Mixed-integer Nonlinear Programming Optimization Problem Research Articles

A centralized EMPC scheme for PV-powered alkaline electrolyzer

Photovoltaic (PV)-powered alkaline electrolyzer system (PVPAES) is an advanced technique to convert the off-grid and intermittent PV-based solar energy into the storable and transportable electrolyzer-based hydrogen energy with zero carbon emissions. However, it is difficult to realize the coordinated control of the off-grid PV module and the alkaline electrolyzer, due to the multiple timescale dynamics. To address this challenge, the PVPAES is decomposed into slow part and fast part based on the dynamic time scale. Exploiting the decomposed subsystems, the slow one is assumed to be managed well by the auxiliary controller. For the fast one, a centralized economic model predictive control (CEMPC) scheme is constituted. This CEMPC integrates the energy management system and local feedback control into a single optimal control framework. A mathematical model of the PVPAES is established, on the basis of which the CEMPC directly adopts the economic indices as the cost function to realize the flexible power point tracking, power supply–demand balance, and dynamic economic optimization. Moreover, the inherent strong nonlinearity of PVPAES results in the nonconvex mixed-integer nonlinear programming optimization problem in the CEMPC. The exhaustive search algorithm utilizing finite converter switching states is adopted to achieve the global economic optimum. The effectiveness of the proposed CEMPC controller is illustrated through simulations under varying irradiance conditions.

Machine Learning-Based Uplink Scheduling Approaches for Mixed Traffic in Cellular Systems

The problem of the uplink resource allocation of mixed-traffic types in cellular networks is a challenging problem that has not been addressed sufficiently in the literature. In this paper, we consider the 5G uplink scheduling for Ultra-Reliable and Low Latency Communications and enhanced Mobile Broad-Band (eMBB) traffic types. There are three main scheduling techniques to be considered, namely, the grant-based (GB), the semi-persistent, and the grant-free (GF) techniques. Furthermore, there are three different schemes used in GF scheduling, namely, the reactive, the k-repetitions, and the proactive schemes. We devise a mathematical model for the GF services using the k-repetitions scheme as the first model to define such traffic in a single cell. In addition, the GB scheduling model for eMBB traffic is adapted to fit our problem. We formulate the scheduling problem as a mixed-integer non-linear programming optimization problem. We introduce a complete system model that includes GF and GB subsystems. We introduce a novel mixed scheduler that combines the advantages of two well-known schedulers in the literature. We introduce novel machine-learning-based scheduling algorithms and evaluate them in comparison to well-known algorithms in the literature in addition to the optimal bound that we also derive. The results show that the proposed algorithms produce near-optimal results in real time.

OPTIMAL ENERGY CONSUMPTION AND COST PERFORMANCE SOLUTION WITH DELAY CONSTRAINTS ON FOG COMPUTING

Cloud computing plays an essential role in development of the Internet of Things, which provides data processing and storage services. Fog computing is the evolution of cloud computing, which helps provide solutions to cloud computing challenges such as latency, location awareness, and real-time mobility support. Fog computing fills the gap between the cloud and IoT devices within the close vicinity of IoT devices. So, computation, networking, storage, data management, and decision making occur along the path between the cloud and IoT devices. The automatic and intelligent management of fog node resources and achieving an effective scheduling policy in the computing model is a necessary requirement and will lead to the improvement of the overall performance of fog computing. Some optimization problems are modeled by mixed-integer nonlinear programming (MINLP). In this paper, a model, i.e. an MINLP optimization problem on fog computing, is designed. Our model has two goals: to increase Cost Performance as well as to reduce energy consumption. Cost Performance is the price, users are charged as benefit/revenue. In other words Cost Performance is defined as the ratio of the average data rate of each user to its cost. Then the exact mathematical method with the GAMS program was used to prove its logical process. In the next step, we solved the model with Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Simulated Annealing+GA (SA+GA), Teaching–Learning-Based Optimization (TLBO), Grey Wolf Optimizer (GWO), Grasshopper Optimization Algorithm (GOA), and random method. According to the TOPSIS comparison, the SA+GA method with a value of 0.23 is the best compared to other methods. Then GWO, GA, TLBO, PSO, and GOA methods are better, respectively.

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.

PAPR Reduction via Constellation Extension in OFDM Systems Using Generalized Benders Decomposition and Branch-and-Bound Techniques

In this paper, a novel constellation extension (CE)-based approach is presented to address the high peak-to-average power ratio (PAPR) problem at the transmitter side, which is an important drawback of orthogonal frequency-division multiplexing (OFDM) systems. This new proposal is formulated as a mixed-integer nonlinear programming optimization problem, which employs generalized Benders decomposition (GBD) and branch-and-bound (BB) methods to determine the most adequate extension factor and the optimum set of input symbols to be extended within a proper quarter plane of the constellation. The optimum technique based on GBD, which is denoted as GBD for constellation extension (GBDCE), provides a bound with relevant improvement in terms of PAPR reduction compared with other CE techniques, although it may exhibit slow convergence. To avoid excessive processing time in practical systems, the suboptimum BB for constellation extension (BBCE) scheme is proposed. Simulation results show that BBCE achieves a significant PAPR reduction, providing a good tradeoff between complexity and performance. We also show that the BBCE scheme performs satisfactorily in terms of power spectral density and bit error rate in the presence of a nonlinear high-power amplifier.

Distribution System Reconfiguration for Annual Energy Loss Reduction Considering Variable Distributed Generation Profiles

In this paper, a new formulation for distribution system reconfiguration (DSR) is proposed for minimizing the annual energy losses considering the variability in active and reactive power demand and distributed generation (DG) profiles. A fuzzy C-means clustering algorithm is used to obtain representative centroids from annual DG and power demand profiles. The DSR study is formulated as a mixed-integer nonlinear programming optimization problem and tested on a 33-bus and an 84-bus system. The minimization is subject to the power balance, bus voltage, and distribution system radiality constraints. Using this formulation, a single optimum configuration that minimizes annual energy losses is found and shown to be different from the optimum configuration, found in previous literature, which focuses on minimizing power losses at peak or average loads. In addition, the prospective advantages of grid automation on DSR are demonstrated to provide further energy loss reduction by including the possibility of interchanging a predefined number of configurations that minimize annual energy losses.

Power Supply Pads Assignment for Maximum Timing Yield

The design of power distribution networks significantly impacts the timing of very large scale integrated chips. Process variations induce uncertainty in the current drawn off the network and, therefore, impose statistical measures on the supply voltage. This brief presents an optimization methodology for assigning power supply pads across the chip for maximizing the timing yield. A mixed-integer nonlinear programming optimization problem subject to the voltage drop and current constraints is efficiently solved to find the optimum number and location of the pads. The experimental results for ISCAS89 benchmark circuits demonstrate as much as a 30% improvement in the timing yield.

Optimization and analysis of the profitability of tariff structures with two-part tariffs

Service providers often offer tariff structures with several two-part tariffs that consist of a fixed fee and a usage price, such that consumers may pick the tariff they prefer. Prices of tariffs have significant impacts on service providers’ profit, because they simultaneously influence consumers’ tariff choices and their usage. The number of tariffs also plays an important role, because more tariffs segment the market better but also increase the administrative burden and require more marketing effort. This article presents a mixed-integer nonlinear programming optimization problem to determine profit-maximizing tariffs; compares several heuristic search methods, in particular, the gradient method, stochastic search, and simulated annealing, to solve this problem; analyses the profitability of different tariff structures; and outlines the factors that drive differences in profitability across various tariff structures. The results show that especially for large samples of more than 100 consumers, simulated annealing performs best and deviates only 0.2% from the optimum. Structures with fewer two-part tariffs are generally sufficient, because additional two-part tariffs only negligibly increase service providers’ profit.

Downlink Scheduling Optimization in CDMA Networks

The problem of allocating radio resources in the downlink of a code-division multiple access (CDMA) network is studied. The modulation and coding schemes, numbers of multicodes, and transmit powers used for all mobile stations (MS) are jointly chosen so as to maximize the total transmission bit rate, subject to certain constraints. Based on the discrete and nonlinear nature of the proposed model, a mixed-integer nonlinear programming optimization problem is formulated. It is shown that the optimal allocation generally involves simultaneous transmissions to several MS. A scheduler which uses knowledge of MS traffic loads is also proposed and shown to yield a significant improvement in throughput.

Synthesis and optimization of an isothermal CSTR-network for the cyclohexane oxidation process

This paper deals with the synthesis and optimization of an isothermal CSTR-network for the industrially widespread cyclohexane oxidation process. Generally the mathematical representation of synthesis and optimization problems is attained by a superstructure, which considers all reasonable process topologies with respect to feasible connectivity options and alternative unit operations. Integer variables indicating the selection of process units from the superstructure and nonlinear process constraints arising from the unit models and thermodynamic calculations lead to a Mixed-Integer Nonlinear Programming (MINLP) optimization problem. Here a new approach is introduced, where the corresponding MINLP optimization problem is handled by a commercial equation-oriented flowsheeting package in combination with a Mixed-Integer Linear Programming (MILP) routine.

Optimal Process Synthesis in a Modular Simulator Environment: New Formulation of the Mixed-Integer Nonlinear Programming Problem

This paper deals with the formulation and the solution of a class of mixed-integer nonlinear programming (MINLP) problems, applied to optimal process synthesis, in a modular simulator environment. What is the first set out is the general solution strategy in a modular simulator environment. The proposed strategy leads to a reduced optimization problem and permits rigorous modeling of both logical and unit nodes of the superstructure. However, it involves implicit relations between the interest variables calculated by the simulator and both continuous decision and binary topological variables. In order to handle these implicit relations, a new formulation of the MINLP optimization problem is proposed. This formulation is based on the introduction of a new set of optimization variables and constraints : the pseudovariables and the pseudotorn streams. The proposed formulation leads to a reduced set of additional variables. The solution method is based on the outer approximation/equation relaxation (OA/ER) algorithm. The master problem (MILP) is constructed by partial application of the modeling/decomposition (M/D) strategy. Three examples illustrate the capabilities of the process synthesizer, one of which is the toluene hydrodealkylation (HDA) process.

A modelling and decomposition strategy for the minlp optimization of process flowsheets

This paper shows that in structural flowsheet optimization problems that are formulated as mixed-integer nonlinear programming (MINLP) problems, modelling can have a great impact in the quality of solutions that are obtained, as well as on the computational efficiency. A modelling/decomposition strategy is proposed to exploit the special structure of flowsheet synthesis problems that are to be solved with the OA/ER algorithm. The objective of this procedure is to reduce the computational effort required to solve the MINLP optimization problem, and to reduce the effect that nonconvexities can have in cutting-off the global optimum. The modelling strategy eliminates nonconvexities in the interconnection nodes through linear constraints and valid outer-approximations. The decomposition strategy has the important feature of only requiring the NLP optimization of the current candidate flowsheet. Nonexisting units in the superstructure are suboptimized through a Lagrangian decomposition scheme. Application of the proposed modelling/decomposition procedure is illustrated with several examples, including the synthesis of the HDA toluene process.