Uniform Probability Research Articles

Efficient Data-Driven Machine Learning Models for Cardiovascular Diseases Risk Prediction.

Cardiovascular diseases (CVDs) are now the leading cause of death, as the quality of life and human habits have changed significantly. CVDs are accompanied by various complications, including all pathological changes involving the heart and/or blood vessels. The list of pathological changes includes hypertension, coronary heart disease, heart failure, angina, myocardial infarction and stroke. Hence, prevention and early diagnosis could limit the onset or progression of the disease. Nowadays, machine learning (ML) techniques have gained a significant role in disease prediction and are an essential tool in medicine. In this study, a supervised ML-based methodology is presented through which we aim to design efficient prediction models for CVD manifestation, highlighting the SMOTE technique's superiority. Detailed analysis and understanding of risk factors are shown to explore their importance and contribution to CVD prediction. These factors are fed as input features to a plethora of ML models, which are trained and tested to identify the most appropriate for our objective under a binary classification problem with a uniform class probability distribution. Various ML models were evaluated after the use or non-use of Synthetic Minority Oversampling Technique (SMOTE), and comparing them in terms of Accuracy, Recall, Precision and an Area Under the Curve (AUC). The experiment results showed that the Stacking ensemble model after SMOTE with 10-fold cross-validation prevailed over the other ones achieving an Accuracy of 87.8%, Recall of 88.3%, Precision of 88% and an AUC equal to 98.2%.

The Basics of Neutrosophic Simulation for Converting Random Numbers Associated with a Uniform Probability Distribution into Random Variables Follow an Exponential Distribution

The Basics of Neutrosophic Simulation for Converting Random Numbers Associated with a Uniform Probability Distribution into Random Variables Follow an Exponential Distribution

Introducing nonlinear activations into quantum generative models

Due to the linearity of quantum mechanics, it remains a challenge to design quantum generative machine learning models that embed nonlinear activations into the evolution of the state vector. However, some of the most successful classical generative models, such as those based on neural networks, involve highly nonlinear dynamics for quality training. In this paper we explore the effect of these dynamics in quantum generative modeling by introducing a model that adds nonlinear activations via a neural network structure onto the standard Born machine framework---the quantum neuron Born machine (QNBM). To achieve this, we utilize a previously introduced quantum neuron subroutine, which is a repeat-until-success circuit with midcircuit measurements and classical control. After introducing the QNBM, we investigate how its performance depends on network size, by training a three-layer QNBM with four output neurons and various input and hidden layer sizes. We then compare our nonlinear QNBM to the linear quantum circuit Born machine (QCBM). We allocate similar time and memory resources to each model such that the only major difference is the qubit overhead required by the QNBM. With gradient-based training, we show that while both models can easily learn a trivial uniform probability distribution, on a more challenging class of distributions, the QNBM achieves an almost three-times-smaller error rate than a QCBM with a similar number of tunable parameters. We therefore provide evidence that suggests that nonlinearity is a useful resource in quantum generative models, and we put forth the QNBM as a model with good generative performance and potential for quantum advantage.

Stochastic dynamic programming solution to transmission scheduling: Multi sensor-multi process with wireless noisy channel

We investigate sensor scheduling for remote estimation when multiple smart sensors monitor multiple stochastic dynamical systems. The sensors transmit their measurements to a remote estimator through a noisy wireless communication channel. Such a remote estimator can receive multiple packets simultaneously sent by local sensors. Sensors transmit their measurements if their Signal Interference and Noise Ratio (SINR) is above a threshold. We compute the optimal policy for sensor scheduling by minimizing expected error covariance subject to total signal transmissions from all sensors. We model this problem as Markov Decision Process (MDP) with discounted cost per stage in the finite time horizon framework, then we employ stochastic Dynamic Programming as the optimization method. A novel algorithm based on sampling and machine learning techniques is proposed as the approximation. At each phase of the DP algorithm, samples are collected using a uniform probability distribution. The data is used to feed Neural Network (NN) and Random Forest (RF) models for cost function and policy approximation. The results of the proposed framework are supported by simulation examples comparing RF and NN as Approximate DP (ADP). Note that this idea builds a bridge among the recent advances in the area of data science, Machine Learning, and the ADP.

Do environmental, social and governance practices affect portfolio returns? Evidence from the US stock market from 2002 to 2020

PurposeThis paper aims to investigate whether environmental, social and governance (ESG) practices influence stock returns in the US stock market, looking at the period from 2002 to 2020.Design/methodology/approachThe authors quasi-replicate two reference articles that found that socially responsible funds used to underperform, but that this underperformance tendency has disappeared in more recent periods.FindingsUsing US data, the authors show that independent of the ESG database used, portfolios of neutral stocks present consistently higher systematic risk (beta) than ESG portfolios, although this difference decreases over time. This may be due to the significant increase in demand for ESG portfolios in the past decade, and their consequent price inflation and increase in volatility. However, concerning risk-adjusted returns and contrary to the authors’ reference literature, the results are highly dependent on the rating provider used, and neither support underperformance nor indicate a tendency over time. These inconsistent results suggest that the “ESG label” is not a determinant of portfolio performance.Research limitations/implicationsIf ESG ratings are a legitim benchmark for sustainability, then the costs of going sustainable in stock portfolios might be marginal for fund managers.Originality/valueTwo different ESG-rating agencies, Morgan Stanley Capital International (MSCI) and Thomson Reuters, are used to identify sustainable stocks. Different from the literature, the authors selected stocks for their portfolios stochastically following a uniform probability distribution, thus avoiding fund manager bias.

Multilevel Markov Chain Monte Carlo for Bayesian inverse problem for Navier-Stokes equation

<p style='text-indent:20px;'>Bayesian inverse problems for inferring the unknown forcing and initial condition of Navier-Stokes equation play important roles in many practical areas. The computation cost of sampling the posterior probability measure can be exceedingly high. We develop the Finite Element Multilevel Markov Chain Monte Carlo (FE-MLMCMC) sampling method for approximating expectation with respect to the posterior probability measure of quantities of interest for a model problem of Navier-Stokes equation in the two dimensional periodic torus. We first consider the case where the forcing and the initial condition are bounded for all the realizations and depend linearly on a countable set of random variables which are uniformly distributed in a compact interval. We establish the essentially optimal convergence rate of the method and verify it numerically. The method follows from that developed in V. H. Hoang, Ch. Schwab and A. M. Stuart, Inverse problems, vol. 29, 2013 for inferring the coefficients of linear elliptic forward equations under the uniform prior probability measure. In the case of the Gaussian prior probability measure, numerical results, using the MLMCMC method developed for the Gaussian prior in V. H. Hoang, J. H. Quek and Ch. Schwab, Inverse problems, vol. 36, 2020, indicate the essentially optimal convergence rates. However, a rigorous theory for the MLMCMC sampling procedure is not available, due to the non-integrability with respect to the Gaussian prior of the theoretical finite element errors of the forward solvers that are available in the literature.</p>

Асимптотика числа помеченных планарных тетрациклических и пентациклических графов

A connected graph with a cyclomatic number k is said to be a k-cyclic graph. We obtain the formula for the number of labelled non-planar pentacyclic graphs with a given number of vertices, and find the asymptotics of the number of labelled connected planar tetracyclic and pentacyclic graphs with n vertices as n → ∞. We prove that under a uniform probability distribution on the set of graphs under consideration, the probability that the labelled tetracyclic graph is planar is asymptotically equal to 1089/1105, and the probability that the labeled pentacyclic graph is planar is asymptotically equal to 1591/1675.

On the properties of residential rooftop azimuth and tilt uncertainties for photovoltaic power generation modeling and hosting capacity analysis

One of the essential epistemic uncertainties that has not yet been studied enough for distributed photovoltaic systems is the azimuth and tilt of rooftop photovoltaic panels, as previous studies of grid impacts and hosting capacity have tended to assume uniform and optimal roof facet conditions. In this study, rooftop facet orientation distributions are presented and analyzed for all single-family buildings in the Swedish city of Uppsala, based on LiDAR-based data that consist of every roof facet from the around 13,500 single-family buildings in the city. From these distributions, novel methods to proportionally include less suitable roofs for every penetration level are proposed using a simple method based on normal and uniform probability density functions, and are tested for both time-series and stochastic hosting capacity analysis. The results show that under the assumption that the best roof facets are utilized first, a uniform distribution for rooftop facet azimuth and a normal distribution for rooftop facet tilt with parameters that depend linearly on the penetration level were shown to be accurate. The hosting capacity simulations demonstrate how the proposed methods perform significantly better in estimating the photovoltaic hosting capacity than the more common simplified methods for both time-series and stochastic hosting capacity analysis. The proposed model could help distribution system operators as well as researchers in this area to model the rooftop facet orientation uncertainty better and improve the quality of aggregated photovoltaic generation models and hosting capacity analyses.

The Asymptotic Statistics of Random Covering Surfaces

AbstractLet$\Gamma _{g}$be the fundamental group of a closed connected orientable surface of genus$g\geq 2$. We develop a new method for integrating over the representation space$\mathbb {X}_{g,n}=\mathrm {Hom}(\Gamma _{g},S_{n})$, where$S_{n}$is the symmetric group of permutations of$\{1,\ldots ,n\}$. Equivalently, this is the space of all vertex-labeled,n-sheeted covering spaces of the closed surface of genusg.Given$\phi \in \mathbb {X}_{g,n}$and$\gamma \in \Gamma _{g}$, we let$\mathsf {fix}_{\gamma }(\phi )$be the number of fixed points of the permutation$\phi (\gamma )$. The function$\mathsf {fix}_{\gamma }$is a special case of a natural family of functions on$\mathbb {X}_{g,n}$called Wilson loops. Our new methodology leads to an asymptotic formula, as$n\to \infty $, for the expectation of$\mathsf {fix}_{\gamma }$with respect to the uniform probability measure on$\mathbb {X}_{g,n}$, which is denoted by$\mathbb {E}_{g,n}[\mathsf {fix}_{\gamma }]$. We prove that if$\gamma \in \Gamma _{g}$is not the identity andqis maximal such that$\gamma $is aqthpower in$\Gamma _{g}$, then$$\begin{align*}\mathbb{E}_{g,n}\left[\mathsf{fix}_{\gamma}\right]=d(q)+O(n^{-1}) \end{align*}$$as$n\to \infty $, where$d\left (q\right )$is the number of divisors ofq. Even the weaker corollary that$\mathbb {E}_{g,n}[\mathsf {fix}_{\gamma }]=o(n)$as$n\to \infty $is a new result of this paper. We also prove that$\mathbb {E}_{g,n}[\mathsf {fix}_{\gamma }]$can be approximated to any order$O(n^{-M})$by a polynomial in$n^{-1}$.

Disjoint Placement Probability of Line Segments via Geometry

We have shown that when any finite number n, of line segments with total combined length less than one, have their centers placed randomly inside the unit interval , the probability of obtaining a mutually disjoint placement of the segments within , is given by the expression where , and denotes the length of the k-th segment, Lk . The result is established by a careful analysis of the geometry of the event, “all segments disjoint and contained within [0,1],” considered as a subset of the uniform probability space of n centers, each of which is in ; that is to say, the unit n-cube of . This event has an interesting geometric structure consisting of disjoint, congruent, (up to a mirror image) polytopes within the unit n-cube. It is shown these event polytopes fit together perfectly to form, except for a set of measure zero, a partition of an n-dimensional cube with common edge length , and hence an n-volume given by the formula. In the case of n = 3 segments, the polytopes form one of the known tetrahedral partitions of the cube as discussed, for example in [4]. In fact for all n > 0, the polytopes comprise a partition of the n-dimensional hypercube, and are therefore n-dimensional space filling.

The acoustic and daylighting effects of external façade sun shading systems

External sun shading devices are increasingly used in sustainable buildings to reduce the greenhouse effect in the summer and the glare effect due to direct solar irradiation through transparent surfaces. The acoustic effects of these devices have been investigated in recent studies that suggest the possibility of optimising these elements to improve acoustic comfort in indoor environments, even with open windows. Nevertheless, there are few studies that analyse the combined effect of these devices on acoustic attenuation and improved daylighting. In this paper, the results of acoustics and daylighting simulations are reported, considering different dimensions, distances of the louvres and orientations of the façade. The main results of previous works concerning the effect of lining the bottom side of each louvre with sound-absorbing material are also briefly summarised. The acoustic effects of different configurations of the louvres are evaluated in terms of Insertion Loss in the façade plane. For the lighting simulations (daylight factor, daylighting uniformity and daylight glare probability), the variation of the shielding effect is studied considering the spacing between the louvres and the orientation of the façade for different times and seasons for latitude in the South of Europe.

Estimating abundance of an elusive cetacean in a complex environment: Harbor porpoises (Phocoena phocoena) in inland waters of Southeast Alaska

The harbor porpoise (Phocoena phocoena) is common in temperate waters of the eastern North Pacific Ocean, including Southeast Alaska inland waters, a complex environment comprised of open waterways, narrow channels, and inlets. Two demographically independent populations are currently recognized in this region. Bycatch of porpoises in the salmon drift gillnet fisheries is suspected to occur regularly. In this study, we apply distance sampling to estimate abundance of harbor porpoise during ship surveys carried out in the summer of 2019. A stratified survey design was implemented to sample different harbor porpoise habitats. Survey tracklines were allocated following a randomized survey design with uniform coverage probability. Density and abundance for the northern and southern Southeast Alaska inland water populations were computed using a combination of design-based line- and strip-transect methods. A total of 2,893 km was surveyed in sea state conditions ranging from Beaufort 0 to 3 and 194 harbor porpoise groups (301 individuals) were detected. An independent sighting dataset from surveys conducted between 1991 and 2012 were used to calculate the probability of missing porpoise groups on the survey trackline (g[0]=0.53, CV=0.11). Abundance of the northern and southern populations were estimated at 1,619 (CV=0.26) and 890 (CV=0.37) porpoises, respectively. Bycatch estimates, which were only obtained for a portion of the drift gillnet fishery, suggest that mortality within the range of the southern population may be unsustainable. Harbor porpoises are highly vulnerable to mortality in gillnets, therefore monitoring abundance and bycatch is important for evaluating the potential impact of fisheries on this species in Southeast Alaska.

Randomized Reference Models for Temporal Networks

Many dynamical systems can be successfully analyzed by representing them as networks. Empirically measured networks and dynamic processes that take place in these situations show heterogeneous, non-Markovian, and intrinsically correlated topologies and dynamics. This makes their analysis particularly challenging. Randomized reference models (RRMs) have emerged as a general and versatile toolbox for studying such systems. Defined as random networks with given features constrained to match those of an input (empirical) network, they may, for example, be used to identify important features of empirical networks and their effects on dynamical processes unfolding in the network. RRMs are typically implemented as procedures that reshuffle an empirical network, making them very generally applicable. However, the effects of most shuffling procedures on network features remain poorly understood, rendering their use nontrivial and susceptible to misinterpretation. Here we propose a unified framework for classifying and understanding microcanonical RRMs (MRRMs) that sample networks with uniform probability. Focusing on temporal networks, we survey applications of MRRMs found in the literature, and we use this framework to build a taxonomy of MRRMs that proposes a canonical naming convention, classifies them, and deduces their effects on a range of important network features. We furthermore show that certain classes of MRRMs may be applied in sequential composition to generate new MRRMs from the existing ones surveyed in this article. We finally provide a tutorial showing how to apply a series of MRRMs to analyze how different network features affect a dynamic process in an empirical temporal network.

The uniform measure for quantum walk on hypercube: A quantum Bernoulli noises approach

In this paper, we present a quantum Bernoulli noises approach to quantum walks on hypercubes. We first obtain an alternative description of a general hypercube, and then, based on the alternative description, we find that the operators ∂k*+∂k behave actually as the shift operators, where ∂k and ∂k* are the annihilation and creation operators acting on Bernoulli functionals, respectively. With the above-mentioned operators as the shift operators on the position space, we introduce a discrete-time quantum walk model on a general hypercube and obtain an explicit formula for calculating its probability distribution at any time. We also establish two limit theorems showing that the averaged probability distribution of the walk even converges to the uniform probability distribution. Finally, we show that the walk produces the uniform measure as its stationary measure on the hypercube provided its initial state satisfies some mild conditions. Some other results are also proven.

Determining Maximal Entropy Functions for Objective Bayesian Inductive Logic

According to the objective Bayesian approach to inductive logic, premisses inductively entail a conclusion just when every probability function with maximal entropy, from all those that satisfy the premisses, satisfies the conclusion. When premisses and conclusion are constraints on probabilities of sentences of a first-order predicate language, however, it is by no means obvious how to determine these maximal entropy functions. This paper makes progress on the problem in the following ways. Firstly, we introduce the concept of a limit in entropy and show that, if the set of probability functions satisfying the premisses contains a limit in entropy, then this limit point is unique and is the maximal entropy probability function. Next, we turn to the special case in which the premisses are categorical sentences of the logical language. We show that if the uniform probability function gives the premisses positive probability, then the maximal entropy function can be found by simply conditionalising this uniform prior on the premisses. We generalise our results to demonstrate agreement between the maximal entropy approach and Jeffrey conditionalisation in the case in which there is a single premiss that specifies the probability of a sentence of the language. We show that, after learning such a premiss, certain inferences are preserved, namely inferences to inductive tautologies. Finally, we consider potential pathologies of the approach: we explore the extent to which the maximal entropy approach is invariant under permutations of the constants of the language, and we discuss some cases in which there is no maximal entropy probability function.

No free theory choice from machine learning

Ravit Dotan argues that a No Free Lunch theorem (NFL) from machine learning shows epistemic values are insufficient for deciding the truth of scientific hypotheses. She argues that NFL shows that the best case accuracy of scientific hypotheses is no more than chance. Since accuracy underpins every epistemic value, non-epistemic values are needed to assess the truth of scientific hypotheses. However, NFL cannot be coherently applied to the problem of theory choice. The NFL theorem Dotan’s argument relies upon is a member of a family of theorems in search, optimization, and machine learning. They all claim to show that if no assumptions are made about a search or optimization problem or learning situation, then the best case performance of an algorithm is that of random search or random guessing. A closer inspection shows that these theorems all rely upon assigning uniform probabilities over problems or learning situations, which is just the Principle of Indifference. A counterexample can be crafted that shows that NFL cannot be coherently applied across different descriptions of the same learning situation. To avoid this counterexample, Dotan needs to privilege some description of the learning situation faced by scientists. However, this means that NFL cannot be applied since an important assumption about the problem is being made. So Dotan faces a dilemma: either NFL leads to incoherent best-case partial beliefs or it is inapplicable to the problem of theory choice. This negative result has implications for the larger debate over theory choice.

Investigation of four-dimensional (4D) Monte Carlo dose calculation in real-time tumor tracking stereotatic body radiotherapy for lung cancers.

To investigate the dosimetric variations and radiobiological impacts as a consequence of delivering treatment plans of 3D nature in 4D manner based on the 4D Monte Carlo treatment planning framework implemented on Cyberknife. Dose distributions were optimized on reference 3D images at end of exhale phase of a 4DCT dataset for twenty-five lung cancer patients treated with 60 Gy / 3Fx or 48 Gy / 4Fx. Deformable image registrations (DIR) between individual 3DCT images to the reference 3DCT image in the 4DCT study were performed to interpolate doses calculated on multiple anatomical geometries back on to the reference geometry to compose a 4D dose distribution that included the tracking beam motion and organ deformation. The 3D and 4D dose distributions that were initially calculated with the equivalent path-length (EPL) algorithm (3DEPL dose and 4DEPL dose) were recalculated with the Monte Carlo algorithm (3DMC dose and 4DMC dose). Dosimetric variations of V60Gy / 48Gy and D99 of GTV, mean doses to the lung and the heart and maximum dose (D1 ) of the spinal cord as a consequence of tracking beam motion in deforming anatomy, dose calculation algorithm, and both were quantified by the relative change from 4DMC to 3DMC doses, from 4DMC to 4DEPL doses, and from 4DMC to 3DEPL doses, respectively. Comparing 4DMC to 3DEPL plans, V60Gy / 48Gy and D99 of GTV decreased considerably by 13 ± 22% (mean ± 1SD) and 9.2 ± 5.5 Gy but changes of normal tissue doses were not more than 0.5 Gy on average. The generalized equivalent uniform dose (gEUD) and tumor control probability (TCP) were reduced by 14.3 ± 8.8 Gy and 7.5 ± 5.2%, and normal tissue complication probability (NTCP) for myelopathy and pericarditis were close to zero and NTCP for radiation pneumonitis was reduced by 2.5 ± 4.1%. Comparing 4DMC to 4DEPL plans found decreased V60Gy / 48Gy and D99 by 12.3 ± 21.6% and 7.3 ± 5.3 Gy, the normal tissues doses by 0.5 Gy on average, gEUD and TCP by 13.0 ± 8.6 Gy and 7.1 ± 5.1%. Comparing 4DMC to 3DMC doses, V60Gy / 48Gy and D99 of GTV was reduced by 5.2 ± 8.8 %and 2.6 ± 3.3 Gy, and normal tissues hardly changed from 4DMC to 3DMC doses. The corresponding decreases of gEUD and TCP were 2.8 ± 4.0 Gy and 1.6 ± 2.4%. The large discrepancy between original 3DEPL plan and benchmarking 4DMC plan is predominately due to dose calculation algorithms as the tracking beam motion and organ deformation hardly influenced doses of normal tissues and moderately decreased V60Gy / 48Gy and D99 of GTV. It is worth to make a thoughtful weight of the benefits of full 4D MC dose calculation and consider 3D MC dose calculation as a compromise of 4D MC dose calculation considering the multifold computation time. This article is protected by copyright. All rights reserved.

Uncertainty Quantification on the Cooling Performance of a Transonic Turbine Vane With Upstream Endwall Misalignment

Abstract With increasing aerodynamic and thermal loads, film cooling has been a popular technology integrated into the design of the modern gas turbine vane endwall, especially for the first-stage vane endwall. A staggering amount of research has been completed to quantify the effect of operating conditions and cooling hole geometrical properties. However, most of these investigations did not address the influence of the manufacturing tolerances, assembly errors, and operation degradations on the endwall misalignment. In this paper, uncertainty quantification (UQ) analysis was performed to quantify the impacts of upstream endwall misalignment uncertainties on the endwall film cooling performance and vane surface phantom cooling performance. The upstream endwall misalignment, step geometry with various step heights, commonly exists between the combustor exit and the first-stage vane endwall. Based on the non-intrusive polynomial chaos expansion (NIPC) and the uniform probability distribution assumption, the deviation (step height) uncertainties of the upstream endwall misalignment were quantified. To predict the endwall secondary flow and film cooling effectiveness in the transonic linear vane passage, the commercial computational fluid dynamic solver ANSYS FLUENT was used to numerically solve the three-dimensional steady-state Reynolds-Averaged Navier–Stokes (RANS) equations. The robustness analysis of endwall film cooling performance and phantom cooling performance to the upstream endwall misalignment was conducted for three design upstream step heights (ΔH): a baseline configuration (ΔH = 0 mm), two misaligned configurations with forward step (ΔH = −5 mm) and backward step (ΔH = 5 mm), respectively. Results show that the actual cooling performance has a high probability of deviating from the nominal value for the baseline configuration. The critical regions that are most sensitive to the upstream step misalignment are also identified by variances. The UQ results also show that the design geometry with a forward step has a more robust film cooling performance on endwall and phantom cooling performance on the vane pressure side surface, which means a smaller variance and a better expectation than the no-step configuration. In contrast, the design geometry with a backward step induces the reductions in the expectation of the film cooling effectiveness and coolant coverage and the amplification of performance fluctuations. This work provides a certain guiding direction for the optimization design for the upstream step geometry.

Robust Optimization of Natural Laminar Flow Airfoil Based on Random Surface Contamination

Natural laminar-flow (NLF) airfoils are one of the most promising technologies for extending the range and endurance of aircrafts. However, there is a lack of methods for the optimization of airfoils based on the surface contamination that destroys the laminar flow. In order to solve this problem, a robust optimization process is proposed using the Non-dominated Sorting genetic algorithm- II (NSGA-II) evolutionary algorithm, and Monte Carlo simulation combined with an aerodynamic calculation software Xfoil. Firstly, the airfoil is optimized normally and the aerodynamic performance of optimized airfoil under surface contamination is analyzed. Then, the original airfoil is robustly optimized under random surface contamination based on the assumption that its locations follow triangular and uniform probability distributions. Finally, all the optimized results and original airfoil are compared. It is found that robust optimization reduces the sensitivity of the airfoil to random surface contamination, hence, improving the robustness of the airfoil. The proposed methods make it possible to improve the aerodynamic performance of NLF airfoils considering surface contamination.

Evaluation of Thermal Insulation Performance of Building Exterior Wall Based on Multiobjective Optimization Algorithm

A complete evaluation of conflicting and nonlinear multiperformance is referred to as an evaluation system. Therefore, multiobjective optimization research for building performance is of great importance. Considering the above problems, this paper proposes a multiobjective performance optimization platform at the architectural design stage. The optimization research is combined with the basic algorithms. It is based on Grasshopper software. It aims to provide a fast and effective method for the optimization design of sustainable buildings. It is important to note that this workflow has no restrictions on what to optimize for or what to target, and can be determined on a case-by-case basis. To evaluate the use of the work platform and make the research results more extensive, the standard model of the inner corridor space building in office buildings in cold areas was extracted. The extracted standard model was taken as the final research object. At the same time, the convergence, distribution, and comprehensive evaluation indexes of the simulation results were analyzed. The quantitative influence parameter system of window parameters on the total building energy consumption, lighting uniformity, and glare probability was established. A series of parametric design models based on the comprehensive optimal solution of building energy consumption and lighting quality was obtained. The main purpose of this paper is to design a green building design method based on the principle of goal-oriented design. This paper, combined with the group search function of nondominated genetic algorithm (NSGA-II), the energy consumption of the building, and the evaluation function of indoor thermal and humid environment, is obtained and linked with MATLAB. The energy consumption of residential buildings and indoor thermal comfort were taken as the optimization objectives of the design scheme. The automatic optimization model of the architectural design scheme was established. Finally, the Pareto solution set of the architectural design scheme is obtained, and the designer can select the appropriate design scheme of the Pareto solution set according to the actual situation of the project, to meet the requirements of green building design. The design scheme optimized by this method can effectively reduce building energy consumption and improve indoor thermal comfort.