Minimum Constraint Research Articles

Scheme and trajectory design of in-situ atmospheric sampling with multi-pass aeroassisted maneuvers

Planetary atmospheric detection is an important way to recognize the physical and chemical properties of planets that inform about their formation and evolution, and atmospheric in-situ sampling is an ideal way to obtain high-resolution information. In this paper, a scheme for in-situ sampling of planetary atmosphere based on multi-pass aeroassisted maneuvers is given, and the corresponding design method for multiple traversal trajectories through the atmosphere is proposed. The aeroassisted maneuvering scheme achieves target-area sampling by crossing the atmosphere circularly, and is able to flexibly adjust the sampling altitude, thus having the advantage of three-dimensional and wide-area sampling. The trajectory design method involves algorithms to determine key design parameters separately. Specifically, the minimum entry periapsis altitude is determined by building its mapping relationship with path constraints to satisfy the minimum flight altitude constraint. Besides, the pass number of atmospheric flights is calculated by giving the upper bound of the energy attenuation and mission-time constraints. Then, a rapid inclination correction method via bank angle reversal is given to satisfy the inclination constraint of the maneuver. In numerical simulations, three Martian atmospheric detection scenarios, designated as high-latitude region with superficial ice water, magnetic anomalies region, and the polar region enriched with atmospheric transport properties, are established, with corresponding maneuvering sampling trajectories and characteristic parameter distributions provided. This paper introduces for the first time the use of multi-pass aeroassisted maneuvers for in-situ atmospheric sampling. Simulation results demonstrate the effectiveness and general applicability of the proposed method.

Technical note: Optimizing spot-scanning proton arc therapy with a novel spot sparsity approach.

One of the main challenges of utilizing spot-scanning proton arc therapy (SPArc) in routine clinics is treatment delivery efficiency. Spot reduction, which relies on spot sparsity optimization (SSO), is crucial for achieving high delivery efficiency inSPArc. This study aims to develop a novel SSO approach based on the alternating directions method of multipliers (ADMM) for SPArc to achieve high treatment delivery efficiency and maintain optimal dosimetric planquality. In this study, SSO for SPArc is based on the least-square dose fidelity term with L0-norm regularization. The novel optimization approach is based on the ADMM framework, in which the minimum monitor unit constraint was considered to improve the plan quality. A state-of-the-art SSO method, the primal-dual active set with continuation (PDASC) algorithm published previously, was utilized as a benchmark. Two SPArc plan groups with the same beam assignment and clinical constraint were generated, in which the former group was SPArc plan with SSO utilizing ADMM, denoted as , and the later group was SPArc with SSO utilizing PDASC, denoted as . Nine clinical cases included five different cancer sites (brain, lung, liver, prostate, and head&neck cancer) were used. The SSO method's performance was evaluated in terms of spot sparsity level (the number of zero-valued elements divided by the total number of elements), beam delivery time, dosimetric plan quality, and plan robustness. Compared to the plan, the plan exhibits superior sparsity and higher delivery efficiency while maintaining good planquality. This study introduces a novel spot sparsity optimization approach using the ADMM framework to improve the delivery efficiency of SPArc. Compared to the existing state-of-the-art SSO method, such an approach could further enhance delivery efficiency while maintaining good plan quality, which could promote the implementation of SPArc in theclinic's.

Non-uniformly Spaced Antenna Arrays with Overlapped Elements Constraint

In the literature, inter-element spacing antenna design methods have been widely discussed and presented as an alternative approach to element excitation amplitude and/or phase control methods that may be relied upon to achieve the required array pattern shapes. However, methods associated with non-uniformly distributed elements suffer from the element overlap problem, where some of the optimized element locations may overlap each other and cause changes in the overall array aperture length. Practically, these element overlaps cannot be implemented, due to the physical antenna element size, without omitting some of them. Consequently, the overall performance of the antenna array is degraded. Further, degradation may occur when considering phased arrays with scanned main beams. In this paper, we first illustrate the effect of the problem of overlapped element locations and then we propose two approaches based on the genetic algorithm to optimize non-uniformly spaced arrays with overlapped element locations, while simultaneously preserving the array's directivity. To solve the problem of overlapping and to determine the physical array element size, the minimum element-spacing constraints are incorporated in a simple way in the proposed approaches. Thus, the time required to perform optimization-related computations is greatly reduced. Simulation results confirm the effectiveness of the two proposed solutions, where the probability of the elements overlapping has been reduced to zero under specific conditions related to the locations of the some of the elements, while the peak sidelobe levels were always kept below -15 dB and directivity was maintained, to the extent possible, at the level of that of standard uniformly spaced arrays.

Two-stage optimal scheduling for flexibility and resilience tradeoff of PV-battery building via smart grid communication

Energy flexibility and energy resilience are now becoming new key features of building energy systems under the context of climate change and energy transition. During the system operation phase, these two performance indexes might be contradictory and require tradeoff. The main contribution of this study is to propose a two-stage mixed-integer linear programming (MILP) model to optimally tradeoff between flexibility and resilience. Its main idea is to improve the resilience of building energy system with minimum constraints on system flexibility using the outage risk information provided by smart grid. Two new concepts are considered in the proposed method, including self-sufficient requirement and continuous outage probability. The insight is to add additional penalty for the time step in which its battery state of charge (SOC) is far from self-sufficient requirement while the corresponding continuous outage probability is high. To validate our proposed method, a probabilistic outage simulation model is developed using sigmoid function and Markov Chain. Comprehensive numerical studies are conducted to compare the proposed method with traditional economic mode and backup mode under two outage patterns. The results demonstrate that the proposed method only uses 6.7 % additional operation cost such that 78.3 % of baseload curtailment and 81.1 % of user discomfort are reduced. The proposed MILP model can provide practical guideline for the flexibility and resilience tradeoff of distributed energy resources.

Explicit Modeling of Multi-Product Customer Orders in a Multi-Period Production Planning Model

In many industries, companies receive customer orders that include multiple products. To simplify the use of optimization models for planning purposes, these orders are broken down, and the quantities of each product are grouped with the same products from other orders to be completed in the same period. Consequently, traditional production planning models enforce minimum demand constraints by product and period rather than by individual orders. An important drawback of this aggregation procedure is that it requires a fixed order fulfillment period, potentially missing opportunities for more efficient resource use through early completion. This paper introduces a novel mathematical formulation that preserves the integrity of customer orders, allowing for early fulfillment when possible. We compare a traditional linear programming model with a new mixed-integer programming approach using a sawmill case study. Although more complex than the traditional model, the proposed formulation reduces costs by approximately 6% by enabling early order completion and offers greater flexibility and control over the production process. This approach leads to better resource utilization and more precise order management, presenting a valuable alternative to conventional production planning models.

Explore the feasibility of using spot-scanning proton arc therapy for a synchrotron accelerator-based proton therapy system - A simulation study.

The aim of this study was to evaluate the feasibility and plan quality of spot-scanning proton arc therapy (SPArc) using a synchrotron-accelerator-based proton therapy system compared to intensity-modulated proton therapy (IMPT). Five representative disease sites, including head and neck, lung, liver, brain chordoma, and prostate cancers, were retrospectively selected. Both IMPT and SPArc plans are generated with the HITACHI ProBEAT PBS system's minimum MU constraints and physics beam model. The SPArc plans are generated with 2.5° sampling frequency. The static delivery time was simulated based on the previously published synchrotron delivery sequence model, and the dynamic delivery time was simulated using a proton arc gantry mechanical model integrated with the synchrotron delivery sequence. Both dosimetric plan quality and delivery efficiency are evaluated. A superior plan quality is reached compared with the IMPT plans generated for the same disease site. However, a relatively prolonged static and dynamic delivery time post new challenge, as static time increased by 49.22% and dynamic time 59.10% on average. This study presents the first simulation results of delivering the SPArc plans using a synchrotron-accelerated proton therapy system. The result shows its feasibility and limitations, which could guide future development.

Influence of feed entrance angle on transverse tearing burr formation in the milling of superalloy honeycomb with ice filling constraint

In the end milling of superalloy honeycomb cores, the contact form between the cutting tool and honeycomb wall and the force state of the honeycomb wall are variable, there will be difficulties in chip removal. The irregular extension of transverse tearing burrs can deteriorate the machining quality of honeycomb core surfaces, thereby adversely affecting the assembly and service performance of sandwich structures. Based on kinematic analysis, modeling of the removal and deflection process of honeycomb walls was conducted. The feed entrance angle in the case of machining thin walls with high feed speeds was characterized, and the force state of the honeycomb wall and the degree of shear or compression it bears were analyzed. Analytical models of damage scale and single-tooth cutting state were established under different feed entrance angles. The impact of feed entrance angle on the minimum burr length and the minimum constraint failure width was analyzed. The milling experiments of GH4099 superalloy honeycomb wall with ice filling constraint were designed and conducted to clarify the influence of different feed entrance angles on cutting force and transverse tearing burr length. The morphology of burrs and the wear form of the cutting tool were analyzed, and the formation mechanism of transverse tearing burr on the honeycomb sidewalls was revealed. The research results indicate that the feed force Fx is 2.1 to 4.7 times greater than the main force Fy or the back force Fz. When the feed entrance angle is <90°, transverse tearing burrs either do not occur, or occur crimped burrs that are gradually removed. Particularly within the range of 0° to 30°, the machining quality is better. The cutting force has a significant shearing effect on the honeycomb wall, making it susceptible to plastic deformation and reaching the fracture strain. The cutting edge can effectively remove material from the honeycomb wall, resulting in normal wear on the minor flank face and tip of the cutting tool. When the feed entrance angle is greater than 90°, it is easy to form large banded burrs, and the burr length is relatively similar to about 1500 μm. The cutting force has a significant extrusion effect on the honeycomb wall, resulting in minimal deflection deformation of the honeycomb wall, and making it difficult to fracture. The cutting tool fails to perform effective cutting, leading to increased friction between the cutting tool and honeycomb wall, which continuously induces irregular extension of the burrs. The research findings are of great significance for achieving damage control in metal honeycomb core machining and guiding process and clamping optimization.

Optimal Battery Storage Configuration for High-Proportion Renewable Power Systems Considering Minimum Inertia Requirements

With the continuous development of renewable energy worldwide, the issue of frequency stability in power systems has become increasingly serious. Enhancing the inertia level of power systems by configuring battery storage to provide virtual inertia has garnered significant research attention in academia. However, addressing the non-linear characteristics of frequency stability constraints, which complicate model solving, and managing the uncertainties associated with renewable energy and load, are the main challenges in planning energy storage for high-proportion renewable power systems. In this context, this paper proposes a battery storage configuration model for high-proportion renewable power systems that considers minimum inertia requirements and the uncertainties of wind and solar power. First, frequency stability constraints are transformed into minimum inertia constraints, primarily considering the rate of change of frequency (ROCOF) and nadir frequency (NF) indicators during the transformation process. Second, using historical wind and solar data, a time-series probability scenario set is constructed through clustering methods to model the uncertainties of wind and solar power. A stochastic optimization method is then adopted to establish a mixed-integer linear programming (MILP) model for the battery storage configuration of high-proportion renewable power systems, considering minimum inertia requirements and wind-solar uncertainties. Finally, through a modified IEEE-39 bus system, it was verified that the proposed method is more economical in addressing frequency stability issues in power systems with a high proportion of renewable energy compared to traditional scheduling methods.

Evaluating the feasibility and economics of hydrogen storage in large-scale renewable deployment for decarbonization

Renewable energy (RE) is pivotal for achieving a net-zero future, with energy storage systems essential for maximizing its utility. This study introduces a modeling framework that simulates large-scale RE deployment in Taiwan, emphasizing hydrogen as a primary storage medium. Utilizing hourly time steps, the model assesses various energy generation and storage configurations to demonstrate the technical feasibility of meeting Taiwan's 2050 net-zero target, which calls for a 60 % RE share primarily through solar and wind resources. However, achieving this target and the ambitious goal of 100 % RE penetration requires substantial enhancements in both generation capacity and storage solutions. The research evaluates the economic impacts by analyzing the levelized cost of energy (LCOE), revealing that optimal configurations, such as a wind capacity of 30 GW with a 5 % minimum capacity factor constraint on electrolyzers, significantly reduce LCOE to $0.176/kWh, underscoring the cost-effectiveness of hydrogen storage compared to battery alternatives in large-scale settings. The study underscores the necessity for ongoing investigations into replacing thermal power plants and maintaining grid stability amidst high RE penetration. To fully harness Taiwan's RE potential and contribute to global sustainability, effective deployment of hydrogen storage will require robust stakeholder support, continual technological advancements, and enabling policies. This framework, while tailored to Taiwan's power system, offers insights applicable to various global contexts.

Irregular IRS-aided SWIPT secure communication system with imperfect CSI

The performance of traditional regular Intelligent Reflecting Surface (IRS) improves as the number of IRS elements increases, but more reflecting elements lead to higher IRS power consumption and greater overhead of channel estimation. The Irregular Intelligent Reflecting Surface (IIRS) can enhance the performance of the IRS as well as boost the system performance when the number of reflecting elements is limited. However, due to the lack of radio frequency chain in IRS, it is challenging for the Base Station (BS) to gather perfect Channel State Information (CSI), especially in the presence of Eavesdroppers (Eves). Therefore, in this paper we investigate the minimum transmit power problem of IIRS-aided Simultaneous Wireless Information and Power Transfer (SWIPT) secure communication system with imperfect CSI of BS-IIRS-Eves links, which is subject to the rate outage probability constraints of the Eves, the minimum rate constraints of the Information Receivers (IRs), the energy harvesting constraints of the Energy Receivers (ERs), and the topology matrix constraints. Afterward, the formulated non-convex problem can be efficiently tackled by employing joint optimization algorithm combined with successive refinement method and adaptive topology design method. Simulation results demonstrate the effectiveness of the proposed scheme and the superiority of IIRS.

Orientation optimization of the Halbach PMG for the levitation and guidance performance of the HTS maglev system

High-temperature superconducting maglev technology has great application potential in rail transit applications due to its advantages such as passive stable levitation and green environmental protection. As one of the key components of the HTS maglev system, the Halbach-type permanent magnet guideway (PMG) enhances the magnetic field on one side of the guideway and weakens that on the other side. Optimizing the PMG, including the geometry and magnetic properties of the magnet, is an effective method to improve the levitation and guidance performance of the system. In addition, since NdFeB permanent magnets are expensive, optimizing the design of the PMG for the HTS maglev system is also an important work to reduce the application cost. In this paper, the Nelder–Mead Simplex method (NMS) in the optimization solver in COMSOL software is used to optimize the geometric parameters of the Halbach PMG according to the different objective requirements of the HTS maglev system. The optimization objectives include the maximum levitation force and guidance force under the constraint of the maximum cross-sectional area of the PMG, as well as the minimum cross-sectional area of the PMG with a minimum levitation force constraint. The results indicate that the NMS method is effective. By comparing four PMGs during the optimization process, it is found that this method can fully improve the utilization of the magnetic field by changing the geometric parameters of the Halbach PMG. This study can provide a valuable reference for the optimal design of the PMG for HTS maglev systems in the future.

Optimization of hydrogen production in multi-Electrolyzer systems: A novel control strategy for enhanced renewable energy utilization and Electrolyzer lifespan

In large-scale water electrolytic hydrogen production system based on renewable energy, the allocation strategy of hydrogen production power among multi-electrolyzers plays a critical role in the efficiency of renewable energy utilization and the quantity of hydrogen production, given a fixed power output from renewable energy sources. This paper considers the minimum hydrogen production power constraint of electrolyzer and proposes a novel control strategy for multi-electrolyzers. The operational phase of multi-electrolyzers is divided into two distinct phases: 1) the rapid start-up phase; 2) the equal power allocation phase. During the rapid start-up phase, by reducing the power of electrolyzer that has reached its rated power to a predetermined level and using this saved power to start another electrolyzer, this strategy ensures that electrolyzers can proactively and quickly exceed the minimum operational power threshold. Upon the activation of all electrolyzers, the system enters second phase, wherein the power is evenly allocated among all electrolyzers. Besides, this strategy employs a priority scheduling method to ensure the uniformity of operating times across all electrolyzers. Compared to the existing three control strategies, this proposed strategy demonstrates significant advantages in minimizing unused wind energy and optimizing the lifespan of electrolyzers. The effectiveness of proposed strategy is validated by the simulation result.

Anatomically and mechanically conforming patient-specific spinal fusion cages designed by full-scale topology optimization

Cage subsidence after instrumented lumbar spinal fusion surgery remains a significant cause of treatment failure, specifically for posterior or transforaminal lumbar interbody fusion. Recent advancements in computational techniques and additive manufacturing, have enabled the development of patient-specific implants and implant optimization to specific functional targets. This study aimed to introduce a novel full-scale topology optimization formulation that takes the structural response of the adjacent bone structures into account in the optimization process. The formulation includes maximum and minimum principal strain constraints that lower strain concentrations in the adjacent vertebrae. This optimization approach resulted in anatomically and mechanically conforming spinal fusion cages. Subsidence risk was quantified in a commercial finite element solver for off-the-shelf, anatomically conforming and the optimized cages, in two representative patients. We demonstrated that the anatomically and mechanically conforming cages reduced subsidence risk by 91% compared to an off-the-shelf implant with the same footprint for a patient with normal bone quality and 54% for a patient with osteopenia. Prototypes of the optimized cage were additively manufactured and mechanically tested to evaluate the manufacturability and integrity of the design and to validate the finite element model.

THE MODIFIED MEAN ABSOLUTE DEVIATION INTEGER LINEAR PROGRAMMING MODEL FOR GLOBAL PORTFOLIO ASSET ALLOCATION

This study develops a practical yet robust Mean Absolute Deviation (MAD) Mixed-Integer Linear Programming (MILP) model for a global investment portfolio tailored to the constraints faced by Malaysian retail investors, such as transactional fees and foreign currency exchange spreads, to provide more accurate estimations of portfolio returns. The MAD ILP model is modified to address these factors, aiming to enhance utility and efficiency. The study utilizes a Maybank 12-month fixed deposit cash account and ten selected Exchange-Traded Funds (ETFs) from iShares, Vanguard, and State Street Global Advisors for global portfolio construction. Forecasting techniques were utilized to generate expected returns for the ETFs and foreign currency exchange spreads. Based on the MAD model proposed by Konno and Wijayanayake (2001), the study introduces three modifications: incorporating transaction cost elements specific to Malaysian investors, including foreign currency exchange spreads in return calculations, and transforming the model from mixed-integer to pure integer model to accommodate minimum transaction lot constraint. Verification and validation exercises demonstrate the model’s ability to replicate real-world portfolio construction and reliable simulations. The model offers a practical tool for self-ascribed investors aiming to optimize global investment portfolios while considering unique constraints and transaction costs.

Microfossil and geochemical evidence for the Storegga tsunami at Budle Bay, Northumberland, UK

Evidence for the Storegga tsunami, which was generated by one of the world’s largest submarine slides, is well documented in Scotland, but the southerly extent of tsunami inundation in the UK is far more uncertain. Here, we combine new sedimentological, geochemical, microfossil, and ground-penetrating radar datasets to investigate the origins of two sand beds at Budle Bay, Northumberland. The lower of these two sand deposits is a fine- to medium-grained sand that fines upwards, is dominated by fragmented marine diatom taxa, and is characterised by elevated calcium concentrations. Two radiocarbon dated samples provide minimum age constraints on the timing of the deposition of the lower sand at around 8120–8380 cal yr BP. It is tentatively interpreted as being deposited by the Storegga tsunami. The upper sand bed is generally finer grained than the lower sand, and the calcium concentrations are considerably lower. One hypothesis is that the upper sand was deposited by the 1953 CE storm surge, but additional chronological control is required to test this interpretation. Our findings highlight the challenges associated with differentiating between storm and tsunami deposits and confirm the localised nature of preservation of Storegga tsunami deposits.

Treatment for the Singularity Problem in the Phase Segregation

In the Eulerian–Eulerian two-fluid model, comprising air and droplets, singularities often arise as the phase fraction of dispersed droplets approaches zero. The nonconservative momentum equations can address this issue, but it will lead to inaccurate solutions when encountering discontinuities. To tackle the singularity problem and ensure accurate solutions for the droplet field, a novel adaptive form of momentum equations is proposed. The adaptive form defaults to the conservative form and smoothly transitions to the phase-intensive form when the phase fraction falls below a critical value, specifically 1/1000 of the inlet. The LU-SGS algorithm, enhanced with the inner iteration step method, is employed for numerical solutions of the droplet field. Comparative analysis reveals that the discrepancy between the results obtained from the adaptive form and the conservative form is negligible, under 0.5‰. Notably, with larger Courant numbers, the conservative form diverges from waterless regions despite imposing the minimum phase fraction constraint. Conversely, the adaptive form consistently maintains a Courant number of five times or more, potentially exceeding a hundredfold in complex flows. Although the adaptive form moderately increases complexity and computational time for a single time step, the improvement of the maximum Courant number will bring significant computational efficiency advantages. Moreover, the adaptive form holds promise for application in various other multiphase flow scenarios.

High-resolution wide-swath SAR imaging with multifrequency pulse diversity mode in azimuth multichannel system

ABSTRACT High-resolution wide-swath (HRWS) imaging has emerged as a focal point in synthetic aperture radar (SAR) research. However, conventional SAR systems face challenges in achieving both high azimuth resolution and wide swath simultaneously due to the minimum antenna area constraint. In this paper, we propose a HRWS imaging method based on multifrequency pulse diversity (MFPD) and azimuth multichannel (AMC) technique, capable of resolving range and Doppler ambiguities concurrently. In MFPD mode, range ambiguous echoes can be separated by matched filters in the range frequency domain, as multifrequency pulses are transmitted by a single channel in the transmitter. To further enhance the ambiguity resolution ability of the system and address azimuth incoherence, a novel scheme applying the MFPD to AMC system is proposed, categorized into two distinct scenarios. 1) Uniform Sampling: This scenario satisfies the displaced phase centre antenna condition. Under this condition, high range resolution imaging can be achieved through spectrum splicing in range frequency domain, simultaneously resolving Doppler ambiguity. 2) Non-uniform Sampling: In this scenario, the ambiguous echoes are processed by spatial digital beamforming and spectrum splicing in two-dimensional frequency domain. Finally, the HRWS imaging can be obtained by performing the traditional SAR algorithm. Furthermore, the proposed method can synthesize a wideband signal from multifrequency signals, thereby enhancing the feasibility of super-high-resolution imaging. Simulation results demonstrate the effectiveness of the proposed method.

Money illusion in retirement savings with a minimum guarantee

We investigate the impact of money illusion on the investment strategy and retirement outcomes of pre-retirees. Money illusion refers to the tendency of individuals to overlook the effects of inflation and focus on nominal rather than real terms. We solve and compare the optimal investment strategies for a pre-retiree who exhibits money illusion and aims to maximize the expected power utility of wealth at retirement, subject to a minimum guarantee constraint. While money illusion leads to welfare losses, implementing a minimum guarantee helps suppress these losses. However, guarantee constraints set under money illusion are ineffective in meeting inflation-adjusted constraints. Our findings emphasize the significant impact of money illusion on pre-retirees' investment strategy and retirement outcomes in the form of utility loss and the risk of falling short of the minimum guarantee.

Optimal design of electro-thermo-mechanical microactuators considering minimum length scale constraints

To ensure the manufacturability of compliant mechanisms, this paper presents a new approach for optimal design of electro-thermo-mechanical microactuators by employing minimum length scale constraints. A sequential coupling method is adopted to carry out finite element analysis for electric-thermal-mechanical coupling multiphysics. The inflection point fields of the solid and void phases are identified by structural indicator functions. The minimum length scales of the solid and void phases are adopted as constraints. The optimization objective is designed to maximize the output displacements of electro-thermo-mechanical microactuators. The validity of the proposed optimal design method is demonstrated through several numerical examples. In the optimal designs obtained by the proposed method, the minimum length scales of the two phases can be properly controlled. The electro-thermo-mechanical microactuator’s output displacements decrease when the allowable value of the minimum length scale is increased. The effects of different mesh discretizations and output spring stiffnesses on the optimized designs are discussed.

A novel fast robust optimization algorithm for intensity-modulated proton therapy with minimum monitor unit constraint.

Intensity-modulated proton therapy (IMPT) optimizes spot intensities and position, providing better conformability. However, the successful application of IMPT is dependent upon addressing the challenges posed by range and setup uncertainties. In order to address the uncertainties in IMPT, robust optimization is essential. This study aims to develop a novel fast algorithm for robust optimization of IMPT with minimum monitor unit (MU) constraint. The study formulates a robust optimization problem and proposes a novel, fast algorithm based on the alternating direction method of multipliers (ADMM) framework. This algorithm enables distributed computation and parallel processing. Ten clinical cases were used as test scenarios to evaluate the performance of the proposed approach. The robust optimization method (RBO-NEW) was compared with plans that only consider nominal optimization using CTV (NMO-CTV) without handling uncertainties and PTV (NMO-PTV) to handle the uncertainties, as well as with conventional robust-optimized plans (RBO-CONV). Dosimetric metrics, including D95, homogeneity index, and Dmean, were used to evaluate the dose distribution quality. The area under the root-mean-square dose (RMSD)-volume histogram curves (AUC) and dose-volume histogram (DVH) bands were used to evaluate the robustness of the treatment plan. Optimization time cost was also assessed to measure computationalefficiency. The results demonstrated that the RBO plans exhibited better plan quality and robustness than the NMO plans, with RBO-NEW showing superior computational efficiency and plan quality compared to RBO-CONV. Specifically, statistical analysis results indicated that RBO-NEW was able to reduce the computational time from to s ( ) and reduce the mean organ-at-risk (OAR) dose from % of the prescription dose to % of the prescription dose ( ) compared toRBO-CONV. This study introduces a novel fast robust optimization algorithm for IMPT treatment planning with minimum MU constraint. Such an algorithm is not only able to enhance the plan's robustness and computational efficiency without compromising OAR sparing but also able to improve treatment plan quality andreliability.