Mixed Problem Research Articles

Convexificators for nonconvex multiobjective optimization problems with uncertain data: robust optimality and duality

In this paper, we investigate robust optimality conditions and duality for a class of nonconvex multiobjective optimization problems with uncertain data in the worst case by the upper semi-regular convexificator. The Fermat principle for a locally Lipschitz function is presented in terms of the upper semi-regular convexificator. We establish robust necessary optimality conditions of the Fritz-John type and KKT type for the uncertain nonconvex multiobjective optimization problems. In addition, robust sufficient optimality conditions as well as saddle point conditions are derived under the generalized ∂ ˆ ∗ -pseudoquasiconvexity and generalized convexity, respectively. The robust duality relations between the original problem and its mixed robust dual problem are obtained under a generalized pseudoconvexity assumption.

Smart and efficient EV charging navigation scheme in vehicular edge computing networks

With the increasing number of electric fast charging stations (FCSs) deployed along roadsides of both urban roads and highways, the long-distance travel of electric vehicles (EVs) becomes possible. The EV charging navigation scheme is significant for the quality of user experience. However, the variable conditions of both power grid and traffic networks make it a serious challenge. In this paper, we propose an efficient EV charging navigation scheme while considering both the electric and computation resource sharing. With the support of vehicular edge computing networks in intelligent transportation systems (ITSs), EVs perform both the flexible power load and edge computing nodes. When the traffic network in the established route starts to become congested, EVs can select to enter the nearest FCS. In addition to being supplemented by electric resources, EVs also benefit by sharing their own computing resource with FCSs. We formulate the EV charging navigation as a mixed integer programming problem, the EV moving route planning, FCS selection, and staying time in FCSs are optimized, to balance the relationships among the traveling time, traveling cost and reward. To address the influence caused by the randomness of traffic conditions and charging prices, a two-stage charging navigation algorithm combined with A∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A^{*}$$\\end{document} algorithm and deep reinforcement learning (DRL) is proposed, with a novel designed reward function. Eventually, numerous experimental results show the effectiveness of the proposed schemes.

Simultaneous capacity configuration and scheduling optimization of an integrated electrical vehicle charging station with photovoltaic and battery energy storage system

The implementation of an optimal power scheduling strategy is vital for the optimal design of the integrated electric vehicle (EV) charging station with photovoltaic (PV) and battery energy storage system (BESS). However, traditional design methods always neglect accurate PV power modeling and adopt overly simplistic EV charging strategies, which might result in suboptimal and infeasible designs. This study proposes a novel simultaneous capacity configuration and scheduling optimization model for PV/BESS integrated EV charging stations, which combines hybrid modeling for PV power prediction and optimal scheduling method for charging piles. The original model is then converted to a mixed integer linear programming problem by the Big-M method to greatly reduce the computational complexity. A typical scenario of commercial region is employed to demonstrate the effectiveness of the proposed approach. The results indicate that the approach could improve economic benefits by 15.67 % and reduce carbon emissions by 37.14 % compared with the entire grid-based mode. Besides, integrating the PV hybrid modeling method and optimal charging scheduling strategy could achieve superior capacity configurations and greatly improve the comprehensive performance of the system. It is thus illustrated that the approach could provide a promising solution for the optimal design and scheduling of PV/BESS integrated EV charging stations.

Stochastic model for active distribution networks planning: An analysis of the combination of active network management schemes

The widespread adoption of distributed generation (DG) is changing the operation of distribution networks. To increase the control of power flows and avoid the detriments of DG intermittency, active distribution networks (ADN) emerge as a feasible solution. In this paper, we propose a convex model for ADN expansion planning. Four active network management (ANM) schemes are considered: DG active power curtailment, DG reactive power control, on-load tap changer (OLTC) tap adjustment, and shunt compensation device control. The problem is formulated as a mixed integer second-order cone programming problem (MISOCP) using the distflow equations and second-order cone relaxations (SOCR). By scenario analysis, we address the uncertainty associated with power demand, renewable generation, and electricity prices. The proposed model is used to study the benefits of different combinations of ANM schemes to a modified IEEE 33-bus system and compare them with the individual benefits of each scheme. The results indicate that ANM schemes can reduce total network costs, reduce losses, delay network reinforcement, and improve the voltage profile. In addition, some combinations of schemes develop synergies in which the combined economic benefits are greater than the sum of the individual benefits.

Bi-level planning approach for incorporating the demand-side flexibility of cloud data centers under electricity-carbon markets

With the prevalence of cloud computing applications, cloud data centers (CDCs) are proliferating around the world. However, in the context of hybrid energy‑carbon markets environment, the high energy costs and environmental expenses caused by CDC operation are pressing CDC owners to restructure the future development of CDC in a more economical and low-carbon manner. The potential spatio-temporal transferability and reducibility of workloads provides CDCs with significant flexibility in their operations and thus may interact with the power grid as active demand users. Nonetheless, other than private data centers, public CDCs have no direct control over the workloads submitted by terminal cloud users. As such, this paper presents a bi-level model for CDC allocation planning, so as to incorporate cloud service-demand response (CS-DR) from the perspective of a hybrid electricity-carbon market. The upper level pertains to multi-domain resource collaborative planning model, which determines the optimum siting and sizing of CDCs as well as the incentive design for CS-DR program, with the objective of maximizing the total expected benefits of CDC. The lower level models correspond to the market clearing (electricity-carbon tariff model) of Independent system operator (ISO) and the decision-making of cloud users regarding CS-DR participation. The proposed model belongs to a bi-level mixed integer nonlinear programming problem with two non-convex lower levels, which can be intractable in mathematics. To solve such difficult problem, a hybrid solution method combining multiple linearization techniques and reformulation and decomposition (R&D) strategy based on column-and-constraint generation (C&CG) algorithm is developed. The proposed model is demonstrated on a modified IEEE 30-bus test case, and the simulation results verified the effectiveness of the proposed approach.

Mixed reality-based online 3D pallet loading problem to achieve augmented intelligence in e-fulfilment processes

Mixed reality-based online 3D pallet loading problem to achieve augmented intelligence in e-fulfilment processes

A new complex variable solution on noncircular shallow tunnelling with reasonable far-field displacement

A new static equilibrium mechanical model on noncircular shallow tunnelling considering initial stress field is proposed in this paper by constraining far-field ground surface, and a mixed boundary value problem thus forms with elimination of displacement singularity at infinity. By applying analytic continuation, the mixed boundaries are transformed to a homogeneous Riemann–Hilbert problem, which is subsequently solved via an efficient and accurate iterative method with boundary conditions of static equilibrium, displacement single-valuedness, and traction along tunnel periphery. The Lanczos filtering technique is used in the final stress and displacement solution to reduce the Gibbs phenomena caused by the constrained far-field ground surface to obtain more reasonable results. Several numerical cases are conducted to intensively verify the proposed solution by examining the utilization of Lanczos filtering, the elimination of displacement singularity, and solution convergence of constraining arc and truncation number, and comparisons with existing solutions, and all the results are in good agreements. Finally, more numerical cases are conducted to investigate the stress and deformation distribution along ground surface and tunnel periphery considering different tunnel geometries, lateral coefficients, and tunnel depths. Further discussions on the defects of the proposed solution are also conducted for objectivity.

Analytical solution for diffraction of magnetoelastic plane waves by a rigid strip in self-reinforced medium: a contour integration method

This study analytically addresses the diffraction of magnetoelastic plane waves by a rigid strip in a self-reinforced infinite elastic medium. Formulation of the studied model includes mixed type boundary value problem and has been solved by the method of integral equation. The expressions of vertical diffracted displacement and normal stress are established in the closed form by employing the contour integration technique. For the sake of validation, the deduced expressions of vertical diffracted displacement and normal stress are reduced to the special cases, such as without magnetoelastic coupling as well as anisotropy and matched with the pre-established results. The diffraction patterns for the vertical displacement component in the considered material medium are calculated numerically, and its dependence on various affecting parameters viz. magnetoelastic coupling parameter, phase velocity, wave number of the propagating magnetoelastic plane wave, and distance has been depicted graphically for self-reinforced and isotropic materials. Moreover, the influence of anisotropy of the infinite medium has been portrayed remarkably by the comparative study.

Distributionally robust optimization model considering deep peak shaving and uncertainty of renewable energy

In order to achieve the goal of carbon neutrality, the capacity of renewable power generation is continuously expanding while thermal power units are transitioning from main power source to auxiliary power source. To alleviate the peak shaving burden of thermal power units under the uncertainty of renewable energy and improve the absorption level of renewable energy, a two-stage distributionally robust optimization (DRO) model considering deep peak shaving and the uncertainty of renewable energy is proposed. The day-ahead unit commitment solutions are determined in the first stage, and the detailed scheduling strategies are obtained in the second stage. Column-and-constraint generation (C&CG) algorithm is applied to solve the model, and the master problem and subproblem are reformulated as duality-free mixed integer linear programming problems. The results show that the scheduling strategy obtained based on the model can alleviate the peak shaving burden brought by the uncertainty of renewable energy and reduce the abandonment rate of wind resources and solar resources, and the proposed DRO model provides a good trade-off between economy and robustness compared to stochastic optimization (SO) and robust optimization (RO).

Evaluation of CO2 Emission and Local Flexibility by Water Pumping Scheduling in Water Distribution System

In recent years, the amount of the photovoltaic (PV) system has been rapidly increasing from the viewpoint of carbon neutral. There are concerns about voltage rises and grid congestion in the electrical distribution network because of large‐scale PV increases. In order to address these issues, we focused on the control of water supply pumps in the water distribution system, which is infrastructure equipment for consumers. By controlling the start/stop of the water pump, it is expected to contribute to the power distribution system by increasing Demand Response (DR) and reduce CO2 emission from the electricity used by the pump. In this paper, with the aim of constructing an optimal operation planning method for water pumps that can evaluate DR and CO2 reduction effects, the optimal operation plan is formulated as a mixed integer linear programming problem. We numerical evaluated impact of water pump operation for CO2 emission and electrical distribution network. © 2023 The Authors. IEEJ Transactions on Electrical and Electronic Engineering published by Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.

Optimal Task Allocation for Battery-Assisted and Price-Aware Mobile Edge Computing

In this paper, we propose a battery-assisted approach to improve energy efficiency for mobile edge computing (MEC) networks by utilizing the space-time-varying characteristics of electricity price. We formulate a price-aware task allocation problem (PATA) that jointly considers the cost for task computation, the cost of task offloading, and the cost of battery degradation. PATA is seemingly a mixed integer non-linear programming problem. By a graph-based reformulation, solving PATA is mapped to finding minimum cost flows or convex cost flows in the graph. This discovery reveals that the global optimum of PATA is obtained in polynomial time. Performance evaluation manifests that the proposed approach significantly outperforms other approaches.

Multi-Edge Server-Assisted Dynamic Federated Learning With an Optimized Floating Aggregation Point

We propose cooperative edge-assisted dynamic federated learning ( CE-FL). CE-FL introduces a distributed machine learning (ML) architecture, where data collection is carried out at the end devices, while the model training is conducted <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">cooperatively</i> at the end devices and the edge servers, enabled via data offloading from the end devices to the edge servers through base stations. CE-FL also introduces floating aggregation point, where the local models generated at the devices and the servers are aggregated at an edge server, which varies from one model training round to another to cope with the network evolution in terms of data distribution and users’ mobility. CE-FL considers the heterogeneity of network elements in terms of communication/computation models and the proximity to one another. CE-FL further presumes a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dynamic</i> environment with online variation of data at the network devices which causes a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">drift</i> at the ML model performance. We model the processes taken during CE-FL, and conduct analytical convergence analysis of its ML model training. We then formulate network-aware CE-FL which aims to adaptively optimize all the network elements via tuning their contribution to the learning process, which turns out to be a non-convex mixed integer problem. Motivated by the large scale of the system, we propose a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">distributed optimization solver</i> to break down the computation of the solution across the network elements. We finally demonstrate the effectiveness of our framework with the data collected from a real-world testbed.

Random Caching Design for Multi-User Multi-Antenna HetNets With Interference Nulling

The strong interference suffered by users can be a severe problem in cache-enabled networks (CENs) due to the content-centric user association mechanism. To tackle this issue, multi-antenna technology may be employed for interference management. In this paper, we consider a user-centric interference nulling (IN) scheme in two-tier multi-user multi-antenna CEN, with a hybrid most-popular and random caching policy at macro base stations (MBSs) and small base stations (SBSs) to provide file diversity. All the interfering SBSs within the IN range of a user are requested to suppress the interference at this user using zero-forcing beamforming. Using stochastic geometry analysis techniques, we derive a tractable expression for the area spectral efficiency (ASE). A lower bound on the ASE is also obtained, with which we then consider ASE maximization, by optimizing the caching policy and IN coefficient. To solve the resultant mixed integer programming problem, we design an alternating optimization algorithm to minimize the lower bound of the ASE. Our numerical results demonstrate that the proposed caching policy yields performance that is close to the optimum, and it outperforms several existing baselines.

Backup Resource Allocation of Virtual Machines With Two-Stage Probabilistic Protection

In a cloud, protection through backup of virtual machines contained in physical machines (PMs) reduces damage to users due to failure of PMs, such as hardware malfunctions. However, from a resource cost perspective, it is necessary to reduce the amount of capacity for backup while limiting the probability of unsuccessful protection. Existing studies suggest the method of sharing backup capacity among primary resources, but the amount of capacity reduction required to protect is limited. This paper proposes a backup resource allocation model with two-stage probabilistic protection to minimize the total required backup capacity for multiple simultaneous failures of PMs. In probabilistic protection, backup resources are allocated so that the probability of backup failure does not exceed a given survivability parameter which represents the acceptable probability of backup failure. Probabilistic protection which achieves efficient sharing of backup capacity enables flexible allocation and reduces the required backup capacity. In order to increase the flexibility of backup capacity allocation, the proposed model extends the probabilistic protection to two stages. By dividing the protection into two stages, the weight of probability between stages can be adjusted, enabling more effective capacity sharing. Since it is uncertain which primary PMs fail, we apply robust optimization to the probabilistic protection. By using a table that takes into account the survivability parameter and the failure probability of PMs, the proposed model is formulated as a mixed integer linear programming problem. We prove the NP-hardness of considered problem. A heuristic is introduced to solve the optimization problem. The proposed model can reduce the total required backup capacity compared to the models with dedicated protection and one-stage probabilistic protection. The model can also provide protection in a range of survivability parameters that the model with one-stage probabilistic protection cannot satisfy.

Coordination of preventive and emergency dispatch in renewable energy integrated power systems under extreme weather

AbstractIn recent years, frequent occurrence of extreme weather events has caused great losses to the power system. Meanwhile, the high penetration of renewable energy has brought new challenges to the safe operation of the system. Coordination of various measures against different stages of disaster can effectively reduce the overall loss and enhance system's resilience. This paper proposed a methodology to coordinate preventive and emergency dispatch stages based on the defender–attacker–defender model, in which various dispatching measures are modelled as defenders, whereas the extreme weather event and wind power's uncertainty are modelled as attackers. Specifically, a two‐stage three‐layer robust optimal dispatching model is established, in which conventional generator's output, wind farm's grid‐connected planning, and load shedding are taken as the main dispatching measures. To solve this model, the column and constraint generation algorithm is used to transform the three‐layer optimization model into a mixed integer linear problem . The effectiveness of the proposed model is verified in the modified IEEE RTS‐79 test system, and the results show that the coordination of preventive and emergency dispatch can effectively reduce the load outage cost under extreme weather, thus enhancing the ability of power system to cope with extreme scenarios.

The Study of Coordinate-Wise Decomposition Descent Method for Optimization Problems

The aim of this paper is to consider a general non-stationary optimization problem whose objective function need not be smooth in general and only approximation sequences are known instead of exact values of the functions. We apply a two-step technique where approximate solutions of a sequence of a generalized mixed variational inequality problem (GMVIP) are inserted in the iterative method of a selective coordinate-wise decomposition descent method. Its convergence is achieved under coercivity-type assumptions.

Risk-constrained probabilistic coordination in coupled transmission and distribution system

High penetration of renewable energy has instigated stochastic power injection at interconnection between transmission system (TS) and distribution system (DS). This paper delves into the intricate collaborative risk based stochastic dispatching challenges due to contingencies and the integration of renewable sources in the TS and DS. A framework of risk constrained probabilistic problem (RCPC) is presented, which is divided into Probabilistic coordination (PC) and risk-based stochastic security-constrained unit commitment (RSSCUC). The PC is a stochastic linear problem and RSSCUC is a stochastic mixed integer non-linear problem. Therefore, the probabilistic analytical target cascading along with polynomial chaos expansion (PCE) has been utilized for solving the PC problem for coupled TS and DS. Here, PCE has provided the proposed algorithm with the needed capability to present stochastic shared variables as coefficients for PC. Further, the benders decomposition algorithm has been utilized for solving RSSCUC, by dividing it into master problem and sub problem to generate feasibility cuts. The proposed technique reduces the computational burden on the system, as it requires single stochastic coordination problem for all scenarios as an alternative of each coordination problem for each scenario and polynomial coefficients instead of multiple scenarios for each shared variable between TS and DS. Different case studies have been performed utilizing the 6-bus system and IEEE 118-bus system as TSs, 7-bus, 9-bus, 85-bus and 69-bus systems as DSs. Results depict the efficacy of the proposed method.

Novel Amalgamation of Bat and Elephant Herd Optimization Algorithms for Generation Mix in Renewable Active Distribution Networks

In this article, a hybrid approach is proposed that amalgamates two prominent nature-inspired, swarm-based, meta-heuristic techniques. The amalgamation is done to solve the mix generation, complex real-life optimization problems for renewable active distribution network (ADN). Some observed shortcomings of the bat algorithm (BA) are overcome by an effective introduction of elephant herding optimization (EHO) without altering its internal mechanism. The new transformations are validated by solving a real-life optimization problem of distributed generations for power loss minimization in power distribution networks. The performance of the proposed hybrid method is found to be promising when compared with some of the well-known optimizations in the literature. The proposed amalgamation has strengthened the exploration and exploitation potential of the new algorithm in a way that, their precise balance seeks the global optima. After validations, this technique is deployed to solve a multiobjective problem of optimal generation mix for renewable ADN for various test cases. Key objectives of the designed model of mix generation in ADN include annual energy losses, bus voltage profiles, and net demand variants of the networks over multiple load levels. The optimization problems model is implemented and solved for two test systems that include a benchmark 33 bus and a real-life 108 bus distribution network. The results comparison reveals that the proposed method significantly improved the system performances in terms of reduced annual energy loss by 55.95% and 44.48%, improved bus voltage profiles by 7.94% and 11.20%, and reduced net power demand fluctuations by 52.00% and 37.60% for 33 bus and 108 bus distribution network, respectively. The suggested optimization model outperforms the current existing approaches and has promising exploration and exploitation capabilities to address optimization problems in engineering.

An Energy-Efficient Multimode Transmission Scheme for Underwater Sensor Network

Underwater sensor network plays a critical role in the ocean data collection owing to its capability of providing reliable and wide communication coverage. How to assure lifetime performance of the network with limited energy supply has always been a key research issue. In this paper, we propose an underwater acoustic sensor network model which supports data delivery from each underwater sensor node (USN) to sea surface sink node (SN) in either direct or relay-assisted transmission mode, i.e., transmission mode between each USN and the SN can be dynamically selected according to network’s current state. To optimize its lifetime performance, we model the mode selection and resource allocation issue jointly into a non-convex and mixed integer programming problem. In order to efficiently solve it, we further divide the original problem into two subproblems: resource allocation subproblem and joint mode and relay selection subproblem. We prove that the reformulated non-convex resource allocation problem can be equivalent to a convex optimization problem, and its optimal solution can be found by using Lagrange dual decomposition method. For the second subproblem, some critical conditions are analyzed to determine optimal relays with the criterion of balancing energy consumption between USNs and a matching approach is designed to obtain the mode and relay selection results based on USNs’ priorities. Simulation results validate that the proposed transmission scheme is effective and superior to the traditional time division multiple access scheme.

RIS Subarray Optimization With Reinforcement Learning for Green Symbiotic Communications in Internet of Things

Symbiotic communications have been deemed as a critical technology for Internet of things (IoT) communications owing to its high spectrum and energy efficiency. Reconfigurable intelligent surface (RIS), which can tune wireless transmission channels by manipulating incident waves through the corresponding electromagnetic elements, is a promising enabler of various symbiotic communications scenarios in IoT. However, when the full electromagnetic elements of RIS are activated, system capacity will be improved and energy efficiency will be reduced inevitably, also with undesirable power consumption. To address this issue, an intelligent dynamic subarray RIS framework based on deep reinforcement learning (DRL) has been proposed. The key idea is to divide RIS electromagnetic elements into several groups and optimize power amplifier factor, independent phase shifts to improve the system energy efficiency under the premise of user’s basic requirements. In particular, we formulate a hybrid optimization problem of RIS subarray partition and beamforming to maximize system energy efficiency. It can be proved that this hybrid optimization is a mixed non-convex integer programming problem. To solve this issue, we proposed a comprehensive DRL framework including two parts, i.e., (1) a Markov decision process (MDP) to model the subarray partition design, amplitude and phase shifts of RIS, and (2) an active RIS subarray optimization scheme based on deep deterministic policy gradient. Numerical results have demonstrated that, compared with the conventional fully-connected RIS, the system energy efficiency can be significantly improved.