Operation Planning Research Articles

Evaluating communication capability across diverse groups for disaster medicine: A time-tracking method for functional exercises

Recent experiences in disaster medicine in Japan have shown the importance of preventing post-disaster health deterioration among citizens during the evacuation and recovery phases. The effective involvement of various medical, social welfare, and nursing organizations is necessary to mitigate these health problems. This study explored the effectiveness of a time-tracking evaluation method for functional exercises in analyzing the communication and joint task-processing capabilities of various medical and social welfare organizations in response to a citywide heavy-rain disaster. Each exercise inject was analyzed in advance to create a task-processing chain according to the emergency medical response plan. The actions of the exercise players were then compared with the expected tasks in the processing chain. The exercise created overload for some player groups. The completion rates and average execution times of the tasks were compared across task types and player groups, indicating the potential weaknesses of the current emergency operation plan. Responses of local medical associations to similar exercise injects were compared to analyze the range of diversity in responses and the merits of past exercise participation. Although the results of this time-tracking evaluation need to be carefully interpreted by combining the results regarding the quality of players' exercise actions, this method provides a new perspective for evaluating emergency operation plans through functional exercises.

Service needs of elderly members in Bangkok Youth Center (Thai-Japan)

The objective of this research is to study the service needs and factors related to elderly members who use the services of the Bangkok Youth Center (Thai-Japan). The study used a questionnaire survey as a data collection tool for 200 samples. The statistics used in the data analysis were frequency, percentage, mean, and standard deviation, t-test (Independent Sample t-test, F-test (Independent Sample F-test)One-way ANOVA, and the Pearson’s correlation coefficient to test the relationship between variables. According to the study, the majority of the samples were men, between 60 – 65 years old, marital status, had a bachelor’s degree, owned business as a career before retirement, did not work after retirement and had a monthly income of 20,001-50,000 baht. The results of testing the demographic factors on service needs, by using t-test and F-test statistics, showed that the different of gender, age, status, career before retirement and career after retirement were not different, whereas educational and monthly income were. The result of testing the motivation factors on service needs, by using the Pearson’s correlation coefficient statistic, showed that both intrinsic motives and extrinsic motives were related in medium level in the same way. Therefore, the study’s results could be useful for involved organization for operation planning.

Single-level laminoplasty approach to selective dorsal rhizotomy with conus localization by rapid spine MRI

IntroductionWhile selective dorsal rhizotomy (SDR) was originally described as a multilevel approach, single-level approaches are now popularized. Conus localization is beneficial for operative planning in single-level selective dorsal rhizotomy. Our approach to SDR involves minimal exposure for a single-level laminoplasty, preserving one attached interspinous ligament. Pre-operative conus localization is required for this tailored approach to determine the laminoplasty level and dictate rostral or caudal division of the superior spinus ligament. While rapid MRI sequences have been popularized for pediatric cranial imaging, its utility for spinal imagining is less well-described, and specific application for conus localization has not been reported.ObjectiveIllustrate that rapid MRI without sedation is sufficient to identify conus level for tailored single-level laminoplasty SDR.Material and methodsPatients undergoing SDR from 2014 to 2022 at one institution were reviewed for type of pre-operative MRI (rapid vs full), conus level, procedural time for MRI, and radiology report. The typical rapid MRI has four sequences utilizing single-shot technique (scout, sagittal T2, axial T2, and axial T1) that typically take less than 1 min each of acquisition time, with non-single-shot sequences added periodically in cooperative patients. To include time for patient positioning, pre-scan shimming, procedural incidentals, and other patient-specific variations, MRI procedure length was recorded as documented in the electronic medical record.ResultsN = 100 patients had documentation of an MRI for pre-operative imaging. Seventy-nine of these had a rapid MRI, and 21 required a full MRI with anesthesia for their treatment plan. Mean total procedure time for rapid MRI was 21.5 min (median 17). Mean procedure time for MRI under general anesthesia was 91.2 min (median 94). Of patients with rapid MRI imaging, 2/79 had an ambiguous conus level (1 from motion artifact, 1 from spinal hardware) vs 1/21 with a full MRI under anesthesia (due to spinal hardware).ConclusionRapid spinal MRI without sedation can be used for conus localization in a pediatric population. This may be routinely used as pre-operative imaging for a single-level approach to selective dorsal rhizotomy, without sedation or intubation procedures.

Evaluation of a New DNA Extraction Method on Challenging Bone Samples Recovered from a WWII Mass Grave.

Bones and teeth represent a common finding in ancient DNA studies and in forensic casework, even after a long burial. Genetic typing is the gold standard for the personal identification of skeletal remains, but there are two main factors involved in the successful DNA typing of such samples: (1) the set-up of an efficient DNA extraction method; (2) the identification of the most suitable skeletal element for the downstream genetic analyses. In this paper, a protocol based on the processing of 0.5 g of bone powder decalcified using Na2EDTA proved to be suitable for a semi-automated DNA extraction workflow using the Maxwell® FSC DNA IQ™ Casework Kit (Promega, Madison, WI, USA). The performance of this method in terms of DNA recovery and quality was compared with a full demineralisation extraction protocol based on Qiagen technology and kits. No statistically significant differences were scored according to the DNA recovery and DNA degradation index (p-values ≥ 0.176; r ≥ 0.907). This new DNA extraction protocol was applied to 88 bone samples (41 femurs, 19 petrous bones, 12 metacarpals and 16 molars) allegedly belonging to 27 World War II Italian soldiers found in a mass grave on the isle of Cres (Croatia). The results of the qPCR performed by the Quantifiler Human DNA Quantification kit showed values above the lowest Limit of Quantification (lLOQ; 23 pg/µL) for all petrous bones, whereas other bone types showed, in most cases, lower amounts of DNA. Replicate STR-CE analyses showed successful typing (that is, >12 markers) in all tests on the petrous bones, followed by the metacarpals (83.3%), femurs (52.2%) and teeth (20.0%). Full profiles (22/22 autosomal markers) were achieved mainly in the petrous bones (84.2%), followed by the metacarpals (41.7%). Stochastic amplification artefacts such as drop-outs or drop-ins occurred with a frequency of 1.9% in the petrous bones, whereas they were higher when the DNA recovered from other bone elements was amplified (up to 13.9% in the femurs). Overall, the results of this study confirm that petrous bone outperforms other bone elements in terms of the quantity and quality of the recovered DNA; for this reason, if available, it should always be preferred for genetic testing. In addition, our results highlight the need for accurate planning of the DVI operation, which should be carried out by a multi-disciplinary team, and the tricky issue of identifying other suitable skeletal elements for genetic testing. Overall, the results presented in this paper support the need to adopt preanalytical strategies positively related to the successful genetic testing of aged skeletal remains in order to reduce costs and the time of analysis.

A Robotic Solution for Precision Smoothing and Roughening of Precast Concrete Surfaces: Design and Experimental Validation.

Prefabricated construction has pioneered a new model in the construction industry, where prefabricated component modules are produced in factories and assembled on-site by construction workers, resulting in a highly efficient and convenient production process. Within the construction industry value chain, the smoothing and roughening of precast concrete components are critical processes. Currently, these tasks are predominantly performed manually, often failing to achieve the desired level of precision. This paper designs and develops a robotic system for smoothing and roughening precast concrete surfaces, along with a multi-degree-of-freedom integrated intelligent end-effector for smoothing and roughening. Point-to-point path planning methods are employed to achieve comprehensive path planning for both smoothing and roughening, enhancing the diversity of textural patterns using B-spline curves. In the presence of embedded obstacles, a biologically inspired neural network method is introduced for precise smoothing operation planning, and the A* algorithm is incorporated to enable the robot's escape from dead zones. Experimental validation further confirms the feasibility of the entire system and the accuracy of the machining path planning methods. The experimental results demonstrate that the proposed system meets the precision requirements for smoothing and offers diversity in roughening, affirming its practicality in the precast concrete process and expanding the automation level and application scenarios of robots in the field of prefabricated construction.

Minimum dose walking path planning in a nuclear radiation environment based on a modified A* algorithm

An additional cost function for the case with turning points is introduced to the A* algorithm, which can reduce unnecessary turning points. Therefore, the modified A* algorithm consists of three parts: the actual cost function, the estimated cost function, and the turning point cost function. The three functions are normalized so that they can be compared without dimensionality to obtain the optimal path planning in radiation environments. Based on the Geant4 Monte Carlo program, the radiation field model is established and the dose distribution data is obtained. We assign weights to the functions to smooth out the three different cost functions and avoid scenarios in which one function is much greater than the other two. In a small-scale simulation experiment, the path generated by the modified algorithm is consistent with that calculated by the traditional A* method, but the number of turning points is significantly reduced. The modified algorithm takes less time and the cumulative dose on the path is slightly lower. Modified A*, traditional A* and PRM algorithms are used for path planning and comparison in the complex radiation environment of multiple γ sources. The PRM algorithm takes the least computation time to search the path, but the cumulative exposure dose is random. For the path planning of multi-task operation in a radiation field, the cumulative radiation dose of the path planned by the modified A* algorithm is equivalent to that of the traditional A* algorithm, but the modified A* algorithm significantly reduces the number of turning points, the calculation time is significantly shortened, and the execution efficiency is improved. The modified A* algorithm can be used as a reference for path planning for workers in radiation workplaces.

Review and analysis of the failure risk mitigation via monitoring for monopile offshore wind structures

Structural health monitoring systems are gaining more attention in the offshore wind industry as they offer valuable insights into the integrity status of operating assets. Whilst most Class Society Rules and International Standards recognise the importance of implementing a condition-based maintenance strategy, they only provide theoretical guidance. Ultimately, it is the asset owner’s responsibility to determine how to integrate this strategy into their broader operation and maintenance planning, including identifying which components to monitor and which monitoring techniques to employ. The present paper applies the Failure Mode, Effects, and Criticality methodology to identify the most critical failure modes to prioritise for monopile offshore wind structures. Hence, the potential benefits of incorporating structural health monitoring systems within a condition-based maintenance strategy and exploiting lifetime extension possibilities are assessed. To achieve this, a novel 4-step methodology is introduced, involving understanding failure mechanisms (time-dependent behaviour and pattern), current regime (inspections at intervals), monitoring options (both direct and indirect), improvement potential evaluation through 5 key performance indicators relevant for optimal O&M, which is more comprehensive and realistic than considering only monetary consequence of failure. The study addressed the prevailing failure modes in 5 categories, namely fatigue, corrosion, deformation, buckling and displacement, and connection failure, aiming to demonstrate potential improvement in terms of risk mitigation against these failure modes. The results of this study can significantly help offshore wind developers optimise where and how to allocate their resources for structural health monitoring, resulting in long-term cost reduction opportunities.

Outlier Detection for Permanent Magnet Synchronous Motor (PMSM) Fault Detection and Severity Estimation

Today, Permanent Magnet Synchronous Motors (PMSMs) are a dominant choice in industry applications. During operation, different possible faults in the system can occur, so early and automated fault detection and severity estimation are required to ensure smooth operation and optimal maintenance planning. In this direction, outlier detection methods are employed in this paper. The motor’s current signals are used to extract useful indicators of the fault, along with d-q transform. Statistical indicators in both time and frequency domains are selected to describe fault-related patterns. Based on the extracted features, three outlier detection methods are investigated: the Isolation Forest, the One Class Support Vector Machine, and the Robust Covariance Ellipse. Each method is investigated through different model parameters to evaluate fault detection and severity estimation capabilities. Finally, an ensemble approach is proposed based on decisions and outlier score ensemble. The proposed methodology is verified through different operating conditions in a PMSM test bench.

A hybrid data-driven method optimized by physical rules for online state collaborative estimation of lithium-ion batteries

Accurate online estimation of state of charge (SOC) and state of health (SOH) is crucial for safe operation and reasonable planning of battery management system (BMS). However, battery internal states are unmeasurable directly and coupled with each other, which results in serious difficulties on multi-states accurate estimation. Considering SOC estimation is deeply influenced by SOH, this paper proposes a collaborative estimation method combined machine learning algorithm with simple physical rule. Integrated the merits of the above methods, it can not only improve the estimating accuracy but also low computational burden to a large extent. Firstly, SOH acts as input of SOC in collaboration, which means SOH should have been already known before SOC estimation operation. Thus, SOH is creatively predicted based on gate recurrent unit network in ahead of SOC estimation. Subsequently, the well-trained SOC data-driven model is combined with the ampere hour (Ah) integration, which act as observation and state equation respectively in the particle filtering algorithm to realize the final estimation of SOC. This way, the sole data-driven model is well improved under physics restriction without any other computational procedure, such as online parameter identification. Simultaneously, the predicted SOH is used to fill the Ah integration expression to realize the collaboration between SOC and SOH. What's more, the SOH is further corrected by the incremental capacity peak at the checkpoint, thereby further reducing the estimation deviation. The experimental result on battery shows that the SOH estimated error is below 0.3Ah (the rated capacity is 32.5Ah) and SOC error is less than 1.5 %. What's more, the generalization capacity of the proposed method is verified on different battery types based on public datasets. Obviously, the proposed method has fairly satisfactory property and performance and can totally support its promotion into state online evaluation of battery energy storage.

From Data to Action: A Graph-Based Approach for Decision Support in Civil Protection Operations Planning

In the face of increasing frequency and severity of crises such as natural disasters, pandemics, and geopolitical conflicts, civil protection organizations are crucial for recovery and support for affected populations. However, the efficiency and effectiveness of these organizations in crisis response are often hindered by the manual generation of operation plans, characterized by cognitive overload and limited analytic overview. Existing systems focus on detecting crises or post-crisis analysis, overlooking proactive planning. We present GRETA, a graph-based operational planning approach utilizing semantic historical data for better decision support. GRETA uses Operational Scenario Patterns to model operations, mapping them onto a knowledge graph in JSON-LD format, thus creating a structured representation of past data to improve future crisis response planning. We tested GRETA with Germany's Federal Agency for Technical Relief, analyzing over 157,450 historic operations from 2012-2022. Results show GRETA enhances plan efficiency, accuracy, and comprehensiveness, aiding especially inexperienced planners.

Comparison of Anthropometric and Cephalometric Measurements Obtained by Stereophotogrammetry and 3D Computed Tomography of the Nose Before Septorhinoplasty.

Computed tomography (CT) is normally used in evaluation of patients with esthetic and functional nasal deformities. Stereophotogrammetry (SPG) is a measurement device that is an alternative to CT and does not harm human health. In this single-center retrospective study, we aimed to evaluate measurements obtained with CT and SPG. The measurements of 18 patients who applied to our clinic between January 2022 and August 2022 and planned for septorhinoplasty were performed on both 3D images obtained with paranasal sinus CT and SPG device (SLR type Vectra H1 system). Measurements included that dorsocolumellar length, columella-filtral length, nasal tip projection ratio (dorsocolumellar length/columella-filtral length), columella-labial angle, nasofrontal angle, tip deviation direction, tip deviation angle, tip deviation distance and dorsal nasal hump. Most of patients were male (61.1%). Mean age was 24.5 years. Only columella-labial angle measurements showed a low level of significant difference (p<0.05). However, there was no significance difference in other measurements (p>0.05). A significant strong correlation was observed between all Vectra and CT measurements (p=0.000). SPG device can be applied quickly in polyclinic without giving radiation to patient. Measurements can be taken automatically using a software. Its use in postoperative period does not carry any risk. Disadvantage of SPG is lack of information about internal nasal passage. However, there is a strong correlation between measurements obtained from both measurement devices. Therefore, SPG can be considered as an alternative to CT imaging in operation planning. This journal requires that authors assign a level of evidence to each article. For a full description of these Evidence-Based Medicine ratings, please refer to the Table of Contents or the online Instructions to Authors www.springer.com/00266 .

Intravascular lithotripsy to address calcific aortic disease

Intravascular Lithotripsy (IVL) is a relatively modern endovascular tool accepted for use to address vascular calcification in the iliac arterial system and below. This case study shows evidence of successful application of IVL followed by stent placement to calcific disease present within the aorta as well. A 78-year-old female with numerous comorbidities and a history of an aorto right femoral left iliac bypass graft in 1998 presented with severe lifestyle limiting claudication secondary to high-grade atherosclerotic stenosis of her infrarenal abdominal aorta at the level of the proximal anastomosis of her bypass graft. Initial ABIs were 0.54 and 0.55 on the right and left respectively. Initially the operative plan was to conduct a retroperitoneal aortic endarterectomy. However, after the surgical optimization center deemed the patient intermediate risk and her pulmonary function decreased prior to the procedure, the decision was made to proceed with IVL followed by angioplasty and aortic stent placement. The patient tolerated the procedure well without complication and she was discharged home the following day. At follow up appointment 6 weeks later, the patient's repeat ABIs were significantly improved to 0.77 in the right and 0.86 in the left with a coinciding improvement in symptoms. In conclusion, IVL is safe and effective in calcific aortic disease and should be considered in patients who are not optimal open surgical candidates.

IN VIVO ACCURACY OF A NEW ROBOTICALLY ASSISTED SYSTEM FOR TOTAL KNEE ARTHROPLASTY: A PROSPECTIVE COHORT STUDY

IntroductionRecent technological advancements have led to the introduction of robotic-assisted total knee arthroplasty to improve the accuracy and precision of bony resections and implant position. However, the in vivo accuracy is not widely reported. The primary objective of this study is to determine the accuracy and precision of a cut block positioning robotic arm.MethodSeventy-seven patients underwent total knee arthroplasty with various workflows and alignment targets by three arthroplasty-trained surgeons with previous experience using the ROSA® Knee System. Accuracy and precision were determined by measuring the difference between various workflow time points, including the final pre-operative plan, validated resection angle, and post-operative radiographs. The mean difference between the measurements determined accuracy, and the standard deviation represented precision.ResultsThe accuracy and precision for all angles comparing the final planned resection and validated resection angles was 0.90° ± 0.76°. The proportion within 3° ranged from 97.9% to 100%. The accuracy and precision for all angles comparing the final intra- operative plan and post-operative radiographs was 1.95 ± 1.48°. The proportion of patients within 3° was 93.2%, 95.3%, 96.6%, and 71.4% for the distal femur, proximal tibia, femoral flexion, and tibial slope angles when the final intra-operative plan was compared to post-operative radiographs. No patients had a postoperative complication requiring revision at the final follow-up.ConclusionsThis study demonstrates that the ROSA Knee System has accurate and precise coronal plane resections with few outliers. However, the tibial slope demonstrated decreased accuracy and precision were measured on post-operative short-leg lateral radiographs with this platform.

A bilevel fast-convergent optimizer via high-fidelity convex models: Application on optimal operation of all-parallel heterogeneous chiller-pump systems

To cope with buildings’ growing and diverse cooling demand, heterogeneous multi-chiller systems with non-dedicated pumps are commonly applied in large-scale centralized chiller plants. All-parallel heterogeneous systems offer high operation flexibility but pose challenges to optimal operation planning. For the deficiencies in convexity tractability, the classical neural networks (NNs) achieved great success in system identification yet were restricted in model-based optimization. In this study, an optimization-oriented convex modeling approach based on input convex neural networks (ICNN) to identify energy consumption models for energy units of chiller-pump systems was presented, which provides convex input–output mappings while leveraging the high-fidelity capability of NNs. Using the convex models, the energy minimization issue subjected to multiple constraints was formulated, the optimality of which was mathematically proven. A bilevel deterministic optimizer was developed to determine the global optimal. Comprehensive data experiments were conducted using practical and simulated operation data to evaluate the modeling and optimization performances of the proposed methods compared with conventional candidates. Numerical results suggest that the ICNN-based convex models exhibit superior modeling performances than physics-based models. A better overall energy saving ratio of 8.86 % and faster convergence time of 3.53 s for average achieved by the proposed bilevel optimizer compared with rule-based and meta-heuristic optimizers under identical external conditions.

Optimal scheduling of active distribution network based on RBF-stochastic response surface method

As the high proportion of distributed generation (DG) and diversification of loads increase, the distribution network faces increasingly greater impact. To address the high-dimensional stochastic problems arising from the multi-dimensional uncertainty of power source and load, this paper proposes a two-stage optimization scheduling scheme for AC distribution networks based on RBF-stochastic response surface method (RBF-SRSM). This scheme takes into account economy, environmental protection and safety, and consists of day-ahead and intra-day stages. The day-ahead decision scheduling is based on an optimal low-carbon economy operation plan, while the intra-day reactive power optimization is achieved by converting nonlinear integral indicators into discrete linear indicators through probabilistic power flow calculation and the first moment derivation principle inspired by SRSM. The mixed integer second-order cone programming (MISOCP) method is used to solve the dispatching plan, and the results suggest that the proposed method is more efficient than the SRSM.

Wonorejo dam operation and storage analysis against climate change

Climate change affecting rain intensity within catchment and increase the potential hydrometeorology disasters. Wonorejo Reservoir as a multipurpose dam requires an operational plan and water allocation to fulfill downstream needs, such as irrigation, hydropower, microhydropower, domestic industry uses and flood control. Wonorejo Dam is a backfill type dam with High Water Level (HWL) elevation is +183.00 mSHVP and Low Water Level (LWL) elevation is +141.00 mSHVP, Total storage capacity Wonorejo Reservoir is 109.118 million m3 (2021) or 89.4% from initial total storage capacity (2000), in 2050 predicted sediment volume increase to 17.73 million m3 or 17.6% reservoir capacity and 2050 capacity volume is 100,585 million m3 or 82.4% from initial total storage capacity. Annual Reservoir Operation Plan and Annual Water Allocation Plan for Wonorejo Reservoir in 2022/2023 as water services December 2022 to November 2023 periode, Wonorejo Reservoir elevation at the end of May 2023 reaches HWL and lowest water elevation is +162.64 mSHVP in the first week of November 2023.

Spallation Neutron Source reliability improvement projects for the Cryogenic Moderator System

The Spallation Neutron Source (SNS) at Oak Ridge National Laboratory (ORNL) operates the Cryogenic Moderator System (CMS) which provides supercritical hydrogen cooling at 20K to three neutron moderators. A helium refrigerator provides 8 kW of cooling capacity to three parallel hydrogen circuits. Several projects have been completed to improve the operational reliability of the CMS. The status of helium compressor oil removal system, helium oil processor, helium purity monitoring, hydrogen circulator bearing investigation and operational procedure improvement will be presented. Future plans for sustained reliable operation at design capacity will also be presented.

Metro Train Stopping Scheme Decision Based on Multisource Data in Express-Local Train Mode

Metro Train Stopping Scheme Decision Based on Multisource Data in Express-Local Train Mode

Integrated Optimisation Model of Daily Freight Train Scheduling and Dynamic Railcar Routing Based on a Two-Layer Space-Time Network

This paper focuses on daily freight train scheduling and dynamic railcar routing problems for rail freight transportation at the operational level. Two mixed integer linear programming models that adopted different strategies were formulated based on a continuous two-layer time-space network. We simultaneously considered the benefits of railroad company and service quality when setting the objective function. By solving the models, we can distribute the dynamic railcar flows to the train paths in the basic train timetable to obtain the daily train operation plan over a short time horizon (e.g. a day), which will be helpful for dispatchers to make decisions such as the empty railcar distribution and car routing (trip planning). Finally, we compared two models on a part of the Chinese railroad network. The results show that the second model can effectively improve the efficiency of railroad freight transportation.

Improved stochastic fractal search algorithm involving design operators for solving parameter extraction problems in real-world engineering optimization problems

The characteristic parameters of renewable energy sources (RESs) are changes over time under changing operating conditions. Therefore, the accuracy of the model is important in order to establish appropriate control and operating plans for the stable operation of such systems. Determining the parameters of RESs and creating an accurate model of them is an inevitable reality and plays an important role in the success of system modeling. Many methods have been used to determine these parameters in the literature. Furthermore, optimization algorithms are now considered to be among the most significant approaches for resolving problems pertaining to system parameter extraction in many scientific areas. In the study, this parameter extraction is done by a new optimization method called stochastic fractal search algorithm (FDB-NSM-SFS-OBLs), which includes natural survivor updating (NSM) and fitness distance balance (FDB) guiding mechanisms, and opposite based learning (OBL) methods. The performance of the proposed FDB-NSM-SFS-OBL algorithm has been tested in two different experimental studies. In the first experimental study, the proposed approach is tested on CEC2020 benchmark test functions and the algorithm structure containing the best OBL approach is determined using nonparametric Wilcoxon and Friedman statistical analysis methods. The second experimental study is carried out with the proposed optimization algorithm to estimate the parameters of the photovoltaic cell used in the modeling, which is the building block of photovoltaic panels used in renewable energy systems, proton-exchange membrane fuel cell (PEMFC) that is another renewable energy source, and Li-Ion battery used as a backup power unit. The FDB-NSM-SFS-OBL algorithm, which is used both in the CEC2020 benchmark test functions and in determining the parameters of photovoltaic (PV) cells, PEMFC and Li-Ion batteries, performed better in searching and finding the global solution point during the optimization process.