A new box selection criterion in interval Bernstein global optimization algorithm for MINLPs

Genetic algorithm for non-linear mixed integer programming problems and its applications

In the past years, the issues of energy efficiency and interference are becoming increasingly serious in wireless local area network (WLAN) since lots of access points (AP) are deployed densely to provide high-speed users access. However, current works focus on solving the two issues separately and the influence of each other is rarely considered. To address these problems, we propose a joint optimization scheme of energy efficiency and interference to reduce energy consumption and interference together without sacrificing users’ traffic demands. Firstly, based on energy consumption measurement of AP and network interference analysis, we establish energy efficiency and interference models respectively. Then, the weighting method is introduced to build the joint optimization to quantify the effects of user-AP association, AP switch, AP transmit power and AP channel on energy consumption and interference. Lastly, we formulate the joint optimization as an Mixed Integer Non-Linear Programming (MINLP) problem. Since the MINLP problem is NP-hard, we proposed an Joint Optimization of Energy Efficiency and Interference (JOEI) algorithm based on greedy method to simplify its computational complexity. The evaluation results show that the proposed algorithm can effectively reduce the network energy consumption while improve the capacity of WLANs.

Assessing solution quality and computational performance in the hydro unit commitment problem considering different mathematical programming approaches

Drone cell (DC) is an emerging technique to offer flexible and cost-effective\nwireless connections to collect Internet-of-things (IoT) data in uncovered\nareas of terrestrial networks. The flying trajectory of DC significantly\nimpacts the data collection performance. However, designing the trajectory is a\nchallenging issue due to the complicated 3D mobility of DC, unique DC-to-ground\n(D2G) channel features, limited DC-to-BS (D2B) backhaul link quality, etc. In\nthis paper, we propose a 3D DC trajectory design for the DC-assisted IoT data\ncollection where multiple DCs periodically fly over IoT devices and relay the\nIoT data to the base stations (BSs). The trajectory design is formulated as a\nmixed integer non-linear programming (MINLP) problem to minimize the average\nuser-to-DC (U2D) pathloss, considering the state-of-the-art practical D2G\nchannel model. We decouple the MINLP problem into multiple quasi-convex or\ninteger linear programming (ILP) sub-problems, which optimizes the user\nassociation, user scheduling, horizontal trajectories and DC flying altitudes\nof DCs, respectively. Then, a 3D multi-DC trajectory design algorithm is\ndeveloped to solve the MINLP problem, in which the sub-problems are optimized\niteratively through the block coordinate descent (BCD) method. Compared with\nthe static DC deployment, the proposed trajectory design can lower the average\nU2D pathloss by 10-15 dB, and reduce the standard deviation of U2D pathloss by\n56%, which indicates the improvements in both link quality and user fairness.\n

Resource allocation for device-to-device (D2D) communications is usually formulated as mixed integer nonlinear programming (MINLP) problems, which are generally NP-hard and difficult to solve. Traditional methods are based on mathematical optimization techniques, which suffer from forbidding computational complexity or unsatisfactory optimality. In this paper, we introduce a machine leaning (ML) technique, imitation learning, to address the resource allocation in D2D communications. The key idea is learning a good prune policy to speed up the widely-used globally optimal algorithm for the MINLP problems, the branch- and-bound (B&B) algorithm. With appropriate feature selection, imitation learning can be converted into a binary classification problem, which can be solved by the classical support vector machine (SVM). Extensive simulation demonstrates that the proposed method can achieve good optimality and reduce computational complexity simultaneously. It only needs hundreds of training samples and has a good generalization ability. Our proposed method can be also applied to the MINLP problems in other wireless communication networks.

The sustainability of water resources is one of the major concerns of the world. Industries are finding ways to minimize water costs and to reduce water pollution through efficient use of supplies. One of effective solutions is the use of water pinch technology or process integration techniques. Property integration emerged as the third trend of process integration technique (aside from energy and mass integration) to solve the problem of water network synthesis by considering physical stream properties such as pH or resistivity. Various techniques have been done to solve this property-based problem. In this paper, mixed integer non-linear programming (MINLP) problems with topological constraints is studied. Nowadays, various evolutionary algorithms are also used to solve such MINLP problems. In this study, particle swarm optimization is used to solve the property integration problem. A comparison is made between this algorithm and commercial genetic algorithm (GA) applications. Particle swarm optimization is observed to perform favorably compared to GA.

Federated learning (FL) over wireless networks has become a key enabler for privacy-preserving distributed artificial intelligence (AI). However, high learning latency remains a critical bottleneck due to the presence of stragglers, limited wireless resources, and frequent model uploads. While model quantization can mitigate this issue by reducing communication overhead, its effectiveness is sensitive to device heterogeneity and time-varying channel conditions. To address this issue, we propose <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FedDamQu</i>, a communication-efficient FL framework with doubly-adaptive model quantization, which dynamically adjusts quantization bit-widths across devices and communication rounds to balance latency and accuracy. Our objective is to maximize the model performance under learning latency constraints. The main contributions are summarized as follows. 1) Convergence Analysis under Unreliable Channels: We derive a novel convergence error upper bound for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FedDamQu</i>, which explicitly quantifies the impact of device selection, unreliable transmission, and quantization error on the global model performance, under both fixed and dynamic quantization gain settings. 2) Joint Optimization Framework: Based on the knowledge from the proposed theoretical bound, we formulate a joint mixed integer nonlinear programming (MINLP) problem that integrates device selection, quantization bit-width configuration, and bandwidth allocation to minimize the convergence error under latency constraints. 3) Efficient Solution Design: The MINLP problem is decomposed into three subproblems, where closed-form solutions for quantization bit-width configuration and bandwidth allocation subproblems are derived, and a lightweight yet effective iterative algorithm is developed to obtain a suboptimal solution for the device selection subproblem. Extensive experiment results validate the theoretical analysis and demonstrate that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FedDamQu</i> consistently outperforms existing methods in terms of convergence rate and model accuracy, while significantly reducing the overall learning latency.

Various wireless manufacturing sensors facilitate the monitoring and control process in industrial internet of things (IIoT) systems. Control and image data generated by control and vision-based monitoring systems are transmitted over shared wireless network to edge computing devices for further decisions. Due to limited spectrum resources and sensor transmit power, it is challenging to design efficient quality of service (QoS) aware transmission mechanism for heterogeneous data with diverse real-time and system performance requirements. In this paper, in order to guarantee control system performance and image clarity, the time slot allocation and transmission power for heterogeneous sensors are jointly optimized by formulating a mixed integer nonlinear programming (MINLP) problem. The MINLP problem is decomposed into multiple subproblems which are proved to have strong duality and can be solved in dual domain. Then, according to acknowledge (ACK) signals, we propose a priority-aware heuristic algorithm to solve each subproblem. Finally, the simulation results prove that our proposed mechanism can reduce the number of slots and energy consumption for transmission while guaranteeing performance requirements of heterogeneous data.

A reliable shortest path problem is focused on finding a reliable a priori shortest path to maximize the probability of travelers arriving at their destination within a given travel time budget in a stochastic network. The mathematical model based on nonlinear mixed integer programming is established to analyze the problem of finding the reliable shortest path in a stochastic traffic network. A penalty method is developed to solve the nonlinear mixed integer programming problem by transforming the proposed problem to an unconstrained nonlinear programming problem through penalty function. Numerical results are provided using a small network and show the validity and feasibility of the proposed method.

Given a set of candidate road projects with associated costs, finding the best subset with respect to a limited budget is known as the discrete network design problem (DNDP). The DNDP is often characterised as a bilevel programming problem which is known to be NP-hard. Despite a plethora of research, due to the combinatorial complexity, the literature addressing this problem for large-sized networks is scarce. To this end, we first transform the bilevel problem into a single-level problem by relaxing it to a system-optimal traffic flow. As such, the problem turns to be a mixed integer nonlinear programming (MINLP) problem. Secondly, we develop an efficient Benders decomposition algorithm to solve the ensuing MINLP problem. The proposed methodology is applied to three examples, a pedagogical network, Sioux Falls and a real-size network representing the City of Winnipeg, Canada. Numerical tests on the network of Winnipeg at various budget levels demonstrate promising results.

The location-allocation problem of manifolds, which is a part of subsea field layout optimization, directly affects the flowline cost. This problem has always been studied as a mixed-integer nonlinear programming (MINLP) problem, or an integer linear programming (ILP) problem when there are location options for the facilities. Making a MINLP model is surely convenient to interpret the optimization problem. However, finding the global optimum of the MINLP model is very hard. Hence, practically, engineers use approximation algorithms to search a good local optimum or give several good location options based on their experience and knowledge to reduce the MINLP model into an ILP model. Nevertheless, the global optimum of the original MINLP model is no longer guaranteed. In this study, enlightened by the graphic theories, we propose a new method in which we reduce the MINLP model into an ILP model---more precisely, a binary linear programming (BLP) model---without compromise of achieving global optimum, but also with extremely high efficiency. The breakthrough in both efficiency and accuracy of our method for the location-allocation problem of manifolds and wellheads is well demonstrated in various cases with comparison to the published methods and the commercial MINLP solver from LINDO. Besides, we also provide our results for larger-scale problems which were considered infeasible for the commercial MINLP solver. More generally, our method can be regarded as a specific MINLP/NIP (nonlinear integer programming) solver which can be used for many other applications. This work is the second of a series of papers which systematically introduce an efficient method for subsea field layout optimization to minimize the development cost.

Spectrum aggregation (SA) is a technique through which a user performs transmission through multiple channels to maximize capacity. In this paper, adaptive SA with optimal channel selection and power allocation for multiuser multichannel access in spectrum sharing wireless networks is proposed. The main objective is to maximize secondary user (SU) nodes capacity subject to: quality-of-service (QoS) requirements on capacity, collision probability threshold to protect primary user (PU) services, SU transit power and the fading wireless channels. This allows multiple SU nodes to dynamically aggregate PU channels without degrading performance of the PU nodes. Convex relaxation is employed to develop a relaxed optimal solution for the otherwise a mixed integer nonlinear programming (MINLP) problem, from which branch-and-bound (BnB) technique is employed to develop the optimal solution for the original MINLP problem. Furthermore, a suboptimal SA scheme with less complexity is developed based on the Hungarian algorithm. The presented simulation results reveal significant performance improvement for the proposed SA schemes in terms of capacity, outage probability and collision probability.

This paper focuses on optimal power flow (OPF) computations in which no more than a pre-specified number of controls are allowed to move. The benchmark formulation of this OPF problem constitutes a mixed integer nonlinear programming (MINLP) problem. To avoid the prohibitive computational time required by classical MINLP approaches to provide a (potentially sub-optimal) solution, we propose instead two alternative approaches. The first one consists in reformulating the MINLP problem as a mathematical program with equilibrium constraints (MPEC). The second approach includes in the classical OPF problem a nonlinear constraint which approximates the integral constraint limiting the number of control variables movement. Both approaches are solved by an interior point algorithm (IPA), slightly adapted to the particular characteristics of each approach. We provide numerical results with the proposed approaches on two test systems and for two practical problems: minimum cost to remove thermal congestion, and minimum cost of load curtailment to restore a feasible equilibrium point.

The explosive demands for mobile broadband service bring a major challenge to 5G wireless networks. Device-to-device communication, adopting side links for user-direct communication, is regarded as a main technical source for offloading large volume of mobile traffic from cellular base station. This article investigates the joint power and subcarrier allocation scheme for device-to-device communication in 5G time division duplex systems. In time division duplex system, instead of utilizing an exclusive portion of the precious cellular spectrum, device-to-device pairs reuse the subcarriers occupied by cellular users, thus producing harmful interference to cellular users in both uplink and downlink communication, and strongly limiting the spectrum efficiency of the system. To this end, we focus on the maximization of device-to-device throughput while guaranteeing both uplink and downlink channel quality of service of cellular users as well as device-to-device pairs. The problem is formulated as a mixed integer non-linear programming (MINLP) problem. To make it tractable, we separate the original MINLP problem into two sub problems: power allocation and sub-carrier reusing. The former is to develop optimal power allocation for each device-to-device pair and each cellular user, with the constraints of maximum power and quality of service. It is solved by geometric programming technique in convex optimization method. The latter is derived as a one-to-many matching problem for scheduling multiple subcarriers occupied by cellulars to device-to-device pairs. It is solved by Hungarian method. Simulation results show that the proposed scheme significantly improves system capacity of the device-to-device underlay network, with quality of service of both device-to-device users and cellular users guaranteed.

The process synthesis and design optimization of energy conversion systems can be modeled as a mixed integer nonlinear programming (MINLP) problem. The nonconvexity potential and the combinatorial nature of the objective functions and constraints largely suggest the application of heuristic search methods for global optimization. In this paper, a modified differential evolutionary algorithm is applied to a MINLP problem for optimizing the design of steam cycles based on a complex superstructure, containing a variable number and varying positions of reheatings, varying layouts of the feedwater preheating train, and a boiler feedpump turbine with steam extractions. The energy-savings potential from the existing system design was studied. The optimization of a 262 bar/600 °C/ 605 °C unit with a single reheat shows that an efficiency improvement between 0.55 percentage points (PP) and 1.28 PP can be achieved. The optimal design of steam cycles over 650 °C was found to be different from those of the designs under current steam conditions: a transition throttle pressure, above which the benefits of steam temperature elevation can be completely realized, is critical and, accordingly, three design zones associated with the match of throttle pressure and the steam temperature level are clearly identified with recommended ranges of reheat pressures.