Day-ahead optimization model for renewable energy communities considering load shifting, electric vehicles and vehicle-to-grid technology

Multi-time scale prediction and bilinear benders decomposition-based optimal dispatch for PIEHS with virtual energy storage

Sizing, economic analysis and optimisation of green hydrogen refuelling stations in a cluster of small islands

The newly constructed renewable energy-oriented virtual power plants (VPPs) suffer from a scarcity of operation data for renewable energy and the uncertainties from both generation and load, which severely impact on the reliable operation and economic dispatch of VPPs. To address this issue, this paper proposes a distributionally robust optimization (DRO) scheduling strategy for VPPs based on data generation augmentation. Firstly, to mitigate the problem of operation data scarcity, this paper integrates the physical model of photovoltaic (PV) with deep learning methodology integrating convolutional neural networks (CNN) and multi-head attention mechanism. Historical meteorological data are utilized to calibrate the parameters of the physical model, thereby enhancing the accuracy of data generation. Secondly, considering the dual uncertainties of sources and loads, a DRO dispatch model for VPP is established based on the Wasserstein distance. Furthermore, this paper proposes to reformulate the dispatch model into a tractable mixed-integer linear programming problem by leveraging linear decision rules and strong duality theory. Finally, simulations verify that the proposed strategy demonstrates advantages in data generation accuracy and robustness under different meteorological conditions. Moreover, the DRO dispatch method can adapt to the dynamic variability characteristics of PV power and load power, thereby reducing the operating costs and simultaneously enhancing operating reliability of VPPs.

This article introduces an approach for signal predictive optimization utilizing real-time detection-based vehicle trajectory data. Unlike traditional trajectory data collected from probe vehicles, the detection-based vehicle trajectories are acquired by integrated radar and video detectors strategically deployed at signalized intersections. The detection comprehensively covers entry and exit lanes around the intersection with nearly complete penetration, thus being able to collect and process trajectory data in real time. A lane-level traffic state representation model is proposed to map vehicle trajectories collected in real time to individual lanes, facilitating the description of traffic flow dynamics. The optimization model is formulated as a mixed-integer linear programming problem with the objective of throughput maximization. Simulation experiments validate the effectiveness of the proposed strategies for network control, demonstrating advantages over fixed-time coordinated schemes, actuated control, and pressure-based adaptive control. While decision-making at each intersection is independent, a certain coordination effect is observed. Sensitivity analyses reveal the performance of the proposed strategy under various demand scenarios, objective functions, and detection ranges. This study explores the application of advanced real-time detection-based trajectory data for urban traffic management.

{Mixed-integer programming and numerical experiments are used to demonstrate globally optimal and scalable threshold regression estimation with improved accuracy.} We develop a mixed-integer programming (MIP) framework for estimating multiple-regime threshold regression models. Least squares and least absolute deviation estimators are reformulated as mixed-integer quadratic and linear programming problems, yielding globally optimal solutions without restrictive design assumptions. To handle large data sets, we design four heuristics based on cumulative sum ideas: binary segmentation, iterative breakpoint tuning, genetic algorithm, and dung beetle optimization. Integrated in a two-stage heuristic-MIP scheme, they serve as fast standalone solvers and provide warm starts and objective cutoffs that substantially speed up MIP. Simulations and real-data applications show that the framework attains competitive or superior estimation accuracy and threshold selection, while combining the flexibility and optimality guarantees of MIP with the scalability of heuristic methods.

As global supply chains increasingly prioritize environmental sustainability and operational efficiency, battery electric freight vehicles (EFVs) have emerged as a pivotal alternative to traditional diesel-powered logistics fleets. This paper addresses the integrated planning and scheduling problem for multi-modal logistics systems utilizing EFVs. An integrated model is proposed to determine the number of electric freight vehicles and optimize dispatch and charging schedules, considering deadheading, and time-of-use electricity pricing. The model is formulated as an integer linear programming (ILP) problem solvable by commercial solvers. A branch-and-price framework and a heuristic algorithm are developed to handle large-scale instances. A case study using real data from a logistics provider in China demonstrates that the EFV system achieves a 45.5% reduction in total monthly costs compared to traditional diesel freight vehicle systems, even after accounting for higher vehicle and infrastructure costs. Sensitivity analyses offer practical insights for EFV adoption in multi-modal logistics.

Unmanned Aerial Vehicles (UAVs) are widely used in modern military missions, primarily for surveillance, reconnaissance, search and detection, and air-to-ground strikes. The widespread use of UAVs in recent conflicts, such as the Russia-Ukraine war, once again highlighted their growing strategic importance. The complexity of military missions carried out by UAVs, coupled with the need for autonomous and coordinated fleet operations, requires analytical approaches to optimize deployment planning and improve operational efficiency. In this study, we address a UAV deployment planning problem for search and detection missions, in which a homogeneous fleet of UAVs is tasked with searching for hostile assets across a network of disjoint regions. Each region is characterized by an a priori probability of target presence, a search difficulty factor which affects the probability of detection, and known inter-region distances. For this purpose, we first develop a mixed-integer nonlinear programming formulation which determines the base locations of UAVs, allocates the limited search time across regions, and sequences the visits to maximize the total time-weighted detection probability mass to achieve the highest probability as much and as early as possible during the operation. Next, we apply a tangent line approximation technique to reformulate the model as a mixed-integer linear programming problem, which we solve using commercial off-the-shelf solvers. We then propose a hybrid heuristic approach based on the ant colony optimization method to generate high-quality solutions. Our computational experiments reveal that the proposed heuristic significantly reduces solution time while maintaining superior performance compared to the linear approximation model.

Purpose This study aims to develop an efficient level-set (LS)-based multi-objective topology optimization framework capable of handling strongly nonlinear electromagnetic design problems, and to demonstrate its applicability through the design of synchronous reluctance motors. Design/methodology/approach The proposed level-set adaptive switching method (LASM) combines an LS-based topology optimization scheme with an adaptive switching mechanism of weighting coefficients. The weights are automatically determined by solving a mixed-integer linear programming problem that maximizes the expected shape variation, and switching is triggered when objective improvement stagnates, deteriorates or oscillates. This dynamic framework enables continuous exploration of Pareto fronts in multi-objective design spaces. Findings Numerical experiments demonstrate that LASM achieves broader and more uniformly distributed Pareto fronts and improved design performance compared with conventional weighted-sum optimization. The obtained geometries maintain smooth and manufacturable boundaries, confirming the practicality of the proposed framework. Originality/value LASM builds upon the LS-based switching concept of Shigematsu et al. (2022) and extends it by introducing a shape-variation-driven automatic weight computation scheme and enabling a scalable application to three or more objectives. Through these extensions, LASM eliminates designer dependency in weight setting, enhances robustness against local minima and provides a practical and fully automated framework for multi-objective electromagnetic design.

We focus here on the program which is a support in learning of solving Integer Linear Programming (ILP) and Binary Integer Programming (BIP) problems. There are many programs solving optimization problems using the simplex algorithm and they also offer the option of solving tasks with the result as integer numbers but our program is specialized for such problems and shows the subsequent stages of solving the tasks with the use of the branch and bound method. In this article, the mentioned method is described. Then, we shortly characterize the environment in which the program was implemented and deliver some details about the implementation. Finally, there is a description and examples of program’s functionalities. This tool can generate arbitrary problem but also the user may introduce own tasks. Program uses standard Python libraries to solve the problem according to the branch and bound method – because this approach generates subproblems, as long as it will not find the integer result, the program gathers all intermediary solutions to be accessible for the user. At the end of program’s operating, the problem, its solution, and subsequent stages are saved to a file.

ABSTRACT Nexus represents the interrelationship among multiple systems. Simultaneous optimization of interdependent sources is essential to ensure optimum production to satisfy demands. To optimize the nexus between two interdependent systems, a multi‐objective linear programming problem is formulated, and a graphical technique is proposed in this work. The proposed method simultaneously determines the minimum production of both sources needed for demand satisfaction. The graphical approach applies the principles of pinch analysis to solve the multi‐objective two‐dimensional nexus problems. A Pareto‐optimal point, recognized as the pinch point for such problems, is identified. The maximum extent to which the external demand of any source can be produced using the existing systems is also identified. Four illustrative examples demonstrate the applicability of the proposed method. The proposed methodology can be used for the optimal design and planning of a two‐dimensional nexus system. Highlights A graphical method is proposed to optimize two‐dimensional nexus systems. The simultaneous optimization of two sources leads to a single Pareto point. The proposed method identifies the maximum external demand of any source. The versatility of the method is demonstrated through multiple applications.

This study examines the fully fuzzy multi-objective linear fractional programming problem (FFMOLFPP), whereby both the objective functions and restrictions incorporate fuzzy parameters represented as triangular fuzzy numbers (TFN), without converting them into crisp values. A hybrid solution approach is presented to tackle the intrinsic nonlinearity and uncertainty. Initially, the imprecise numbers are transformed into parametric representations via the y- cut method. A first-order Taylor series expansion is subsequently utilized to linearize each fractional objective function around a fuzzy decision point. The linearized objectives are then consolidated by the weighted sum approach, transforming the multi-objective fuzzy model into a single-objective linear program. Numerical examples validate the strategy and demonstrate the improved accuracy and efficiency of the proposed methodology.

The blending process in raw material yards is essential for maintaining precise material proportions in downstream production, directly influencing product quality and energy efficiency in industries such as steel and coal processing. However, stringent operational constraints, including silo capacity limits, discharge rates, equipment movement delays, and a strict no-empty-silo requirement, result in a strongly coupled, high-dimensional combinatorial scheduling problem. In this paper, we develop a mixed-integer nonlinear programming (MINLP) model to capture the complex dynamics of silo weight and equipment operations. The primary scientific contribution of this work lies in the theoretical discovery of a structural decoupling property within the complex MINLP. We analytically prove that by fixing the replenishment sequence, the intractable global problem can be rigorously decomposed into two subproblems: a linear programming (LP) problem for silo-filling cart scheduling and a shortest-path problem solvable via dynamic programming (DP) for reclaimer scheduling. Leveraging this decomposition, a two-stage metaheuristic algorithm is proposed, combining greedy initialization with multi-round simulated annealing enhanced by local search. Experimental validation using real industrial data demonstrates that the proposed method consistently outperforms the greedy algorithm. Crucially, while the commercial solver Gurobi struggles to converge within a practical 1800 s time limit, our approach yields comparable solution quality in mere seconds. Furthermore, robustness analysis under a 20% demand surge confirms the algorithm’s adaptive capability, maintaining the silo weight stability through re-optimization. This research provides a robust, computationally efficient solution for the blending process in raw material yards.

Lightweight cryptography aims to achieve security with minimal resource footprints and low computational overhead. In particular, efficient implementations of linear layers are recognized as a crucial component. Boyar et al. showed that finding an optimal implementation of linear layers reduces to the Shortest Linear Program (SLP) problem, which is NP-hard. Consequently, various heuristic methods have been developed to search for near-optimal solutions. In this work, low-latency implementations are prioritized, and a heuristic search algorithm named HILL (Heuristic Implementation for Low-Latency Linear layers) is proposed. To further balance cost and delay, the h-XOR metric is integrated into HILL, where 2/3-input XOR gates are dynamically weighted to achieve an optimized trade-off between the circuit area and depth. Compared with the heuristic search proposed by Li et al. (FSE 2019), which yields an AES MixColumns implementation requiring 315 gate equivalents (GEs) at depth 3, our approach achieves 270.4 GEs at the same depth, corresponding to a 14.2% area reduction. To the best of our knowledge, this is one of the most efficient hardware implementations of AES linear layers in terms of both area and depth. Furthermore, implementation costs are minimized for all 4254 Maximum Distance Separable (MDS) matrices proposed by Li et al.

Linear fractional programming problems in an interval environment

Compared with rule-based and optimization energy management strategies, online optimal energy management control strategies for a dual-mode power-split hybrid electric vehicles (PSHEVs) are able to achieve better fuel economy and real-time performance. Global online optimization of a finite time domain energy management strategy based on the hybrid model predictive control (HMPC) algorithm is proposed in this study. To reduce the computing time, a linearized predictive model is built; because dual-mode PSHEVs can be considered hybrid systems that include continuous and discrete states, the hybrid states can be expressed uniformly. Therefore, a mixed logical dynamic (MLD) predictive model is built based on hybrid system theory, and an HMPC energy management strategy is proposed based on the MLD predictive model. To solve the optimal control problem online to obtain the optimal control sequence, the optimal control problem is converted into a mixed-integer linear programming (MILP) problem. The HMPC-based energy management strategy is compared with dynamic programming (DP)-based and rule-based energy management strategies over two different driving cycles. Simulation results indicate that the HMPC-based EMS achieves 80.60% and 83.79% of the fuel economy performance obtained by the DP-based EMS. In comparison, the rule-based EMS only achieves 66.46% and 70.51% of the DP-based control performance. Therefore, the HMPC-based energy management strategy is favorable for real-time control while effectively improving fuel economy.

In this paper, we mainly focus on the solving approach for a class of nonlinear trilevel programming problem. Firstly, based on the Karush–Kuhn–Tucker (K–K–T) optimality conditions of the lower level problem, we transform the nonlinear trilevel programming problem into the nonlinear bilevel programming problem with complementary constraints. The complementary constraints of the lower level problem are added to the upper level objective as the penalties. Secondly, for the nonlinear bilevel programming problem, the lower bounding problem is constructed by relaxing the constraint, which contains the parametric optimal solution value function of the lower level problem. The upper bounding problem is obtained by testing some feasible points. Thirdly, a bounding algorithm is proposed and the convergence is also presented. Finally, to illustrate the bounding algorithm, we consider some nonlinear trilevel programming problems. It shows that the bounding algorithm proposed can terminate finitely to a ε-optimality point of the nonlinear trilevel programming problem.

Collaborative optimization of hydrogen-based multipark integrated energy systems under multiple heterogeneous uncertainties

The real world optimization problems in hierarchical decision making systems, often encounter multiple functions in fractional forms with uncertain parameters. To tackle such situation of uncertainty, this paper proposes a novel methodology to find a compromise solution of a bi-level multi-objective linear fractional programming problem which is designed in a fuzzy environment with its parameters expressed as intuitionistic triangular fuzzy numbers. Based on the concept of intuitionistic fuzzy (α, β)-cuts and some theoretical aspects, the bi-level intuitionistic fuzzy model is formulated into an equivalent bi-level optimization with multiple interval valued fractional functions. The method proposed by Chakraborty and Gupta, is utilized to compute the individual compromise solution of each interval valued fractional objective function. Subsequently, the upper and lower level compromise solutions are computed to ascertain the aspiration values of the multiple interval valued fractional functions and the decision variables controlled at the upper level. Goal programming approach using a proposed modified linearization technique for fractional functions, is implemented to derive the compromise solution of the bi-level fuzzy optimization model. An existing numerical example, a practical problem in production sector are solved and the comparative discussion on result analysis is incorporated to demonstrate the feasibility and efficiency of the proposed approach.

ABSTRACT The Interior‐Point Methods are a class for solving linear programming problems that rely upon the solution of linear systems. At each iteration, it becomes important to determine how to solve these linear systems when the constraint matrix of the linear programming problem includes dense columns. In this paper, we propose a preconditioner to handle linear programming problems with dense columns, and we prove theoretically that the final linear system to solve is uniformly bounded when the Interior‐Point Method is converging to an optimal solution. This result is illustrated through computational experiments, which show that our proposed method is robust and competitive in terms of running time and/or number of iterations compared with existing methods.