Mixed-integer Nonlinear Problem Research Articles

A Coordinated Reconfiguration Strategy for Multi-Stage Resilience Enhancement in Integrated Power Distribution and Heating Networks

The tight coupling of power distribution system (PDS) and district heating system (DHS) makes it imperative to devise a coordinated strategy for the resilience enhancement of integrated electric and heating system (IEHS) in natural disasters. The PDS reconfiguration serves as a critical tool for service restoration by the optimal adjustment of PDS topology with designated tie and sectionalizing switches. Similarly, the DHS reconfiguration provides a viable solution for countering disasters by the optimal adjustment of heating supply topology with targeted tie and sectionalizing valves in DHS. In this paper, a multi-stage resilience enhancement strategy considering the coordinated reconfiguration of PDS and DHS is proposed, which coordinates degradation, fault isolation, and service restoration stages after disasters. The proposed model is formulated as a mixed-integer nonlinear problem, which addresses the coordinated regulation of PDS switches and DHS valves to achieve efficient fault isolation and provide a better service restoration. To make the proposed model tractable, a linearized Distflow model is proposed by introducing current-oriented auxiliary variables and the approximation of power flow and voltage drop equations. Extensive case studies are conducted to validate the efficiency and accuracy of the proposed model and illustrate the performance of coordinated reconfiguration of PDS and DHS on resilience enhancement.

Fill‐rate service level constrained distribution network design

AbstractThe design of distribution networks that simultaneously consider location and inventory decisions seeks to balance costs and product availability. The most commonly observed measure of product availability in practical settings is the fill‐rate service level. However, the optimal design of a distribution network that considers the fill rate to control shortages of fast‐moving consumer goods (FMCG) is considered intractable and has only been addressed by heuristic methods. This paper addresses the optimal design of a distribution network for FMCG able to provide high fill‐rate service level under a continuous review policy. Considering the exact formulation for the provided fill rate, we formulated a joint location–inventory model with fill‐rate service level constraints as a convex mixed integer nonlinear problem for which a novel decomposition‐based outer approximation algorithm is proposed. Numerical experiments have shown that our solution approach provides good‐quality solutions that are on average 0.15% and, at worst, 2.2% from the optimal solution.

Fairness in maximal covering location problems

This paper provides a mathematical optimization framework to incorporate fairness measures from the facilities’ perspective to discrete and continuous maximal covering location problems. The main ingredients to construct a function measuring fairness in this problem are the use of (1) ordered weighted averaging operators, a popular family of aggregation criteria for solving multiobjective combinatorial optimization problems; and (2) α-fairness operators which allow generalizing most of the equity measures. A general mathematical optimization model is derived which captures the notion of fairness in maximal covering location problems. The models are first formulated as mixed integer non-linear optimization problems for both the discrete and the continuous location spaces. Suitable mixed integer second order cone optimization reformulations are derived using geometric properties of the problem. Finally, the paper concludes with the results obtained from an extensive battery of computational experiments on real datasets. The obtained results support the convenience of the proposed approach.

Mathematical programming formulations for the Collapsed k-Core Problem

In social network analysis, the size of the k-core, i.e., the maximal induced subgraph of the network with minimum degree at least k, is frequently adopted as a typical metric to evaluate the cohesiveness of a community. We address the Collapsed k-Core Problem, which seeks to find a subset of b users, namely the most critical users of the network, the removal of which results in the smallest possible k-core. For the first time, both the problem of finding the k-core of a network and the Collapsed k-Core Problem are formulated using mathematical programming. On the one hand, we model the Collapsed k-Core Problem as a natural deletion-round-indexed Integer Linear formulation. On the other hand, we provide two bilevel programs for the problem, which differ in the way in which the k-core identification problem is formulated at the lower level. The first bilevel formulation is reformulated as a single-level sparse model, exploiting a Benders-like decomposition approach. To derive the second bilevel model, we provide a linear formulation for finding the k-core and use it to state the lower-level problem. We then dualize the lower level and obtain a compact Mixed-Integer Nonlinear single-level problem reformulation. We additionally derive a combinatorial lower bound on the value of the optimal solution and describe some pre-processing procedures, and valid inequalities for the three formulations. The performance of the proposed formulations is compared on a set of benchmarking instances with the existing state-of-the-art solver for mixed-integer bilevel problems proposed in (Fischetti, Ljubić, Monaci, and Sinnl, 2017).

Impact of demand side management approaches for the enhancement of voltage stability loadability and customer satisfaction index

This research work presents the tri-level optimization framework for the optimal scheduling of grid-connected and autonomous microgrids to diminish power losses and maximize loadability. Since the network's voltage profile depends on the loading level, the flexible load shaping-based demand-side management strategy is incorporated to investigate its impact on microgrid loadability. With the consideration of uncertain parameters related to renewable power generation, load demand, and power loss, voltage limit constraints, the resultant problem is formulated as a stochastic mixed-integer non-linear problem to enhance microgrid loadability and optimize daily operating costs. The interdependency of demand side management program and microgrid loadability is investigated. The seasonal load profiles covering the weekend and weekday loads in winter, summer, and spring/fall seasons are examined in this research work. The enhanced versions of the distribution networks IEEE-33 and IEEE-69 based microgrid test systems are chosen to evaluate the proposed framework in both off-grid and autonomous modes of operation. Simultaneously, the overall customer satisfaction index is evaluated and improved according to the seasonal load profiles winter weekday, winter-weekend, summer-weekday, summer-weekend, spring-weekday, and spring-weekend by 8.68%, 7.97%, 16.7%, 19.62%, 17.14%, 20.50% respectively. The recently reported Whale Optimization Algorithm is adopted to solve the proposed optimization problem, and the obtained simulation results are validated by comparing them with popular metaheuristic algorithms. The computational burden on the utility is reduced for optimal scheduling of grid-integrated microgrid to extract maximum power by maintaining network voltage profile.

QoS-Oriented Sensing–Communication–Control Co-Design for UAV-Enabled Positioning

Unmanned aerial vehicle (UAV)-enabled positioning that uses UAVs as aerial anchor nodes has been envisioned as a promising solution for providing positioning services in harsh environments. In previous research, state sensing and control of UAVs was either ignored or assumed to be performed continuously, resulting in system instability or a waste of wireless resources. Therefore, in this paper, we propose a quality-of-service (QoS)-oriented sensing-communication-control (SCC) co-design scheme for UAV-enabled positioning systems. We first establish mathematical models of UAV state sensing and control. Then, we analyze the influence of sensing scheduling and transmission failure on the stability of UAV, as well as the performance of positioning services in the presence of UAV control error. Based on these models and analysis results, we further study the problem of minimizing the amount of data transmitted by optimizing the sensing scheduling and blocklength allocation under the condition of meeting each user’s requirement on position accuracy. Finally, a heuristic algorithm is developed to solve this mixed-integer nonlinear problem. Numerical results demonstrate the validity and superiority of the proposed scheme. Compared with two benchmark schemes, our scheme reduces the failure rate or resource consumption of positioning services by more than 75% or 80%.

Heuristic Algorithm for Resource Allocation in an Internet of Battle Things

Internet of Things has been experiencing unprecedented deployment from the civilian to the military ones like the Internet of battle Things (IoBT). Different from the civilian applications, the presence of various electronic countermeasures (ECM) in IoBT would destroy the infrastructure of a network, making the mobile edge computing (MEC) with quality of service (QoS) guaranteed in such a resource-limited IoBT more challenging. To improve the QoS of mobile users under an ECM environment, we address the optimization scheme in an MEC network with heterogeneous edge servers, considering that the connections in a network might be destroyed and therefore switch to the other connections for data transmission due to ECM. Mathematically, we characterize the optimization of wireless resource allocation as a mixed-integer nonlinear problem to maximize the relative improvement in task computation time and energy consumption. We decompose the original problem into a few suboptimization problems and propose a heuristic algorithm that can achieve a suboptimal solution in polynomial time by solving this NP-hard problem. The analytic results show that our proposed scheme can save task computation time and energy consumption over traditional approaches under an ECM environment.

Joint Optimization of Multi-User Partial Offloading Strategy and Resource Allocation Strategy in D2D-Enabled MEC

With the emergence of more and more computing-intensive and latency-sensitive applications, insufficient computing power and energy of user devices has become a common phenomenon. Mobile edge computing (MEC) is an effective solution to this phenomenon. MEC improves task execution efficiency by offloading some tasks to edge servers for execution. In this paper, we consider a device-to-device technology (D2D)-enabled MEC network communication model, and study the subtask offloading strategy and the transmitting power allocation strategy of users. The objective function is to minimize the weighted sum of the average completion delay and average energy consumption of users, which is a mixed integer nonlinear problem. We first propose an enhanced particle swarm optimization algorithm (EPSO) to optimize the transmit power allocation strategy. Then, we utilize the Genetic Algorithm (GA) to optimize the subtask offloading strategy. Finally, we propose an alternate optimization algorithm (EPSO-GA) to jointly optimize the transmit power allocation strategy and the subtask offloading strategy. The simulation results show that the EPSO-GA outperforms other comparative algorithms in terms of the average completion delay, average energy consumption, and average cost. In addition, no matter how the weight coefficients of delay and energy consumption change, the average cost of the EPSO-GA is the least.

Integrated model for optimal energy management and demand response of microgrids considering hybrid hydrogen-battery storage systems

Hybrid hydrogen-battery (HHB) based energy storage technologies have recently become matters of significant interest to enable sustainable and net zero-emission microgrids characterized with high penetration levels of variable renewable energy sources (RES) such as solar and wind. In this regard, there are multiple objectives and constraints controlling the scheduled decision-making framework that manages these microgrid resources while supplying the demand. As such, this paper introduces an integrated energy management system (IEMS) to concurrently optimize the operation schedule of the HHB storage system and provide demand response (DR) via adequate shifting slots for the elastic loads of a microgrid setup. The proposed IEMS aims to optimally manage the microgrid’s energy by minimizing three conflicting objective functions: the electricity and battery degradation costs, customers’ discomfort, and peak-to-average ratio (PAR). The proposed IEMS is developed for microgrids containing a mix of variable RES, an HHB storage system, and a local power consumption considering dynamic grid tariff. The IEMS is formulated as a mixed-integer nonlinear problem and is solved using a multi-objective artificial hummingbird optimizer (MOAHA). To account for the variability and uncertainty of RES, the proposed IEMS is tested under four scenarios: good, bad, average weather scenarios, and a forecasted weather profile based on a stochastic model of RES. The performance of the proposed IEMS is evaluated via comprehensive comparative analyses with the conventional energy management strategy (CEMS) without and with consideration of the HHB storage system and DR. Moreover, the performance of MOAHA has been assessed versus the state-of-the-art multi-objective particle swarm optimizer (MOPSO). For the purpose of these comparisons, four quality metrics have been utilized to quantify the benefits of the proposed IEMS: renewable contribution factor (RCF), greenhouse gas (GHG) emission, loss of power supply probability (LPSP), and saving cost (SC). The results show that the proposed IEMS yields better-optimized values that help the microgrid operator identify the sweet spot of the conflicting objectives, where it has increased the customer saving to be (82.95%, 29.65%, 33.33%, and 33.00 %), (73%,23.94%, 25.49%, and 31.65%) and (10.69%,3.62%, 1.59%, and 1.67%) compared to the CEMS without/with including HHB. and IEMS based-MOPSO over the four studied scenarios, respectively. Also, the results show the superiority of the proposed IEMS in improving the identified four quality metrics compared to the CEMS without/with considering HHB storage systems and IEMS-based-MOPSO. Accordingly, integrating HHB and implementing optimized IEMS based-MOAHA with considering the DR approach plays a vital role in providing a profit for the customer, protecting the environment from emissions, and enhancing the system’s reliability with considering the weather uncertainty.

Energy-Efficient DNN Partitioning and Offloading for Task Completion Rate Maximization in Multiuser Edge Intelligence

Deep Neural Network (DNN) has become an essential technology for edge intelligence. Due to significant resource and energy requirements for large-scale DNNs’ inference, executing them directly on energy-constrained Internet of Things (IoT) devices is impractical. DNN partitioning provides a feasible solution for this problem by offloading some DNN layers to execute on the edge server. However, the resources of edge servers are also typically limited. An energy-constrained and resource-constrained optimization problem is generated in such a realistic environment. Motivated by this, we investigate an optimization problem of DNN partitioning and offloading in a multiuser resource-constrained environment, which is considered an intractable Mixed-Integer Nonlinear Problem (MINLP). We decompose the problem into two subproblems and propose an Energy-Efficient DNN Partitioning and Offloading (EEDPO) strategy to solve it in polynomial time based on the minimum cut/maximum flow theorem and dynamic programming. Finally, we test the impact of energy constraint, DNN type, and device number on the performance of EEDPO. Simulation results on realistic DNN models demonstrate that the proposed strategy can significantly improve the DNN inference task completion rate compared to other methods.

Integreted strategic and tactical optimization planning of biomass to bioethanol supply chains coupled with operational plan using vehicle routing: A case study in Ethiopia

The optimization of supply chain, a subject of active research in process system engineering, frequently leads to large Mixed Integer Linear or Non-Linear Problems more particularly when applied to realistic industrial cases. In this domain, one main challenge concerns multi scale modeling to accurately integrate the different decision scales (from strategic to operational) and to study the impact of the decision across these scales, in order to effectively contributes to intelligent and coherent decision making. Unfortunately, very few papers cover the three decision levels - strategic (long-term decisions: supply network design), tactical (medium-term decisions: management of network design) and operational (short- term decisions: routing, inventory management…) to have a holistic perspective of the supply chain. Therefore, the first objective of this paper is to model as finely as possible the three decision levels by focusing more particularly on the transport related decision due to their importance on the supply chain performances. As a progress, the Vehicle Routing Problem, one of the most studied problem in logistic and one of the most complex, is integrated into a strategic and tactical model. But, the resulting large-scale MILP model must be solved in a reasonable computational time. To achieve this second objective, we developed a novel iterative multi scale strategy that optimizes the model at two spatial and two temporal scales. This strategy is based on a deep knowledge of the mathematical models and especially of the variables that strongly influence the resolution. The real biofuel supply chain in the Ethiopian country is used to demonstrate the capabilities of the approach, and the improvement in computing time and solution strategy. In addition to the change in the design of the supply chain network, the use of an operational model that finely describes the transport activities shows that the costs related to these activities are often underestimated by a factor between 2 and 3 in the classical models of the literature. The main perspectives of this work are to address the two main shortcomings of the proposal: writing and solving in a reasonable computational time a single model rather than using a decomposition (especially useful for multi-objective optimization) and integrating other decisions at the operational level to not be limited to those related to transportation.

Accelerating Federated Edge Learning via Topology Optimization

Federated edge learning (FEEL) is envisioned as a promising paradigm to achieve privacy-preserving distributed learning. However, it consumes excessive learning time due to the existence of straggler devices. In this article, a novel topology-optimized FEEL (TOFEL) scheme is proposed to tackle the heterogeneity issue in federated learning and to improve the communication-and-computation efficiency. Specifically, a problem of jointly optimizing the aggregation topology and computing speed is formulated to minimize the weighted summation of energy consumption and latency. To solve the mixed-integer nonlinear problem, we propose a novel solution method of penalty-based successive convex approximation (SCA), which converges to a stationary point of the primal problem under mild conditions. To facilitate real-time decision making, an imitation-learning-based method is developed, where deep neural networks (DNNs) are trained offline to mimic the penalty-based method, and the trained imitation DNNs are deployed at the edge devices for online inference. Thereby, an efficient imitation-learning-based approach is seamlessly integrated into the TOFEL framework. Simulation results demonstrate that the proposed TOFEL scheme accelerates the federated learning process and achieves a higher energy efficiency. Moreover, we apply the scheme to 3-D object detection with multivehicle point cloud data sets in the CARLA simulator. The results confirm the superior learning performance of the TOFEL scheme over conventional designs with the same resource and deadline constraints.

Reinforcement Learning for Efficient Design Space Exploration With Variable Fidelity Analysis Models

Abstract Reinforcement learning algorithms can autonomously learn to search a design space for high-performance solutions. However, modern engineering often entails the use of computationally intensive simulation, which can lead to slower design timelines with highly iterative approaches such as reinforcement learning. This work provides a reinforcement learning framework that leverages models of varying fidelity to enable an effective solution search while reducing overall computational needs. Specifically, it utilizes models of varying fidelity while training the agent, iteratively progressing from low- to high fidelity. To demonstrate the effectiveness of the proposed framework, we apply it to two multimodal multi-objective constrained mixed integer nonlinear design problems involving the components of a ground and aerial vehicle. Specifically, for each problem, we utilize a high-fidelity and a low-fidelity deep neural network surrogate model, trained on performance data generated from underlying ground truth models. A tradeoff between solution quality and the proportion of low-fidelity surrogate model usage is observed. Specifically, high-quality solutions are achieved with substantial reductions in computational expense, showcasing the effectiveness of the framework for design problems where the use of just a high-fidelity model is infeasible. This solution quality-computational efficiency tradeoff is contextualized by visualizing the exploration behavior of the design agents.

Voltage regulation and power loss mitigation by optimal allocation of energy storage systems in distribution systems considering wind power uncertainty

Due to the ever increasing in the energy demand and the growth of the pollution problem, further interest in renewable energy becomes prominent, especially wind energy. However, the intermittent nature of the wind speed results in the system's insecurity problems. Integrating the energy storage system (ESS) optimally is the best so far solution. In this paper, a probabilistic discretizing method is derived and generalized to consider the uncertainties of the wind generators. Moreover, a mixed integer non-linear optimisation problem is constructed comprises three objective functions to be minimized simultaneously. The objectives comprising the total operation and planning cost of ESSs, the average voltage deviation and average power losses. The solving method is a hybrid algorithm incorporates the non-dominated sorting genetic algorithm (NSGAII), multi-objective particle swarm optimisation (MOPSO) and a decision-making algorithm. The aim is to determine the optimal location and sizing of ESSs considering their reactive power capability. 69 radial bus distribution system is adopted to demonstrate the efficacy of the proposed hybrid algorithm and performing some case studies. The simulation results verified the capability of ESSs to enhance the voltage profile and reduce the power losses, notably when reactive power capability is examined.

Edge Computing Task Scheduling with Joint Blockchain and Task Caching in Industrial Internet

Deploying task caching at edge servers has become an effective way to handle compute-intensive and latency-sensitive tasks on the industrial internet. However, how to select the task scheduling location to reduce task delay and cost while ensuring the data security and reliable communication of edge computing remains a challenge. To solve this problem, this paper establishes a task scheduling model with joint blockchain and task caching in the industrial internet and designs a novel blockchain-assisted caching mechanism to enhance system security. In this paper, the task scheduling problem, which couples the task scheduling decision, task caching decision, and blockchain reward, is formulated as the minimum weighted cost problem under delay constraints. This is a mixed integer nonlinear problem, which is proved to be nonconvex and NP-hard. To solve the optimal solution, this paper proposes a task scheduling strategy algorithm based on an improved genetic algorithm (IGA-TSPA) by improving the genetic algorithm initialization and mutation operations to reduce the size of the initial solution space and enhance the optimal solution convergence speed. In addition, an Improved Least Frequently Used algorithm is proposed to improve the content hit rate. Simulation results show that IGA-TSPA has a faster optimal solution-solving ability and shorter running time compared with the existing edge computing scheduling algorithms. The established task scheduling model not only saves 62.19% of system overhead consumption in comparison with local computing but also has great significance in protecting data security, reducing task processing delay, and reducing system cost.

Quality-Aware Incentive Mechanism for Social Mobile Crowd Sensing

The mobile crowd sensing perception paradigm relies on the participation of generous users, and an appropriate incentive mechanism can promote the participation of more users. Moreover, social relationships among users can promote users’ willingness to complete the sensing tasks, which in turn boosts the collection of high-quality data for the platform. In this letter, we study the problem of designing a suitable incentive mechanism combined with data quality under social influence. Specifically, we divide the design of the incentive mechanism into two stages: participant selection considering social influence; reward payment considering quality measurement. We use the KKT system to get an optimal time of users in stage I. Furthermore, the reward payment stage can be equivalently transformed into a mixed-integer nonlinear problem, and we devise a heuristic algorithm HEAL to solve the problem. Finally, we conduct certain numerical comparative simulation experiments to evaluate the effectiveness and correctness of HEAL.

Discrete Mixed-Integer Shooting (DMIS): Algorithm and Application to Plug-In Hybrid Electric Vehicle Energy Management Accounting for Fuel Cranking and Actual Powertrain Efficiency Maps

This article presents an algorithm for mixed-integer nonlinear optimal control problems (OCPs) formulated directly in discrete time. In our current application, we address the energy management of a plug-in hybrid electric vehicle (PHEV) seeking to achieve minimum trip fuel consumption under a terminal state-of-charge (SOC) equality constraint while avoiding powertrain efficiency map approximations in order to maximize its fuel economy (FE). An additional engine cranking state with a nonsmooth state and control transition cost is then incorporated to prevent undesired engine on/off behaviors. We pursue a single shooting-based numerical algorithm, motivated by the success of the computationally efficient Pontryagin’s Minimum Principle (PMP)-based single shooting in achieving similar FE results as dynamic programming (DP) for the power-split optimization problem without the additional engine cranking state shown in prior work. The Discrete Mixed-Integer Shooting (DMIS) algorithm, with costate backward-in-time propagation, is presented here, avoiding unstable shooting iterations that are typically encountered in PMP-based single shooting. When applying DMIS to solve the power-split problem with cranking fuel consideration, we show through simulation that it leads to better FE results than the PMP-based single shooting without the cranking state, thus demonstrating the effectiveness of the DMIS algorithm. Finally, experimental dynamometer test results with the model predictive powertrain controller solved by DMIS for minimum trip fuel consumption are presented and discussed, demonstrating its real-time execution and the cranking fuel reduction capability.

Task Offloading in Multi-Access Edge Computing Enabled UAV-Aided Emergency Response Operations

In emergency response operations, using uncrewed aerial vehicles (UAVs) has recently become a promising solution due to their flexibility and easy deployment. However, tasks performed by the UAVs, e.g., object detection and human pose recognition, usually require a high computation capacity and energy supply. Furthermore, offloading tasks to the edge server-equipped base stations may not always be possible because of a lack of infrastructure or distance. Therefore, UAV-aided edge servers can be deployed near UAV scouts to provide computing services. However, a UAV can not perform all types of tasks since it has limitations on memory, available software, central processing unit (CPU), and graphics processing unit (GPU) capacity. Therefore, this study focuses on task offloading (TO), power, and computation resource allocation (PRA) problems in a multi-layer MEC-enabled UAV network while taking into account CPU and GPU requirements of tasks, the capacity of the devices (i.e., computational resources, power, and energy), and limitations on the type of tasks a UAVs can perform. The problem is formulated as a non-convex mixed-integer nonlinear problem to minimize the weighted sum of the maximum energy consumption ratio in the network and total task execution latency ratio, and then decomposed and converted into an integer and a convex problem. A messy genetic algorithm (mGA)-based TO and PRA strategy (mGA-TPR) is proposed to solve the problem, where two PRA strategies are based on the Karush–Kuhn–Tucker conditions used to solve the PRA problem. Simulation results verify that the proposed scheme can outperform the baseline methods.

Weapon Target Assignment Model for Small Unit Ground Combat Using Mixed Integer Nonlinear Program and Lagrangian Relaxation

The importance of the weapon target assignment problem is increasing as weapon systems are expected to become intelligent and unmanned on the future battlefield. This study discusses the weapon-target assignment in small-scale ground force combat, which has not been addressed much in other studies. In ground combat, target assignment means the start of an engagement, so assignment should be made taking into account not only the probability of killing an enemy but also the probability of surviving friendly forces. We introduce the WTAG (WTA ground) model that reflects these characteristics and describes methodologies for solving the problem including mixed integer nonlinear problems and Lagrangian relaxation approaches. Our finding is that the algorithm presented can efficiently provide the bounds of the problem in a practical size.

An exact solution method and a genetic algorithm-based approach for the unit commitment problem in conventional power generation systems

The unit commitment problem (UCP) is one of the fundamental problems in power systems planning and operations that comprises two decisions: commitment and dispatching of conventional generating units. The objective is to minimize total operating costs -fuel and start-up costs- while satisfying several operational and technical constraints. The UCP is characterized as a highly constrained mixed-integer nonlinear NP-hard problem, which makes it difficult to develop a rigorous optimization method for real-size systems. Hence, we devise an efficient mixed-integer quadratic programming formulation as an exact method with brand-new linear representations for each of the three crucial constraint sets, namely minimum uptime/downtime, start-up and ramp-up/down constraints. Furthermore, to be able to solve a large-scale UCP and to deal with its complexities, we propose a Genetic Algorithm-based matheuristic approach that can provide optimal/near-optimal solutions quickly, thanks to its unique binary-integer coding scheme and several problem-specific operators. During the genetic evolution, commitment and dispatching schedules are determined by combining genetic operations and the Improved Lambda Iteration Method reinforced by the incorporation of average fuel cost optimization and ramp rate limits. The final dispatching schedule is then determined via a start-up adjustment procedure and an efficient quadratic programming model. The computational experiments show that both proposed exact approach and GA-based matheuristic can provide satisfactorily good schedules even for large-scale conventional power systems in quite a reasonable computation time.