Multi-objective Planning Model Research Articles

Expansion planning of hybrid electrical and thermal systems using reconfiguration and adaptive bat algorithm

_ This study introduces a comprehensive model for the concurrent expansion planning of various energy systems and their associated equipment. The need to reduce network costs, emissions, losses, and feeder loading, as well as to enhance network reliability and voltage profile, mandates the utilization of proper multi-objective planning models that respect all network constraints. The introduced framework includes units for generating both electrical and thermal energies. The model leverages conventional expansion alternatives such as the installation of new lines, network reconfiguration, rewiring, and the addition of new thermal and electrical generating units to the network. Expansion planning involves determining the optimal time, location, and type of new installations to meet future energy demands while minimizing costs and emissions. Reconfiguration refers to altering the network topology to improve reliability and reduce losses. The proposed expansion planning is formulated as a discrete, nonlinear, and non-convex optimization problem, which is solved using the Self Adaptive Learning Bat Algorithm (SALBA). This algorithm improves convergence speed and increases the diversity of the search population, enhancing the likelihood of finding the global optimum. Numerical simulations of the proposed methodology on two modified standard IEEE test systems corroborate the efficacy and feasibility of the suggested approach. Key innovations include the comprehensive modeling for concurrent expansion planning, the use of an advanced optimization algorithm, and a focus on reducing costs, emissions, losses, and feeder loading while enhancing network reliability and voltage profile.

Designing a multi-purpose network of sustainable and closed-loop renewable energy supply chain, considering reliability and circular economy

Since renewable energy systems have a limited lifespan and cannot be used after a while, it seems imperative to pay attention to recycling and sustainability in the supply chain network design of these systems. Also, modern power systems have high complexity and a large number of problems that affect the reliability of electricity supply to consumers. Therefore, organizations should consider broader goals, including the maximum use of resources and the minimization of waste, which is known as lean economy. In this research, a multi-objective non-linear forward optimization model has been considered for the design of the supply chain network of photovoltaic and wind systems based on the aspects of stability and taking into account the reliability. Also, adding the reverse flow, in addition to the forward flow, is also considered, which, in addition to economic advantages, also pays attention to environmental and social issues. The objective function includes minimizing all costs and negative environmental effects as well as increasing reliability. In order to convert the multi-objective planning model into a single-objective one, the epsilon method of the enhanced constraint is used. Uncertainty has been considered for all variables (except binary variables) and parameters of demand, intensity of sun radiation and amount of wind speed. Then, the efficiency of the model has been investigated through its implementation on a case study and the results have been obtained. Eventually, the model's efficiency is illustrated by discussing a real-world case, through which prominent managerial results are acquired.

A multi-objective planning and scheduling model for elective and emergency cases in the operating room under uncertainty

Hospitals are paramount hubs for delivering healthcare services, with their Operating Rooms (ORs) as a pivotal and financially substantial component. Efficient surgery ward planning is crucial in healthcare institutions, aiming to improve medical service quality while reducing costs. This research delves into the intricacies of integrated OR planning and scheduling, focusing on elective and emergency patients in an uncertain environment. To address these challenges, a mixed integer programming (MIP) framework is developed to minimize inactivity and patient wait times while optimizing high-priority resource allocation. Both upstream and downstream units of the ward, the Pre-operative Holding Unit (PHU), Post Anesthesia Care Unit (PACU), and Intensive Care Unit (ICU) are included. The inherently uncertain aspects of surgery, including surgical duration, Length of Stay (LOS), and the influx of emergency patients, demand an intelligent optimization approach. Consequently, a robust optimization strategy is harnessed to effectively grapple with this pervasive uncertainty. A deterministic model is introduced and improved using an enhanced epsilon constraint method. The culmination of this analytical journey yields a collection of Pareto-optimal solutions. Empirical results, supported by managerial insights, highlight the superiority of the proposed method over the traditional weighting approach.

Research on Light Pollution Based on AHP and Fuzzy Comprehensive Evaluation Methods

In the current context of increasing global light pollution, we urgently need an effective control system. In this study, we constructed an extensive and objective evaluation model through the AHP method to classify light pollution into standard and index layers, and successfully established an evaluation model that accurately predicts the level of light pollution. Through practical tests, we found that light pollution is higher in cities, followed by suburbs, and lower in rural areas and protected areas. Based on the established evaluation model, we propose three most effective intervention strategies: regulating the use of LED billboards, reducing the use of reflective building materials, and controlling nighttime construction lighting. In response to the possible negative impacts, we propose specific solutions and verify the effectiveness of the intervention programs through a multi-objective planning model, achieving significant results in reducing light pollution levels. This study provides a useful reference and lesson for light pollution management.

Research on optimal allocation of surface ship formation based on index method and multi-objective programming

In recent times, marine engineers have progressively turned to collaborative efforts involving multiple ships to accomplish intricate tasks at sea and enhance the efficacy of maritime transportation. This trend is also observed in the context of surface ships, where coordinated actions among multiple vessels can enhance combat capabilities. Nevertheless, the assessment of ship formation coordination’s effectiveness has emerged as a significant challenge. Consequently, this research paper presents a quantitative evaluation framework for ship performance indicators and develops a ship formation model grounded in multi-objective constraints that account for the complexities of the marine environment. This paper presents the establishment of a ship evaluation system that encompasses the impact of auxiliary equipment, the ship’s platform, and trained personnel. The study utilizes aircraft carrier battle groups from four distinct countries as case examples to obtain quantitative evaluation results regarding combat performance. Furthermore, the analysis examines the effects of two extreme marine environments on surface ships. The organization of new surface ship formations is conducted based on a multi-objective planning model that is tailored to specific surface ship formations. All kinds of combat performance indexes are better than the formation of this particular surface ship. The experimental results show that the model can integrate different kinds of equipment performance parameters into a unified system and consider the comprehensive factors of equipment, platform and people. According to the requirements of task formation and the limitations of the actual Marine environment, a stable formation can be formed quickly, which can be superior to a specific formation in all aspects. Good results are obtained and the effectiveness of the model is verified.

Particle Swarm Optimization-Based Multiobjective Planning Model for Marketing Strategy Decision

Particle Swarm Optimization-Based Multiobjective Planning Model for Marketing Strategy Decision

Impacts of Land Use Conversion on Soil Erosion in the Urban Agglomeration on the Northern Slopes of the Tianshan Mountains

The serious problem of soil erosion not only has a profound impact on people’s lives but also results in a series of ecological and environmental challenges. To determine the impact of changes in land use type on soil erosion in the urban agglomeration on the northern slopes of the Tianshan Mountains, this study commences by employing the InVEST-SDR (integrated valuation of ecosystem services and tradeoffs–sediment delivery ratio) model to calculate soil erosion levels spanning from 2000 to 2020. Subsequently, it forecasts land use and land cover (LULC) conditions for the year 2030 under three scenarios: Q1 (natural development), Q2 (ecological protection), and Q3 (economic priority). This projection is accomplished through the integration of a coupled Markov chain and multi-objective planning model (MOP) alongside patch-generating land use simulation (PLUS) models. Ultimately, based on these outcomes, the study predicts soil erosion levels for the year 2030. There has been a consistent decline in soil erosion from 2000 to 2020 with high-intensity erosion concentrated in the Tianshan Mountain region. Grasslands, glaciers, and permafrost are identified as the most erosion-prone land types in the study area, with forests exhibiting the highest capacity for soil retention. Converting from grassland and barren land to forest within the same area results in a substantial reduction in soil erosion, specifically by 27.3% and 46.3%, respectively. Furthermore, the transformation from barren land to grassland also leads to a noteworthy 19% decrease in soil erosion. Over the past two decades, the study area has witnessed a significant decline in the area of grasslands, with a notable shift towards barren and impervious surfaces due to economic development and mining activities. The three predicted scenarios depict significant expansion towards barren land, grassland, and impervious area, respectively. Soil erosion decreases under different shared socio-economic pathway (SSP) scenarios relative to 2020. There is an increase in soil erosion in the Q1 scenario and in the Q3 scenario, whereas the amount of soil erosion in the Q2 scenario exhibits a continued decrease when only the effect of land change on soil erosion is considered. Persistently rapid economic development can exacerbate soil erosion problems, underscoring the need to find a balance between economic growth and ecological conservation. As economic expansion slows down, greater emphasis should be placed on environmental protection to maintain ecological stability.

Multi-Objective Optimization of the Planting Industry in Jiangsu Province and Analysis of Its “Water-Energy-Carbon” Characteristics

The modern development of the planting industry needs to not only ensure food supply but also to consider social and environmental issues. This poses higher demands for rational planning of planting structures to achieve green development while meeting demands and conserving resources. Therefore, this paper takes Jiangsu Province as a representative case, accounting for and analyzing the water footprint, energy consumption, and carbon emissions of seven major crops. Based on this analysis, a multi-objective planning model is established to explore the optimization of its planting structure. The results show that: (1) from 2010 to 2020, the overall water footprint of these seven crops in Jiangsu Province initially increased and then decreased, while energy consumption showed a fluctuating upward trend; (2) carbon emissions from planting in Jiangsu Province initially increased and then fluctuated downward over time, and exhibited significant spatial clustering characteristics, with overall emissions being higher in northern Jiangsu, followed by central Jiangsu, and then southern Jiangsu; (3) the optimization results indicate that economic benefits increased by 4.06%, while the carbon emission and grey water footprints decreased by 3.78% and 7.62%, respectively, resulting in comprehensive improvements in economic and ecological benefits. This study can provide theoretical support for adjusting the planting structure in crop-producing areas and promoting the green and sustainable development of the planting industry.

Research on emergency transport planning for E-commerce logistics network based on simulated annealing algorithm

In response to the issue of insufficient demand for logistics facilities during holidays or the temporary or permanent closure of logistics facilities due to sudden events such as epidemics, natural disasters, etc., this paper proposes a planning model and solution algorithm based on multi-objective dynamic decision-making to optimize the emergency transport plan and structure of the e-commerce logistics network. Firstly, an LSTM model is utilized to predict the transportation demand for a certain period in the future. Decision variables are introduced to indicate whether to open or close new routes after closing a logistics facility. The objective functions are set to minimize the number of routes with changes in cargo volume, minimize the load imbalance of each route, and minimize the cumulative total of parcels that cannot circulate normally. Considering factors such as normal circulation of parcels, circulation capacity, transportation capacity after opening or closing facilities, and time constraints, a multi-objective planning model is constructed. Finally, the simulated annealing algorithm is employed for solution, obtaining a circulation plan that meets the requirements. Simulation experiment results demonstrate that the model can rapidly and accurately respond to the paralysis of the e-commerce logistics network caused by sudden events, showcasing high efficiency and practical application value.

A study of the pathway to peak carbon in China

The achievement of the peak carbon target is a complex and comprehensive project that involves vari-ous aspects such as the economy, society, and ecological environment. At the same time as reaching the carbon peak, how to balance economic and social development has become an important issue. This study uses the environmental Kuznets curve (EKC) model to predict China’s carbon peaking situation. Three key parameters, namely carbon peaking, economy, and society, are selected, and relevant decision variables are established. A multi-objective planning model is developed to facilitate the coordinated development of carbon peaking, economy, and society, which is solved using a sequential algorithm. The results show that: China’s carbon emissions were 6928.905 million t in 2020 and are expected to reach the carbon peak in 2030. At the peak, the per capita gross domestic product (GDP) is estimated to be 16 281.95 $, correspond-ing to a per capita CO2 emission of 9.66 t. During China’s carbon peak, the GDP is projected to be 23 249.58 billion $, with an arable land area of 121 747 510 ha and sulfur dioxide emissions of 180.64 million t, meeting the expected target values. However, certain indicators such as the ratio of three industries, energy consumption, rural residents’ per capita disposable income, and water consumption fall short of expected. Based on these findings, relevant countermeasures have been proposed for the realization path and key breakthroughs for China’s carbon peak.

Application of Intelligent Algorithms for Optimal Allocation of Accounting Education Resources in Higher Education Environments

Abstract Inadequate allocation of accounting education resources and uneven spatial distribution are the key issues affecting the high-quality development of accounting education, and the arrival of the era of intelligent technology provides ideas for the rational allocation of higher education resources and transformation and upgrading. This paper constructs a multi-objective planning model for accounting education resource allocation and explores the solution method based on the fuzzy particle swarm algorithm. Population initialization is achieved by combining input-output fuzzification processing and particle swarm optimization search in fuzzy control. Subsequently, the fitness of every particle is assessed. Next, according to the formula of PSO algorithm update iteration, the position and speed are updated, the optimal solution of itself and the optimal solution of the population are updated, and the optimization search is continuously iterated. After the model is put into use the institutions in the western region with low and lower levels of efficiency in the allocation of accounting education resources decreased by 7%, and all the regions with low levels of efficiency have decreased. The number of configuration rounds of this paper’s method is smaller than the number of rounds of configuration conflicts of the PCA method and SVM method, which indicates that this paper’s method has good performance and optimizes the allocation of accounting education resources, making accounting education develop in a balanced way.

Aptenodytes forsteri optimization algorithm for low-carbon logistics network under demand uncertainty.

As China's "double carbon" goal continues to advance, logistics as a key area of carbon emissions and low-carbon logistics center site selection are key links in the process. However, existing studies on logistics center location often ignore the impact of demand uncertainty, which leads to a waste of resources in the planning and construction processes. We take logistics cost and carbon emission as the objectives, and the multi-objective site selection model established based on stochastic programming theory takes demand uncertainty as a stochastic constraint. We transform the stochastic constraint model into a 0-1 mixed integer multi-objective planning model by utilizing the idea of equivalence transformation. The Aptenodytes Forsteri Optimization (AFO) algorithm is combined with the Ideal Point Method to solve the model, and the algorithm is compared with the Particle Swarm Optimization (PSO), Differential Evolutionary (DE), Tabu Search (TS), Sparrow Search (SS) algorithms, and the exact solver Linear Interactive and General Optimizer (LINGO). The examples verify the validity of the models and algorithms, with an average reduction of 6.2% and 3.6% in logistics costs and carbon emissions in the case of demand determination, and at the confidence level of 0.9 under demand uncertainty, both logistics costs and carbon emissions are decreased to varying degrees. This study provides a new research idea for the low-carbon logistics location problem under demand uncertainty, which helps to promote the transformation of the logistics industry to low-carbon and high-efficiency.

The application of carbon footprint assessment under intelligent computing in green consumption decision-making

Abstract Reducing carbon emissions is a basic policy long insisted on by the Chinese government, and the calculation of carbon footprint is of great application significance for reducing carbon emissions and realizing green consumption. Based on the multi-objective planning model this paper establishes a carbon footprint assessment model based on multi-objective planning from the economic, environmental, and social benefits of carbon footprint. It optimizes the particle swarm algorithm to solve the objective function of the carbon footprint multi-objective assessment model. The designed model is utilized in green consumption decision-making to forecast the carbon footprint and structure of green energy consumption in the future. The comparison shows that after the optimization of the carbon footprint assessment model based on multi-objective planning designed in this paper, the proportion of coal and oil consumption in the carbon footprint of energy consumption decreases by 1.2% and 0.5%, respectively, and the energy intensity can be optimized. The per capita carbon footprint of energy consumption of residents in eastern, central, and western China grows by 11.3%, 15.2%, and 2.7%, respectively, from 2024 to 2026. The carbon footprint of per capita energy consumption in the three regions is quite different. The results of the two projections show that the carbon footprint assessment model based on multi-objective planning designed in this paper is important for improving the energy consumption structure in different regions and realizing green consumption decisions.

Vessel voyage schedule planning for maritime ore transportation

This paper introduces a vessel voyage schedule planning problem for maritime ore transportation arising from a real-world project in Boffa, Guinea. In this problem, delay of vessel arrivals at the loading port often occurs which interrupts the ore loading operation and further impacts the yearly throughput of ore transportation, which dues to variable weather conditions at sea and changing loading/discharging time at ports. Thus, factors regarding the uncertainty of vessel voyages must be considered in order to ensure continuous vessel arrivals and uninterrupted loading operations at the original port, leading to an increase in the overall productivity of the project. And at the same time, since every voyage entails an increase in costs, cost control is necessary to be accounted for, so there is also a need to consider minimizing operating costs. In this study, to address the uncertainty in voyage duration, a chance-constrained model is introduced to obtain sailing schedules as well as the associated costs within a given confidence level. And then, for the multi-objective requirements, we develop a multi-objective planning model and the actual system operating capacity limitation constraints are considered. After that, considering that the multi-objective model cannot be solved by the solver directly, the weighting method is introduced. Afterwards, since the direct solving of the model is rather time-consuming, valid cuts are designed to accelerate it. Finally, considering that the Pareto solutions of multi-objective problems are numerous, a nondominated sorting genetic algorithm II (NSGA-II) is launched with the aim of providing more solutions to the manager in a shorter time. In terms of experiments, each of the aforementioned issues and proposed remedies are verified. The results confirm the effectiveness of the valid cuts and NSGA-II, and demonstrate that the obtained vessel voyage schedule is more robust and outperforms manual decisions.

Research on Optimizing the Path of education of ideologic and politic Combined with Multi-Objective Planning for the Cultivation of Innovative and Entrepreneurial Abilities

Abstract The co-development process between the two is enhanced by this study, which integrates the advancement of creativity and entrepreneurship skills with political and ideological instruction. The multi-objective planning model’s many benefits are utilized to accomplish this. Weak, medium, and strong levels are established based on internal, external, and environmental aspects in order to assess the extent to which political and ideological education has an impact on the development of creativity and entrepreneurial potential. Examine the relationship between national creation and entrepreneurship policies, creation and entrepreneurship courses, creation and entrepreneurship activities, creation and entrepreneurship competitions, and college students’ capacity for creation and entrepreneurship to determine the factors that influence this capacity. The examination of the institution of higher education determines the degree of creativity and entrepreneurship education by collecting data on demand, carrying out access channels, and the degree of cognition of creativity and entrepreneurship education. An optimization path for the education of creative and political students combined with multi-objective planning is suggested after the cultivation of the creation and entrepreneurial capacity of the students’ education is examined. The subjective cognition of creative and political students’ own creation and entrepreneurship capacity is not adequately taught; only 12.35% of them believe that their capacity for innovation is very good or very good, and 42.37% believe that it is not so good and needs to be strengthened.

Process Exploration of New Materials for Building Decoration Engineering Based on Multi-Objective Planning Modeling

Abstract Firstly, on the basis of the multi-objective planning model, we determine the objective function of building energy consumption, the objective function of material cost and the objective function of uncomfortable time percentage. We propose to use a multi-objective genetic algorithm to obtain the Pareto frontier solution for the decision variables of the model by selecting them. The target constraints are determined based on the construction of the building decoration project, and the model of remodeling material cost-schedule-carbon emission’ is constructed. The discrete simulation model of the decoration project is constructed based on the design parameters of the enclosure structure and air conditioning. Considering the structural rigor of the research and analysis, it is necessary to set and explain the parameters of the simulation model, and the materials of the decoration project are studied and analyzed. The results show that on the engineering case analysis, the value of building energy consumption, building cost and the value of uncomfortable time percentage have increased by 23%-45% compared with the value before optimization. In the simulation model, the optimized construction solution’s carbon emission, cost, and duration were reduced by 6.22%, 10.65%, and 45.48%, respectively, compared to the original solution. This study illustrates the aesthetic performance and functional performance on the basis of the process of new materials, which is a guiding reference value for the application of new materials in architectural decoration engineering.

Multi-objective optimization of capacity and technology selection for provincial energy storage in China: The effects of peak-shifting and valley-filling

To support long-term energy storage capacity planning, this study proposes a non-linear multi-objective planning model for provincial energy storage capacity (ESC) and technology selection in China. The model aims to minimize the load peak-to-valley difference after peak-shaving and valley-filling. We consider six existing mainstream energy storage technologies: pumped hydro storage (PHS), compressed air energy storage (CAES), super-capacitors (SC), lithium-ion batteries, lead-acid batteries, and vanadium redox flow batteries (VRB). The optimized results show that 1) the accumulated ESC in China could increase at an average annual rate of 14.4–17.6% in 2020–2035, reaching 271.1–409.7 GW in 2035 at a total cost of 34.9–41.6 trillion yuan. 2) With favorable technical development levels and application prospects, lithium-ion batteries will be the dominant technology in 2035 in all scenarios. SC has the fastest growth rate among the six technologies in most scenarios because of its flexible location and long lifetime. 3) In the BAU scenario, Xinjiang, Inner Mongolia, Hebei, Ningxia, and Qinghai are the provinces with the largest ESC in 2035 while the four municipalities of Chongqing, Beijing, Tianjin, and Shanghai, as well as Tibet, have the smallest. This layout depends on the differences in the installed capacity of renewable energy in the provinces.

Multiobjective Electric Vehicle Charging Network Planning Considering Chance-Constraint on the Travel Distance for Charging

Electric vehicle charging stations (EVCSs) are important infrastructures to support sustainable development of electric vehicles (EVs), by providing convenient, rapid charging services. Therefore, the planning of electric vehicle charging network (EVCN) has attracted wide interest from both industry and academia. In this paper, a multiobjective planning model for EVCN is developed, where a fixed number of EVCSs are planned in the traffic network (TN) to achieve two objectives, i.e., minimizing both average travel distance for charging (TDfC) of EVs and investment costs of EVCN. According to the random characteristics of EVs’ TDfC, its constraint is presented as a chance constraint in the developed EVCN planning model. The nondominated sorting genetic Algorithm II with the constraint domination principle (NSGA-II-CDP) is customized to solve the developed multiobjective EVCN planning model, by designing a special coding scheme, a crossover operator, and a mutation operator. Then, a maximum gradient principle of investment revenue is designed to select the optimal planning strategy from the Pareto-optimal solution set, when taking the investment return ratio as primary consideration. A 25-node TN is used to justify the effectiveness of the developed methodology.

Optimization and Simulation of Mountain City Land Use Based on MOP-PLUS Model: A Case Study of Caijia Cluster, Chongqing

Mountainous cities face various land use challenges, including complex topography, low land use efficiency, and the insufficient control of land use in small-scale areas at the urban fringe. Considering population changes, environmental conservation, and urban planning, this study first established three scenarios: economic priority (Econ. Prior.), ecological priority (Ecol. Prior.), and balanced development (BD), and then used the Multi-Objective Planning (MOP) model to calculate the optimal land use structure. Finally, it carried out land use spatial layout optimization based on the Patch-generating Land Use Simulation (PLUS) model in 2035, Caijia Cluster, Chongqing, China. This approach, known as MOP-PLUS modeling, aimed to optimize land use. Meanwhile, the applicability of the PLUS model in simulating land use changes was discussed in small-scale mountainous areas. The results show the following: (1) The “quantity + space” approach in the MOP-PLUS model demonstrated the feasibility of the PLUS model in simulating land use change in small-scale mountainous areas. The overall accuracy (OA) of land use change simulation reached 81.60%, with a Kappa value of 0.73 and a Figure of Merit (FoM) coefficient of 0.263. (2) Land use optimization: Under the Econ. Prior. scenario, economic benefits peaked at 4.06 × 1010 CNY. Urban expansion was the largest, leading to increased patch fragmentation. The Ecol. Prior. scenario yielded the highest ecological benefits, reaching 7.46 × 107 CNY. The urban development pattern exhibited inward contraction, accompanied by urban retrogression. In the BD scenario, economic benefits totaled 3.89 × 1010 CNY, and ecological benefits amounted to 7.16 × 107 CNY. Construction land tended to concentrate spatially, leading to relatively optimal land use efficiency. Therefore, based on a comprehensive consideration of the regional land use constraint policies and spatial layout, we believe that a balance point for land use demands can be found in the BD scenario. It can ensure economic growth without compromising the ecological environment.

Coupling coordination analysis of industrial mining land, landscape pattern and carbon storage in a mining city: a case study of Ordos, China

Analyzing and optimizing the spatio-temporal characteristics of terrestrial ecosystem carbon storage, as well as examining their coupling and coordination relationships with industrial mining land and landscape pattern, can become a reference in the pursuit of carbon peaking and carbon neutrality for mining cities. This research takes the typical mining city of Ordos as the study target. Based on the LULC, the Multi-objective Planning (MOP) and Patch-generating Land Use Simulation (PLUS) model are used to predict the LULC under the natural development (Q1), ecological protection (Q2) and economic development (Q3) scenarios of 2030, and the Integrated Valuation of Ecosystem Services and Trade-offs (InVEST) model is used to analyze the dynamics of carbon storage, finally a coupling coordination of industrial mining land, landscape pattern and carbon storage is constructed to investigate the interrelationship between them. The results show: (1) From 2000 to 2020, carbon storage shows an inverted ‘V’ shape of rising and then falling; (2) Compared to carbon storage in 2020, the Q1 demonstrates a decrease, while the Q2 and Q3 demonstrate increases; (3) From 2000 to 2020, the coupling coordination degree decreases, and in the future, Q2 and Q3 show an increase in it relative to the Q1.