband Aerial-Ground wireless networks. It is shown that no single spectrum band can meet the requirements of high data rate and wide coverage simultaneously. Moreover, from the network-level point of view, THz-band communications can significantly benefit from the mobility of the flying drones, and on average 4 - 6 times higher (rather than lower) throughput can be achieved in mobile than in static environments.

RIS-Assisted Joint Transmission in a Two-Cell Downlink NOMA Cellular System

This paper investigates the integration of reconfigurable intelligent surface (RIS) with downlink non-orthogonal-multiple-access (NOMA) in a multi-user two-cell network assisted by the joint-transmission coordinated multipoint (JT-CoMP). Specifically, the RIS is deployed at the edge of two adjacent cells to assist the JT-CoMP from these two cells to multiple far NOMA users located at their edges. Under this setup, we jointly optimize the power allocation (PA) coefficients at the base stations (BSs), the user clustering (UC) policy, and the phase-shift (PS) matrix of the RIS with the objective of maximizing the network sum-rate subject to a target quality-of-service, defined in terms of the minimum required data rate at each cellular user, and the successive interference cancellation (SIC) constraints. The formulated problem ends to be a non-convex mixed-integer non-linear program that is difficult to be solved in a straightforward manner. To alleviate this issue, and with the aid of alternating optimization (AO), the original optimization problem is decomposed into two sub-problems, a joint PA and UC sub-problem and a PS sub-problem, that are solved in an alternating way. For the first sub-problem, we invoke the bi-level optimization approach to decouple the PA sub-problem from the UC sub-problem. For the PA sub-problem, closed-form expressions for the optimal PA coefficients are derived. On the other hand, the UC problem is projected to multiple 2-dimensional assignment problems, each of which is solved using the Hungarian method. Finally, the PS sub-problem is formulated as a difference-of-convex problem and an efficient solution is obtained using the successive convex approximation technique. The numerical results reveal that the network sum-rate of the proposed RIS-assisted CoMP NOMA networks outperforms the conventional CoMP NOMA scheme without the assistance of the RIS, the RIS-assisted CoMP orthogonal multiple access (OMA) scheme, and RIS-assisted NOMA scheme, especially for low transmit power from the BSs.

Residual Energy Maximization for Wireless Powered Mobile Edge Computing Systems With Mixed-Offloading

This paper studies a joint design of resource allocation and task offloading in a wireless powered mobile edge computing network involving different types of computation tasks. To deal with diverse computation tasks, we explore a mixed-offloading paradigm to support the coexistence of partial and binary offloading modes. Specifically, devices harvest energy from an access point (AP) via wireless power transfer (WPT) and utilize the harvested energy to execute their computation tasks using partial or binary offloading. Based on a practical non-linear energy harvesting model, a residual energy maximization problem is formulated by jointly optimizing the transmit power of the AP, the offloading power of devices, the time allocation on WPT and task offloading, and the task partitions and the binary offloading decisions of devices, which turn out to be a non-convex mixed-integer non-linear programming problem. Thus, we develop an efficient dual-layer optimization algorithm by decomposing the optimization problem into an inner and outer layer structure that aims to obtain resource allocation and offloading decisions. Simulation results show that our proposed scheme achieves residual energy gains compared to existing schemes.

Green resource allocation for mobile edge computing

We investigate the green resource allocation to minimize the energy consumption of the users in mobile edge computing systems, where task offloading decisions, transmit power, and computation resource allocation are jointly optimized. The considered energy consumption minimization problem is a non-convex mixed-integer non-linear programming problem, which is challenging to solve. Therefore, we develop a joint search and Successive Convex Approximation (SCA) scheme to optimize the non-integer variables and integer variables in the inner loop and outer loop, respectively. Specifically, in the inner loop, we solve the optimization problem with fixed task offloading decisions. Due to the non-convex objective function and constraints, this optimization problem is still non-convex, and thus we employ the SCA method to obtain a solution satisfying the Karush-Kuhn-Tucker conditions. In the outer loop, we optimize the offloading decisions through exhaustive search. However, the computational complexity of the exhaustive search method is greatly high. To reduce the complexity, a heuristic scheme is proposed to obtain a sub-optimal solution. Simulation results demonstrate the effectiveness of the developed schemes.

Variable Bound Tightening and Valid Constraints for Multiperiod Blending

Multiperiod blending has a number of important applications in a range of industrial sectors. It is typically formulated as a nonconvex mixed integer nonlinear program (MINLP), which involves binary variables and bilinear terms. In this study, we first propose a reformulation of the constraints involving bilinear terms using lifting. We introduce a method for calculating tight bounds on the lifted variables calculated by aggregating multiple constraints. We propose valid constraints derived from the reformulation-linearization technique (RLT) that use the bounds on the lifted variables to further tighten the formulation. Computational results indicate our method can substantially reduce the solution time and optimality gap.Summary of Contribution: In this paper, we study the multiperiod blending problem, which has a number of important applications in a range of industrial sectors, such as refining, chemical production, mining, and wastewater management. Solving this problem efficiently leads to significant economic and environmental benefits. However, solving even medium-scale instances to global optimality remains challenging. To address this challenge, we propose a variable bound tightening algorithm and tightening constraints for multiperiod blending. Computational results show that our methods can substantially reduce the solution time and optimality gap.

Adjustable Robust Optimization for the Multi-period Planning Operations of an Integrated Refinery-Petrochemical Site under Uncertainty

This paper concentrates on the formulation of a large-scale nonconvex mixed-integer nonlinear programming model and the application of robust optimization for the multi-period operational planning of real-world integrated refinery-petrochemical site in China under uncertain product demands and crude oil price. To avoid excessive conservativeness resulting from classical static robust optimization, an adjustable robust counterpart incorporating resource decisions via an affinely adjustable linear decision rule is first derived. On the basis of a proposed polyhedral dynamic uncertainty set that mimics the dynamic behavior of the product demand over time, an adjustable robust counterpart with a dynamic uncertainty set is further formulated. Classical static robust optimization, adjustable robust optimization, and adjustable robust optimization with dynamic uncertainty sets are systematically compared for case studies. The results clearly illustrate the advantages of the affinely adjustable robust optimization with a dynamic uncertainty set over the classic robust optimization in decision making.

Convex Heuristics for Optimal Placement and Operation of Valves and Chlorine Boosters in Water Networks

This paper investigates the problem of optimal placement and operation of valves and chlorine boosters in water networks. The objective is to minimize average zone pressure while penalizing deviations from target chlorine concentrations. The problem formulation includes nonconvex quadratic terms within constraints representing the energy conservation law for each pipe, and discretized differential equations modeling advective transport of chlorine concentrations. Moreover, binary variables model the placement of valves and chlorine boosters. The resulting optimization problem is a nonconvex mixed integer nonlinear program, which is difficult to solve, especially when large water networks are considered. We develop a new convex heuristic to optimally place and operate valves and chlorine boosters in water networks, while estimating the optimality gaps for the computed solutions. We evaluate the proposed heuristic using case studies with varying sizes and levels of connectivity and complexity, including two large operational water networks. The convex heuristic is shown to generate good-quality feasible solutions in all problem instances with bounds on the optimality gap comparable to the level of uncertainty inherent in hydraulic and water quality models.

Non-convex nested Benders decomposition

We propose a new decomposition method to solve multistage non-convex mixed-integer (stochastic) nonlinear programming problems (MINLPs). We call this algorithm non-convex nested Benders decomposition (NC-NBD). NC-NBD is based on solving dynamically improved mixed-integer linear outer approximations of the MINLP, obtained by piecewise linear relaxations of nonlinear functions. Those MILPs are solved to global optimality using an enhancement of nested Benders decomposition, in which regularization, dynamically refined binary approximations of the state variables and Lagrangian cut techniques are combined to generate Lipschitz continuous non-convex approximations of the value functions. Those approximations are then used to decide whether the approximating MILP has to be dynamically refined and in order to compute feasible solutions for the original MINLP. We prove that NC-NBD converges to an varepsilon -optimal solution in a finite number of steps. We provide promising computational results for some unit commitment problems of moderate size.

Wireless power transfer supported device-to-device multicast energy cooperative transmission scheme

The cluster heads (CHs) will face the contradiction between the lack of available energy and the demand of high energy consumption in energy harvesting-supported device-to-device multicast communications (EH-D2MD). Wireless power transfer (WPT) technology is a possible way to address the above contradiction. The members of a device-to-device (D2D) multicast cluster can transfer part of their available energy to the CH by WPT and jointly undertake contents unloading. As a result, the transmission robustness of the multicast cluster can be improved. Therefore, a transmission scheme with energy cooperation (EC) is designed on the premise of cellular spectrum reusing. The EC scheme designs elaborately the energy harvesting, energy cooperation and data transmission of the spectrum reusing process. To realize the EC scheme, this work is to maximize the transmission rate of a multicast cluster and give the joint optimal solution of multi-domain resources including spectrum resource allocation, cooperative time factor planning, and power control. The rate maximization problem is a typical non-convex mixed integer non-linear programming (non-convex MINLP) problem. To investigate the performance of EH-D2MD communication scenario, a convex approximate lower-bound algorithm is proposed, which can transfer the non-convex problem into convex MINLP and can give a joint solution. Simulation results show that the proposed algorithm obtains a lower-bound solution of the rate maximization problem in comparison with the exhausted searching method. Furthermore, compared with the scheme without energy cooperation, the established EC transmission scheme can increase the transmission rate of D2MD by more than 45% and enhance the robustness of EH-D2MD.

A Branch and Bound Algorithm for Transmission Network Expansion Planning Using Nonconvex Mixed-Integer Nonlinear Programming Models

The branch and bound (BB) algorithm is widely used to obtain the global solution of mixed-integer linear programming (MILP) problems. On the other hand, when the traditional BB structure is directly used to solve nonconvex mixed-integer nonlinear programming (MINLP) problems, it becomes ineffective, mainly due to the nonlinearity and nonconvexity of the feasible region of the problem. This article presents the difficulties and ineffectiveness of the direct use of the traditional BB algorithm for solving nonconvex MINLP problems and proposes the formulation of an efficient BB algorithm for solving this category of problems. The algorithm is formulated taking into account particular aspects of nonconvex MINLP problems, including (i) how to deal with the nonlinear programming (NLP) subproblems, (ii) how to detect the infeasibility of an NLP subproblem, (iii) how to treat the nonconvexity of the problem, and (iv) how to define the fathoming rules. The proposed BB algorithm is used to solve the transmission network expansion planning (TNEP) problem, a classical problem in power systems optimization, and its performance is compared with the performances of off-the-shelf optimization solvers for MINLP problems. The results obtained for four test systems, with different degrees of complexity, indicate that the proposed BB algorithm is effective for solving the TNEP problem with and without considering losses, showing equal or better performance than off-the-shelf optimization solvers.

Optimal Coordinated Operation of Distributed Static Series Compensators for Wide-area Network Congestion Relief

Relieving network congestions is a critical goal for the safe and flexible operation of modern power systems, especially in the presence of intermittent renewables or distributed generation. This paper deals with the real-time coordinated operation of distributed static series compensators (DSSCs) to remove network congestions by suitable modifications of the branch reactance. Several objective functions are considered and discussed to minimize the number of the devices involved in the control actions, the total losses or the total reactive power exchanged, leading to a non-convex mixed-integer non-linear programming problem. Then, a heuristic methodology combining the solution of a regular NLP with k-means clustering algorithm is proposed to get rid of the binary variables, in an attempt to reduce the computational cost. The proposed coordinated operation strategy of the DSSCs is tested on several benchmark systems, providing feasible and sufficiently optimal solutions in a reasonable time frame for practical systems.

Pro-social control of connected automated vehicles in mixed-autonomy multi-lane highway traffic

We propose pro-social control strategies for connected automated vehicles (CAVs) to mitigate jamming waves in mixed-autonomy multi-lane traffic, resulting from car-following dynamics of human-driven vehicles (HDVs). Different from existing studies, which focus mostly on ego vehicle objectives to control CAVs in an individualistic manner, we devise a pro-social control algorithm. The latter takes into account the objectives (i.e., driving comfort and traffic efficiency) of both the ego vehicle and surrounding HDVs to improve smoothness of the entire observable traffic. Under a model predictive control (MPC) framework that uses acceleration and lane change sequences of CAVs as optimization variables, the problem of individualistic, altruistic, and pro-social control is formulated as a non-convex mixed-integer nonlinear program (MINLP) and relaxed to a convex quadratic program through converting the piece-wise-linear constraints due to the optimal velocity with relative velocity (OVRV) car-following model into linear constraints by introducing slack variables. Low-fidelity simulations using the OVRV model and high-fidelity simulations using PTV VISSIM simulator show that pro-social and altruistic control can provide significant performance gains over individualistic driving in terms of efficiency and comfort on both single- and multi-lane roads.

Service Provisioning for UAV-Enabled Mobile Edge Computing

Unmanned aerial vehicle (UAV)-enabled mobile edge computing has been recognized as a promising technology to flexibly and efficiently handle computation-intensive and latency-sensitive tasks in the era of fifth generation (5G) and beyond. In this paper, we study the problem of Service Provisioning for UAV-enabled mobile edge computiNg (SPUN). Specifically, under task latency requirements and various resource constraints, we jointly optimize the service placement, UAV movement trajectory, task scheduling, and computation resource allocation, to minimize the overall energy consumption of all terrestrial user equipments (UEs). Due to the non-convexity of the SPUN problem as well as complex coupling among mixed integer variables, it is a non-convex mixed integer nonlinear programming (MINLP) problem. To solve this challenging problem, we propose two alternating optimization-based suboptimal solutions with different time complexities. In the first solution with relatively high complexity in the worst case, the joint service placement and task scheduling subproblem, and UAV trajectory subproblem are iteratively solved by the Branch and Bound (BnB) method and successive convex approximation (SCA), respectively, while the optimal solution to the computation resource allocation subproblem is efficiently obtained in the closed form. To avoid the high complexity caused by BnB, in the second solution, we propose a novel approximation algorithm based on relaxation and randomized rounding techniques for the joint service placement and task scheduling subproblem, while the other two subproblems are solved in the same way as that of the first solution. Extensive simulations demonstrate that the proposed solutions achieve significantly lower energy consumption of UEs compared to three benchmarks.

Deep Reinforcement Learning-Based Resource Allocation in Cooperative UAV-Assisted Wireless Networks

We consider the downlink of an unmanned aerial vehicle (UAV) assisted cellular network consisting of multiple cooperative UAVs, whose operations are coordinated by a central ground controller using wireless fronthaul links, to serve multiple ground user equipments (UEs). A problem of jointly designing UAVs’ positions, transmit beamforming, as well as UAV-UE association is formulated in the form of mixed integer nonlinear programming (MINLP) to maximize the sum UEs’ achievable rate subject to limited fronthaul capacity constraints. Solving the considered problem is hard owing to its non-convexity and the unavailability of channel state information (CSI) due to the movement of UAVs. To tackle these effects, we propose a novel algorithm comprising of two distinguishing features: (i) exploiting a deep Q-learning approach to tackle the issue of CSI unavailability for determining UAVs’ positions, (ii) developing a difference of convex algorithm (DCA) to efficiently solve for the UAV’s transmit beamforming and UAV-UE association. The proposed algorithm recursively solves the problem of interest until convergence, where each recursion executes two steps. In the first step, the deep Q-learning (DQL) algorithm allows UAVs to learn the overall network state and account for the joint movement of all UAVs to adapt their locations. In the second step, given the determined UAVs’ positions from the DQL algorithm, the DCA iteratively solves a convex approximate subproblem of the original non-convex MINLP problem with the updated parameters, where the problem’s variables are transmit beamforming and UAV-UE association. Numerical results show that our design outperforms the existing algorithms in terms of algorithmic convergence and network performance with a gain of up to 70%.

Freeway network design with exclusive lanes for automated vehicles under endogenous mobility demand

Automated vehicles (AV) have the potential to provide cost-effective mobility options along with overall system-level benefits in terms of congestion and vehicular emissions. Additional resource allocation at the network level, such as AV-exclusive lanes, can further foster the usage of AVs rendering this mode of travel more attractive than legacy vehicles (LV). However, it is necessary to find the crucial locations in the network where providing these dedicated lanes would reap the maximum benefits. In this study, we propose an integrated mixed-integer programming framework for optimal AV-exclusive lane design on freeway networks which accounts for commuters’ demand split among AVs and LVs via a logit model incorporating class-based utilities. We incorporate the link transmission model (LTM) as the underlying traffic flow model due to its computational efficiency for system optimum dynamic traffic assignment. The LTM is modified to integrate two vehicle classes namely, LVs and AVs with a lane-based approach. The presence of binary variables to represent lane design and the logit model for endogenous demand estimation results in a nonconvex mixed-integer nonlinear program formulation. We propose a Benders’ decomposition approach to tackle this challenging optimization problem. Our approach iteratively explores possible lane designs in the Benders’ master problem and, at each iteration, solves a sequence of system-optimum dynamic traffic assignment problems in an attempt to find fixed-points representative of logit-compatible demand splits. The proposed approach is implemented on three hypothetical freeway networks with single and multiple origins and destinations. Our numerical results reveal that the optimal lane design of freeway network is non-trivial while accounting for endogenous demand of each mode.