An MILP-Based Optimal Power Flow in Multicarrier Energy Systems

Distribution systems (DS) are a focal connection point for existing and new renewable energy sources. DS have increasing sizes; they connect increasing numbers of renewable energy sources and have a mandate to operate as financial entities seeking to maximize their profits in an electricity market. To achieve these goals, DS require highly efficient planning tools. In this paper, we propose a successive fuzzy mixed integer linear programming (MILP) method for optimally placing and sizing capacitors in a DS that explicitly models induction run wind electric generators (WEGs). The optimization problem is linearized, transformed into a fuzzy MILP model and is solved successively while updating the solution vector. The fuzzy MILP method employs fuzzy models of voltage constraints that are often violated in a planned system that lacks reactive power support. The use of fuzzy constraints makes the proposed solution method very robust by avoiding infeasibility and reducing the need for user expertise. Further, the fuzzy MILP method represents the dual objectives of capacitor cost and annual energy loss minimization as fuzzy sets with individual satisfaction functions. The method maximizes the minimum of these satisfaction functions during optimization. Tests on 69-bus and 2002-bus DS show that the method performs well and is robust.

Minimizing energy consumption by joint radio and computing resource allocation in Cloud-RAN

Knowledge representation of mathematical optimization problems and constructs for modeling

The surveillance problem is to find optimal trajectories of agents that patrol a given area as evenly as possible. In this paper, we consider multiple agents with fuel constraints. The surveillance area is given by a weighted directed graph, where the weight assigned to each arc corresponds to the fuel consumption/supply. For each node, the penalty to evaluate the unattended time is introduced. Penalties, agents, and fuels are modeled by a mixed logical dynamical system model. Then, the surveillance problem is reduced to a mixed integer linear programming (MILP) problem. Based on the policy of model predictive control, the MILP problem is solved at each discrete time. In this paper, the feasibility condition for the MILP problem is derived. Finally, the proposed method is demonstrated by a numerical example.

The generalized lock scheduling problem (GLSP) is a mixed integer optimization problem which consists of a ship placement (SP) and a lockage operation scheduling (LOS) sub-problem. In previous research, the GLSP is solved by different exact and heuristic methods, which are confirmed inferior with respect to computation time and solution quality. Consequently, none of those methods is efficient for handling practical large-scale GLSP. For the first time, we show that high-quality solutions of GLSP can be efficiently obtained by using an innovative approach proposed in this paper. Specifically, an ingenious solution structure of GLSP is designed, by which the GLSP is converted to a combinatorial optimization problem. Furthermore, an adaptive large neighborhood search (ALNS) heuristic based on the principle of destruction and reconstruction of solutions is proposed for solving the GLSP. Test results using a large number of instances reported in the literature are compared with those obtained by two exact methods, the mixed integer linear programming (MILP) and combinatorial Benders' decomposition (CBD) method. The results show that our ALNS achieves optimal solutions within less time in terms of most of the small-scale instances. Much better solutions are obtained by the ALNS within a few minutes for those large-scale instances that cannot be solved to optimality by exact methods within 2 h. Especially, the advantage of the proposed method is more remarkable when there is no specific chronological rules forced, which indicates that the proposed method is capable of handling the GLSP in a broader scope of situations.

More realistic than deterministic vehicle routing, stochastic vehicle routing considers uncertainties in traffic. Its two representative optimization models are the probability tail (PT) and the stochastic shortest path problem with delay excess penalty (SSPD), which can be approximately solved by expressing them as mixed-integer linear programming (MILP) problems. The traditional method to solve these two MILP problems, i.e., branch and bound (B&B), suffers from exponential computation complexity because of integer constraints. To overcome this computation inefficiency, we propose a partial Lagrange multiplier method. It benefits from the total unimodularity of the incidence matrix in the models, which guarantees an optimal integer solution by only solving a linear programming (LP) problem. Thus, this partial Lagrange multiplier problem can be further solved using the subgradient method, and the proposed method can guarantee polynomial computation complexity. Moreover, we theoretically prove the convergence and the efficiency, which are also assessed by the experiments on three different scales of graphs (road networks): small scale, medium scale, and large scale. More importantly, the experimental results on the Beijing road network with real traffic data show that our method can efficiently solve the time-dependent routing problem. Additionally, the implementation on the navigation system based on the Singapore road network further confirms that our method can be applied to efficiently solve the real-world stochastic vehicle routing problem.

The Unmanned Aerial Vehicles (UAVs), commonly known as drones, are significant in the agriculture sphere to automate the work such as: data acquisition, crop spraying among others. This paper proposes a path planning solution for a team of UAVs that is required to whiten a greenhouse’s roof, this problem having both social-economic impact, as well as scientific-technical impact. First, the space around the roof is partitioned into cells based on a 3D cell decomposition technique, labeling the cells including the surface of the roof as regions of interest (ROIs). Based on this representation, a Petri net (PN) model captures the motion of drones, while their trajectories are returned by a Mixed Integer Linear Programming (MILP) problem which optimizes the energy consumption. An adaptable strategy is used such that the MILP problem considers only the available UAVs with enough energy to reach the ROIs. The algorithm is implemented in MATLAB and the simulation results are captured in a video link, evaluating the impact of the size of the team and the precision used for mapping the environment over the running time.

Microgrids have become valuable assets because they improve the reliability of consumers while integrating renewables via distributed energy resources (DERs). Thus, making them cost-efficient is essential to secure their proliferation. This paper proposes a new method for the optimal design of microgrids. The proposed two-stage method optimizes the size and the location of the DERs, i.e., the renewable energy sources (RESs), distributed generation (DG) units, and battery energy storage systems (BESSs). Furthermore, the overall operation of the microgrid is optimized using a stochastic scenario-based approach, considering grid-connected and unintentional islanded modes. The proposed method also considers internal network reinforcements. Thus, the first stage is an energy-based approach, formulated as a mixed-integer linear programming (MILP) problem, and it is used to size the DERs, whereas the second stage uses an optimal AC power flow (AC-OPF) to formulate a mixed-integer nonlinear programming (MINLP) model that allocates the DERs and selects the best conductor for each circuit. The multi-objective nature of the problem is addressed via Pareto optimization to analyze the trade-off between operational and capital costs. The MINLP model is linearized through piece-wise approximations and solved using commercial solvers. Furthermore, the impact of battery degradation is analyzed through a simple adaptation of the Stage 1 model. Results were obtained with data from the real university campus microgrid CampusGrid, located at the State University of Campinas (UNICAMP), in São Paulo, Brazil.

This study proposes an improved particle swarm optimization method to find optimal power flow by using the power transmission loss as an objective function. In the literature, PSO is a well — known intelligent search method to handle the solution of optimal power flow problem. A novel scheme which is called Improved PSO (IPSO) is defined by modifying the initialization step of PSO algorithm and choosing the load bus voltages, generator active and reactive powers, line flow capacities as penalty functions in the objective function. PSO and IPSO-based optimal power flow solutions are compared with each other on IEEE 118 and 300 bus systems. According to the test results, the power loss obtained by IPSO-based solution has less power loss than PSO-based solution. This proposed method can be used to obtain faster desirable solutions and better power loss results for the optimal power flow problem in case of power loss minimization.

Mixed-integer linear programming (MILP) can be used for a variety of optimization problems. However, it is limited to relatively small-scale problems, because its computation time increases dramatically with the number of integer variables. Decomposition methods have been presented to derive good feasible solutions of MILP problems. The objective of this paper is to propose a strategy for partitioning variables in using a decomposition method presented by the authors. The strategy proposed here is to decompose an original MILP problem into the smallest MILP subproblems, each of which has a single integer variable, and enables one to assume the values of part of integer variables efficiently to obtain a reduced MILP master problem. A single-period operational planning problem of a simplified heat supply system is investigated analytically to show the meaning and validity of the strategy. A multi-period operational planning problem of a practical heat supply system is also investigated numerically to show the validity and effectiveness of the decomposition method into which the strategy is incorporated.

In diffusion MRI (dMRI), a good sampling scheme is important for efficient acquisition and robust reconstruction. Diffusion weighted signal is normally acquired on single or multiple shells in q-space. Signal samples are typically distributed uniformly on different shells to make them invariant to the orientation of structures within tissue, or the laboratory coordinate frame. The Electrostatic Energy Minimization (EEM) method, originally proposed for single shell sampling scheme in dMRI, was recently generalized to multi-shell schemes, called Generalized EEM (GEEM). GEEM has been successfully used in the Human Connectome Project (HCP). However, EEM does not directly address the goal of optimal sampling, i.e., achieving large angular separation between sampling points. In this paper, we propose a more natural formulation, called Spherical Code (SC), to directly maximize the minimal angle between different samples in single or multiple shells. We consider not only continuous problems to design single or multiple shell sampling schemes, but also discrete problems to uniformly extract sub-sampled schemes from an existing single or multiple shell scheme, and to order samples in an existing scheme. We propose five algorithms to solve the above problems, including an incremental SC (ISC), a sophisticated greedy algorithm called Iterative Maximum Overlap Construction (IMOC), an 1-Opt greedy method, a Mixed Integer Linear Programming (MILP) method, and a Constrained Non-Linear Optimization (CNLO) method. To our knowledge, this is the first work to use the SC formulation for single or multiple shell sampling schemes in dMRI. Experimental results indicate that SC methods obtain larger angular separation and better rotational invariance than the state-of-the-art EEM and GEEM. The related codes and a tutorial have been released in DMRITool.

Bit-based division property was first proposed to find integral for SIMON32 by Todo \(et al.\) at FSE 2016. Xiang \(et al.\) improved the work with aid of Mixed Integer Linear Programming(MILP) method and applied the method to block ciphers with wider block size. Later on, Sun \(et al.\) applied division property to ARX block ciphers. Todo \(et al.\) proposed a more precise division property using three subsets method to describe integral propagation at FSE 2016, which can not be applied to wide state ARX block ciphers. In this paper, we extend bit-based division property using three subsets and propose an automatic method for finding integral distinguishers for ARX block ciphers with SAT/SMT solvers. Firstly, we study bit-based division property using three subsets through three basic operations (Copy, AND, XOR). Then, we model division property using three subsets through Addition Modulo function. Finally, by constructing and solving division property using three subsets propagation system, we find integral distinguishers for round reduced ARX block cipher. As a result, we propose 15 round integral distinguishers for SIMON32 automatically and verify the secure margins Todo \(et al.\) proposed for \(\hbox {SIMON}48,64,96,128\). Also, we can find one more 6 round integral distinguishers for SPECK32, which can not be found with conventional division property without using three subsets. It is interesting that no more integral distinguishers are found for SPECK48,64,96,128. Moreover, we apply to SIMECK, HIGHT, LEA, TEA and XTEA \(et al.\) Unfortunately, we find no more new results than conventional division property can do.

Deoxys-BC is the internal tweakable block cipher of Deoxys, a third-round authenticated encryption candidate at the CAESAR competition. In this study, by adequately studying the tweakey schedule, we seek a six-round related-tweakey impossible distinguisher of Deoxys-BC-256, which is transformed from a 3.5-round single-key impossible distinguisher of AES, by application of the mixed integer linear programming (MILP) method. We present a detailed description of this interesting transformation method and the MILP-modeling process.Based on this distinguisher, we mount a key-recovery attack on 10 (out of 14) rounds of Deoxys-BC-256.Compared to previous results that are valid only when the key size $>204$ and the tweak size $<52$, our method can attack 10-round Deoxys-BC-256 as long as the key size $\\geq174$ and the tweak size $\\leq82$. For the popular setting in which the key size is 192 bits, we can attack one round more than previous studies.Note that this paper only gives a more accurate security evaluation and does not threaten the security of full-round Deoxys-BC-256.

Uncertainty has always been a significant yet unresolved issue in geography. Uncertainty in spatial optimization models, particularly in coverage maximization problems, stems from the limitations of binary coverage metrics for areal-based demand units. Traditional models classify units as either fully covered or not, ignoring partial coverage scenarios. This binary approach creates discrepancies between modeled and actual service demand, as even marginally covered units may count as fully serviced. The propagation of such errors is amplified by variations in the unit size and coverage thresholds, leading to suboptimal solutions in urban planning tasks such as urban greenway planning. To address these limitations, we proposed a deep reinforcement learning (DRL)-driven optimization framework that quantifies the optimality gap caused by spatially induced uncertainty and provides superior solutions. By employing a three-module structure that incorporates a graph neural network (GNN)-driven agent for data representation, a policy and a value network for decision-making, and a stochastic environment for simulating individual-level demand distributions, our model dynamically adapts to spatial uncertainty and generates robust solutions. We tested our framework in solving the maximal covering location problem for lines (MCLP-Line) for urban greenway route planning. The experimental results demonstrated that traditional mixed integer linear programming (MILP) methods yielded highly variable outcomes with different coverage metrics, whereas our proposed model consistently outperformed MILP across diverse scenarios. Our findings underscore the potential of modern AI-driven approaches in mitigating spatial uncertainty and achieving optimized solutions in geographic applications.

Robustness verification of ‘s is becoming increasingly crucial for their potential use in many safety-critical applications. Essentially, the problem of robustness verification can be encoded as a typical Mixed-Integer Linear Programming (MILP) problem, which can be solved via branch-and-bound strategies. However, these methods can only afford limited scalability and remain challenging for verifying large-scale neural networks. In this paper, we present a novel framework to speed up the solving of the MILP problems generated from the robustness verification of deep neural networks. It employs a semi-planet relaxation to abstract ReLU activation functions, via an RNN-based strategy for selecting the relaxed ReLU neurons to be tightened. We have developed a prototype tool L2T and conducted comparison experiments with state-of-the-art verifiers on a set of large-scale benchmarks. The experiments show that our framework is both efficient and scalable even when applied to verify the robustness of large-scale neural networks.KeywordsRobustness verificationLearning methodsSemi-planet relaxationNeural networks