Search Results (9)

Pressure management through pressure-reducing valves (PRVs) is among the most cost-effective leakage-control measures in water distribution networks, and the underlying placement problem is a nonconvex mixed-integer nonlinear programme. This paper revisits the classical 25-node benchmark of Sterling and Bargiela with two independent tools—a spatial branch-and-bound solver applied to the quadratic-friction MINLP of Eck and Mevissen, and a documented reimplementation of a published Harmony Search method—validating every candidate solution by exact EPANET resimulation. Both find placements better than the one published for this benchmark; the best-known placement attains 705.7 m of total nodal pressure against 722.8 m, and supplying the metaheuristic incumbent to the exact solver tightens the optimality gap from 6.4% to 4.5%, so the best-known solution is provably within 4.5% of the global optimum of the quadratic model, with the residual gap traced to the relaxation of the nonconvex energy constraints. The study also isolates, through a dedicated control experiment, a tolerance effect of broader relevance: placements whose settings are optimal for the approximate model violate the minimum-pressure requirement by centimetres in the exact hydraulics, and rankings can shift by metres; sensitivity analyses on tolerances, setting discretization and demands show that all reported rankings are nevertheless stable. On the 445-node Balerma network, re-optimization with a 2 m safety margin yields a strictly feasible three-valve solution reducing the sum of nodal pressures by 19.6%, with pressures reproduced by EPANET within 3.8%. These results imply that exact resimulation and explicit safety margins on the pressure requirement should become standard steps of model-based valve placement, and that pairing metaheuristic incumbents with global solvers offers a practical route to certified pressure-management decisions. Full article

An increasing penetration of distributed energy resources and electrification-driven peak demand pose significant challenges to distribution networks, often resulting in voltage violations and congestion. This paper presents a multi-stage optimization framework that enables battery storage unit (BSU) to act as a flexible non-wire alternative to traditional grid expansions conducted by Distribution System Operators (DSO), but also helpful for Transmission System Operators (TSO). The proposed method integrates a mixed-integer planning model with a quadratically constrained, second-order-cone–relaxed, AC optimal power flow to determine the optimal siting and sizing of battery storage. Representative operating days are obtained through clustering, while the operational optimization model evaluates battery participation in energy and reserve markets under network constraints. The value of flexibility the DSO procures from an independently-owned battery storage unit is determined as the opportunity cost of providing this flexibility as opposed to taking part in the fast reserves and day-ahead energy markets. The results obtained offer valuable information when weighing the decision between network expansion and alternative strategies and determine the price of flexibility that the DSO can offer to an independently owned storage unit. The results confirm that battery storage can defer network investments while providing transparent and economically justified flexibility remuneration. The proposed framework is implemented sequentially, with strong coupling between planning and operational stages through physical constraints and economic signals. Full article

Unmanned Aerial Vehicles (UAVs) were originally designed for military and surveillance applications but are now significant in smart agriculture, wireless communication, and product delivery. In contrast to an Internet Service Provider (ISP), which typically relies on fixed base stations, which can fail in the event of a disaster, UAVs offer more stable alternatives. Because IoT devices, sensors, and ground users have limited processing power and battery life, there is a need for energy-efficient solutions. Meanwhile, users still expect high data rates. UAV-based wireless networks can meet these needs, even in harsh or disaster-hit areas. Current research focuses on improving energy efficiency and data transmission by optimizing UAV flight paths and scheduling. In this work, we tackle these issues by formulating a mixed-integer non-convex optimization problem that jointly considers device scheduling and UAV trajectory. We further decompose it into the following two parts: energy-efficient scheduling among ground users ($P_2$) and the trajectory optimization of UAVs ($P_3$). To address these issues, we develop a linear programming relaxation approach, a Quadratically Constrained Quadratic Programming (QCQP)-based Successive Convex Approximation (SCA) scheme, and the Block Coordinate Descent (BCD) algorithm. Experimental results demonstrate that our approach outperforms the state of the art in both power consumption and transmission rate. Full article

Model Predictive Control (MPC) has emerged as a promising approach for energy management in hybrid electric vehicles, enabling predictive optimization of powertrain operation. The energy management problem in parallel hybrid powertrains constitutes a Mixed-Integer Nonlinear Programming (MINLP) problem, combining continuous decision variables such as torque distribution with discrete decisions including engine on/off states and clutch engagement. This problem structure presents distinct challenges for different optimization approaches. Gradient-based methods such as Sequential Quadratic Programming (SQP) solve continuous, differentiable optimization problems and require auxiliary methods to handle integer variables, while metaheuristic approaches such as Genetic Algorithms (GA) can handle the mixed-integer structure directly at the cost of increased computational effort. This study presents a systematic comparison between GA and SQP as optimization solvers within an MPC framework for a P1P3 parallel hybrid powertrain. A multi-objective cost function is formulated to simultaneously optimize system efficiency, battery state of charge management, and noise emissions. Both approaches are evaluated across the WLTC as well as a real-world RDE scenario. On the WLTC, both MPC approaches reduce fuel consumption by 0.5–1.0% and improve system efficiency by 3.7–4.6% compared to a state-of-the-art deterministic reference strategy optimized for fuel consumption. At the same time, both approaches additionally achieve substantial reductions in noise emissions compared to the deterministic reference, which was not optimized for acoustic behavior. On both cycles, the GA-based MPC achieves favorable performance compared to SQP, with the performance gap widening from the WLTC to the RDE cycle. Both methods achieve real-time capability, yet SQP reduces computational time by a factor of four compared to GA. As long as computational resources in automotive ECUs remain constrained, this efficiency advantage positions gradient-based optimization for series production applications, whereas metaheuristic methods offer greater flexibility for concept development stages with relaxed real-time requirements. The findings contribute to the understanding of optimization algorithm selection for MINLP energy management problems in hybrid electric vehicles. Full article

Portfolio optimization is fundamental to modern finance, enabling investors to construct allocations that balance risk and return while satisfying practical constraints. When transaction costs and cardinality limits are incorporated, the problem becomes a computationally demanding mixed-integer quadratic program. This work demonstrates how principles from biomimetics—specifically, the computational strategies employed by biological neural systems—can inspire efficient algorithms for complex optimization problems. We demonstrate that this problem can be reformulated as a constrained quadratic program and solved using dynamics inspired by spiking neural networks. Building on recent theoretical work showing that leaky integrate-and-fire dynamics naturally implement projected gradient descent for convex optimization, we develop a solver that alternates between continuous gradient flow and discrete constraint projections. By mimicking the event-driven, energy-efficient computation observed in biological neurons, our approach offers a biomimetic pathway to solving computationally intensive financial optimization problems. We implement the approach in Python and evaluate it on portfolios of 5 to 50 assets using five years of market data, comparing solution quality against mixed-integer solvers (ECOS_BB), convex relaxations (OSQP), and particle swarm optimization. Experimental results demonstrate that the SNN solver achieves the highest expected return (0.261% daily) among all evaluated methods on the 50-asset portfolio, outperforming exact MIQP (0.225%) and PSO (0.092%), with runtimes ranging from 0.5 s for small portfolios to 8.4 s for high-quality schedules on large portfolios. While current Python runtimes are comparable to existing approaches, the key contribution is establishing a path to neuromorphic hardware deployment: specialized SNN processors could execute these dynamics orders of magnitude faster than conventional architectures, enabling real-time portfolio rebalancing at institutional scale. Full article

In recent years, parcel volumes have reached record highs, prompting the logistics industry to explore innovative solutions to meet growing demand. In densely populated areas, delivery robots offer a promising alternative to traditional truck-based delivery systems. These autonomous electric robots operate on sidewalks and deliver time-sensitive goods, such as express parcels, medicine and meals. However, their limited cargo capacity and battery life require a return to a depot after each delivery. This challenge can be modeled as an electric vehicle-routing problem with soft time windows and single-unit capacity constraints. The objective is to serve all customers while minimizing the quadratic sum of delivery delays and ensuring each vehicle operates within its battery limitations. To address this problem, we propose a mixed-integer quadratic programming model and introduce an enhanced formulation using a layered graph structure. For this layered graph, we present two solution approaches based on relaxations that reduce the number of nodes and arcs compared to the expanded formulation. The first approach, Iterative Refinement, solves the current relaxation to optimality and refines the graph when the solution is infeasible for the expanded formulation. This process continues until a proven optimal solution is obtained. The second approach, Branch and Refine, integrates graph refinement into a branch-and-bound framework, eliminating the need for restarts. Computational experiments on modified Solomon instances demonstrate the effectiveness of our solution approaches, with Branch and Refine consistently outperforming Iterative Refinement across all tested parameter configurations. Full article

In this paper, we investigate a resource allocation and computation offloading problem in a heterogeneous mobile edge computing (MEC) system. In the considered system, a wireless power transfer (WPT) base station (BS) with an MEC sever is able to deliver wireless energy to the mobile devices (MDs), and the MDs can utilize the harvested energy for local computing or task offloading to the WPT BS or a Macro BS (MBS) with a stronger computing server. In particular, we consider that the WPT BS can utilize full- or half-duplex wireless energy transmission mode to empower the MDs. The aim of this work focuses on optimizing the offloading decision, full/half-duplex energy harvesting mode and energy harvesting (EH) time allocation with the objective of minimizing the energy consumption of the MDs. As the formulate problem has a non-convex mixed integer programming structure, we use the quadratically constrained quadratic program (QCQP) and semi-definite relaxation (SDR) methods to solve it. The simulation results demonstrate the effectiveness of the proposed scheme. Full article

The problem of optimal siting and sizing of distribution static compensators (STATCOMs) is addressed in this research from the point of view of exact mathematical optimization. The exact mixed-integer nonlinear programming model (MINLP) is decoupled into two convex optimization sub-problems, named the location problem and the sizing problem. The location problem is addressed by relaxing the exact MINLP model, assuming that all the voltages are equal to $1\angle 0^{\circ }$, which allows obtaining a mixed-integer quadratic programming model as a function of the active and reactive power flows. The solution of this model provides the best set of nodes to locate all the STATCOMs. When all the nodes are selected, it solves the optimal reactive power problem through a second-order cone programming relaxation of the exact optimal power flow problem; the solution of the SOCP model provides the optimal sizes of the STATCOMs. Finally, it refines the exact objective function value due to the intrinsic non-convexities associated with the costs of the STATCOMs that were relaxed through the application of Taylor’s series expansion in the location and sizing stages. The numerical results in the IEEE 33- and 69-bus systems demonstrate the effectiveness and robustness of the proposed optimization problem when compared with large-scale MINLP solvers in GAMS and the discrete-continuous version of the vortex search algorithm (DCVSA) recently reported in the current literature. With respect to the benchmark cases of the test feeders, the proposed approach reaches the best reductions with $14.17\%$ and $15.79\%$ in the annual operative costs, which improves the solutions of the DCVSA, which are $13.71\%$ and $15.30\%$, respectively. Full article

The secure operation of 110-kV networks should be considered in the optimal generation dispatch of regional power grids in large central cities. However, since 110-kV lines do not satisfy the premise of R << X in the direct current power flow (DCPF) model, the DCPF, which is mostly applied in the security-constrained unit commitment (SCUC) problem of high-voltage power grids, is no longer suitable for describing the active power flow of regional power grids in large central cities. Hence, the quadratic active power flow (QAPF) model considering the resistance of lines is proposed to describe the network security constraints, and an SCUC model for power system with 110-kV network and pumped-storage hydro (PSH) units is established. The analytical expressions of the spinning reserve (SR) capacity of PSH units are given considering different operational modes, and the SR capacity of PSH units is included in the constraint of the SR capacity requirement of the system. The QAPF is a set of quadratic equality constraints, making the SCUC model a mixed-integer nonlinear non-convex programming (MINNP) model. To reduce the computational complexity of solving the model when applied in actual large-scale regional networks, the QAPF model is relaxed by its convex hull, and the SCUC model is transformed into a mixed-integer convex programming (MICP) model, which can be solved to obtain the global optimal solution efficiently and reliably by the mature commercial solver GUROBI (24.3.3, GAMS Development Corporation, Guangzhou, China). Test results on the IEEE-9 bus system, the PEGASE 89 bus system and the Shenzhen city power grid including the 110-kV network demonstrate that the relaxed QAPF model has good calculation accuracy and efficiency, and it is suitable for solving the SCUC problem in large-scale regional networks. Full article