Real-world Problems Research Articles

Some notes on the basic concepts of support vector machines

Support vector machines (SVMs) are classic binary classification algorithms and have been shown to be a robust and well-behaved technique for classification in many real-world problems. However, there are ambiguities in the basic concepts of SVMs although these ambiguities do not affect the effectiveness of SVMs. Corinna Cortes and Vladimir Vapnik, who presented SVMs in 1995, pointed out that an SVM predicts through a hyperplane with a maximal margin. However existing literatures have two different definitions of the margin. On the other hand, Corinna Cortes and Vladimir Vapnik converted an SVM into an optimization problem that is much easier to solve. Nevertheless, existing papers do not explain how the optimization problem derives from an SVM well. These ambiguities may cause certain troubles in understanding the basic concepts of SVMs. For this purpose, this paper defines a separating hyperplane of a training data set and, hence, an optimal separating hyperplane of the set. The two definitions are reasonable since this paper proves that w0Tx+b0=0 is an optimal separating hyperplane of a training data set when w0 and b0 constitute a solution to the above optimization problem. Some notes on the above margin and optimization problem are given based on the two definitions. These notes should be meaningful for clarifying the basic concepts of SVMs.

Tracking the Distance to Criticality in Systems with Unknown Noise

Many real-world systems undergo abrupt changes in dynamics as they move across critical points, often with dramatic and irreversible consequences. Much existing theory on identifying the time-series signatures of nearby critical points, such as increased signal variance and slower timescales, is derived from analytically tractable systems, typically considering the case of fixed, low-amplitude noise. However, real-world systems are often corrupted by unknown levels of noise that can distort these temporal signatures. Here we aim to develop noise-robust indicators of the distance to criticality (DTC) for systems affected by dynamical noise in two cases: when the noise amplitude is either fixed or is unknown and variable across recordings. We present a highly comparative approach to this problem that compares the ability of over 7000 candidate time-series features to track the DTC in the vicinity of a supercritical Hopf bifurcation. Our method recapitulates existing theory in the fixed-noise case, highlighting conventional time-series features that accurately track the DTC. But in the variable-noise setting, where these conventional indicators perform poorly, we highlight new types of high-performing time-series features and show that their success is accomplished by capturing the shape of the invariant density (which depends on both the DTC and the noise amplitude) relative to the spread of fast fluctuations (which depends on the noise amplitude). We introduce a new high-performing time-series statistic, the rescaled autodensity (RAD), that combines these two algorithmic components. We then use RAD to provide new evidence that brain regions higher in the visual hierarchy are positioned closer to criticality, supporting existing hypotheses about patterns of brain organization that are not detected using conventional metrics of the DTC. Our results demonstrate how large-scale algorithmic comparison can yield theoretical insights that can motivate new theory and interpretable algorithms for solving important real-world problems. Published by the American Physical Society 2024

Re-understanding of SERS for General and Standardized Quantitative Analysis.

We proposed two physical concepts, i.e., an intramolecular relative cross section (RCS) and an intermolecular relative scattering ability (RSA), to re-understand and re-describe surface-enhanced Raman scattering (SERS) and established a general SERS quantification theory. Interestingly, RCS and RSA are intrinsic factors and are experimentally measurable to form datasheets of molecules, namely, SERS cards, with which a standard SERS quantification procedure was established. The validity of the theory and quantification procedure was confirmed by experiments. Surprisingly, RCS and RSA are also valid for complex systems being considered as virtual molecules and are experimentally measurable. This simplifies complex systems into analyte-virtual molecule binary systems. With this consideration, trace-level mitoxantrone (a typical cancer drug metabolite) in artificial urine was accurately predicted. The theory, the SERS cards, the standard quantification procedure, and the virtual molecule concept pave a way toward quantitative and standardized SERS spectroscopy in dealing with real-world problems and complex samples.

Intuitionistic fuzzy three-way decision method based on data envelopment analysis

As a powerful mathematical tool for tackling uncertain decision problems, three-way decision has garnered substantial attention since its inception. However, real-world decision problems are inherently complex, and decision-makers often exhibit characteristics of incomplete rationality. Traditional three-way decision models, which rely on functions or relationships, face challenges when confronted with multi-output problems. In response to this challenge, this paper introduces an intuitionistic fuzzy three-way decision model grounded in data envelopment analysis (DEA). Initially, we propose an input–output correlation degree that integrates hesitancy information and serves as a procedural indicator for benefit scores. Subsequently, the traditional DEA is extended to accommodate the intuitionistic fuzzy environment and utilized to construct a comprehensive loss function. Furthermore, a novel intuitionistic fuzzy three-way decision model is developed, incorporating three dimensions: optimism, neutrality, and pessimism, and corresponding decision rules and algorithms are provided. Finally, the effectiveness of the proposed model is rigorously validated through a series of experiments and comparative analyses. The model offers a pioneering approach to address uncertain multi-input–output decision problems, effectively integrating decision-maker’s risk preferences within an intuitionistic fuzzy environment.

Improved multi-strategy artificial rabbits optimization for solving global optimization problems

Artificial rabbits optimization (ARO) is a metaheuristic algorithm based on the survival strategy of rabbits proposed in 2022. ARO has favorable optimization performance, but it still has some shortcomings, such as weak exploitation capacity, easy to fall into local optima, and serious decline of population diversity at the later stage. In order to solve these problems, we propose an improved multi-strategy artificial rabbits optimization, called IMARO, based on ARO algorithm. In this paper, a roulette fitness distance balanced hiding strategy is proposed so that rabbits can find better locations to hide more reasonably. Meanwhile, in order to improve the deficiency of ARO which is easy to fall into local optimum, an improved non-monopoly search strategy based on Gaussian and Cauchy operators is designed to improve the ability of the algorithm to obtain the global optimal solution. Finally, a covariance restart strategy is designed to improve population diversity when the exploitation is stagnant and to improve the convergence accuracy and convergence speed of ARO. The performance of IMARO is verified by comparing original ARO algorithm with six basic algorithms and seven improved algorithms. The results of CEC2014, CEC2017, CEC2022 show that IMARO has a good exploitation and exploration ability and can effectively get rid of local optimum. Moreover, IMARO produces optimal results on six real-world engineering problems, further demonstrating its efficiency in solving real-world optimization challenges.

Developing valid assessments in the era of generative artificial intelligence

Generative Artificial Intelligence (GAI) holds tremendous potential to transform the field of education because GAI models can consider context and therefore can be trained to deliver quick and meaningful evaluation of student learning outcomes. However, current versions of GAI tools have considerable limitations, such as social biases often inherent in the data sets used to train the models. Moreover, the GAI revolution comes during a period of moving away from memorization-based education systems toward supporting learners in developing the ability to apply knowledge and skills to solve real-world problems and explain real-world phenomena. A challenge in using GAI tools for scoring assessments aimed at fostering knowledge application is ensuring that these algorithms are scoring the same construct attributes (e.g., knowledge and skills) as a trained human scorer would score when evaluating student performance. Similarly, if using GAI tools to develop assessments, one needs to ensure that the goals of GAI-generated assessments are aligned with the vision and performance expectations of the learning environments for which these assessments are developed. Currently, no guidelines have been identified for assessing the validity of AI-based assessments and assessment results. This paper represents a conceptual analysis of issues related to developing and validating GAI-based assessments and assessment results to guide the learning process. Our primary focus is to investigate how to meaningfully leverage capabilities of GAI for developing assessments. We propose ways to evaluate the validity evidence of GAI-produced assessments and assessment scores based on existing validation approaches. We discuss future research avenues aimed at establishing guidelines and methodologies for assessing the validity of AI-based assessments and assessment results. We ground our discussion in the theory of validity outlined in the Standards for Educational and Psychological Testing by the American Educational Research Association and discuss how we envision building on the standards for establishing the validity of inferences made from the test scores in the context of GAI-based assessments.

A Case for the Use of Open Data as a Tool to Incorporate Socioscientific Topics into Neuroscience Education.

Education scholars have called for an increased focus on developing curricula based on culturally relevant pedagogy (Ladson-Billings, 1995). A key tenet of Ladson-Billings' (1995; 2014) theory of culturally relevant pedagogy is the development of students' sociopolitical consciousness, whereby students feel empowered and encouraged to evaluate and solve real-world interdisciplinary problems. Here, we propose that open science datasets could serve as a valuable tool for neuroscience educators to foster their students' sociopolitical consciousness. Using the open data available through the Seattle Alzheimer's Disease Brain Cell Atlas (SEA-AD) as a case study, this article will explore how open science can be leveraged as a tool to encourage socioscientific thinking amongst neuroscience students. We overview a collection of lessons created by the Allen Institute's Education & Engagement team that provides a scaffolded exploration of an open science resource through a socioscientific lens. We supplement our discussion of the lessons with feedback from students who completed the lessons during a day-long workshop hosted at the Allen Institute in Seattle, WA. We conclude by reflecting on the future role this type of interdisciplinary, open science-based approach to curricula could have across neuroscience education more broadly.

Innovative thermal management in the presence of ferromagnetic hybrid nanoparticles

In the present work, a simple intelligence-based computation of artificial neural networks with the Levenberg-Marquardt backpropagation algorithm is developed to analyze the new ferromagnetic hybrid nanofluid flow model in the presence of a magnetic dipole within the context of flow over a stretching sheet. A combination of cobalt and iron (III) oxide (Co-Fe2O3) is strategically selected as ferromagnetic hybrid nanoparticles within the base fluid, water. The initial representation of the developed ferromagnetic hybrid nanofluid flow model, which is a system of highly nonlinear partial differential equations, is transformed into a system of nonlinear ordinary differential equations using appropriate similarity transformations. The reference data set of the possible outcomes is obtained from bvp4c for varying the parameters of the ferromagnetic hybrid nanofluid flow model. The estimated solutions of the proposed model are described during the testing, training, and validation phases of the backpropagated neural network. The performance evaluation and comparative study of the algorithm are carried out by regression analysis, error histograms, function fitting graphs, and mean squared error results. The findings of our study analyze the increasing effect of the ferrohydrodynamic interaction parameter β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta$$\\end{document} to enhance the temperature and velocity profiles, while increasing the thermal relaxation parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document} decreases the temperature profile. The performance on MSE was shown for the temperature and velocity profiles of the developed model about 9.1703e−10, 7.1313ee−10, 3.1462e−10, and 4.8747e−10. The accuracy of the artificial neural networks with the Levenberg-Marquardt algorithm method is confirmed through various analyses and comparative results with the reference data. The purpose of this study is to enhance understanding of ferromagnetic hybrid nanofluid flow models using artificial neural networks with the Levenberg-Marquardt algorithm, offering precise analysis of key parameter effects on temperature and velocity profiles. Future studies will provide novel soft computing methods that leverage artificial neural networks to effectively solve problems in fluid mechanics and expand to engineering applications, improving their usefulness in tackling real-world problems.

A bay design problem in less-than-unit-load production warehouse

In this paper, we consider a bay design problem in a less-than-unit-load production warehouse, which is motivated by a real-world problem in a semiconductor company. The objective is to maximize the utilization of the vertical space in bays by considering several practical storage requirements. To solve the problem, a non-linear integer programming model is first formulated. Since the problem is similar to a two-stage cutting stock problem (CSP), a column-and-row generation (CRG) method is developed, in which the original problem is decomposed into a restricted master problem and three subproblems, including two classical column generation subproblems and a row generation subproblem. The two former subproblems are solved as unbounded knapsack problems and for the latter, a two-stage approach is applied. The results of computational experiments on randomly generated instances show that the proposed CRG method is more efficient than the classic column-generation-based method, solving the non-linear model directly and solving a cut model in the literature directly. The results of a case study show that our strategy can improve the utilization of the existing warehouse storage space significantly by about 24%. The CRG method is also tested on basic two-stage two-dimensional CSP benchmarks and its performance is compared to those of other pattern-based methods. The results show its potential for effectively solving the basic two-stage two-dimensional CSPs.

Artificial bee colony optimization algorithm with full dimensional updating strategy and its application

For the low accuracy and slow convergence speed of artificial bee colony(ABC) algorithm in solving complex optimization problems, an improved artificial bee colony(ABC) algorithm based on the new full dimensional updating ABC/best /1 strategy, namely FNABC was proposed in this paper. In the FNABC, for the low efficiency of one-dimensional search, the full dimensional updating search strategy and ABC/best /1 strategy were combined to design a new full dimensional updating ABC/best/1 strategy, which expanded the search space, improved the mining ability and search efficiency. Then, a new evolutionary phase is designed to balance the global search ability and local mining ability to avoid falling into local optimum and improve the convergence accuracy. Finally, the FNABC is compared with eight state-of-the-art ABC variants such as AABC, iqABC, MEABC, ABCVSS, GBABC, DFSABC, MABC-NS, MGABC in solving 12 complex functions. All functions have obtained the best optimal values among 9 algorithms. Additionally, FNABC is applied to solve a real-world train operation adjustment problem. The experiment results indicate that the FNABC has better optimization ability, scalability and robustness. It obtains the ideal train operation adjustment results.

EOFA: An Extended Version of the Optimal Foraging Algorithm for Global Optimization Problems

The problem of finding the global minimum of a function is applicable to a multitude of real-world problems and, hence, a variety of computational techniques have been developed to efficiently locate it. Among these techniques, evolutionary techniques, which seek, through the imitation of natural processes, to efficiently obtain the global minimum of multidimensional functions, play a central role. An evolutionary technique that has recently been introduced is the Optimal Foraging Algorithm, which is a swarm-based algorithm, and it is notable for its reliability in locating the global minimum. In this work, a series of modifications are proposed that aim to improve the reliability and speed of the above technique, such as a termination technique based on stochastic observations, an innovative sampling method and a technique to improve the generation of offspring. The new method was tested on a series of problems from the relevant literature and a comparative study was conducted against other global optimization techniques with promising results.

Practicality of Student-Centered Assessment/Learning using Mathematics Modeling Process Worksheets to Improve the Quality of Education

It is necessary to consider reforms to improve the quality of education through assessment/learning. The problem formulation of this research is how to design student-centered assessment/learning using practical mathematical modeling process worksheets to improve the quality of education? This research uses a development research approach developed by Akker, Gravemeijer, McKenney and Nieveen. This development research consists of 3 steps, namely analysis, design and evaluation. In the analysis step, student analysis, curriculum, mathematical modeling and real world problems are implemented. Second step, design and product. In the final step, researchers used a formative evaluation design consisting of self-evaluation, one-to-one, expert review, small group, and field test. Data were analyzed using descriptive analysis methods: (1) walk through, analysis based on solutions and student comments in small groups to obtain student-centered assessment/learning using mathematical modeling process worksheets using the best practical transportation context to improve the quality of education; (2) analyzing the results of the review of small group results. Based on the results of the small group worksheet, the mathematical modeling process is practical for improving the quality of education. Students commented that this mathematical modeling process worksheet was interesting, confusing but challenging and had never been found in their classrooms. Students can solve problems on process worksheets even though the mathematization process has not yet appeared, because students only solve them using informal methods. So, this is a golden opportunity to implement in order to improve the quality of education through assessment/learning. So, a practical mathematical modeling process worksheet is obtained to implement student-centered assessment/learning in order to improve the quality of education.

Derivation and numerical resolution of 2D shallow water equations for multi-regime flows of Herschel–Bulkley fluids

This paper presents mathematical modelling and simulation of thin free-surface flows of viscoplastic fluids with a Herschel–Bulkley rheology over complex topographies with basal perturbations. Using the asymptotic expansion method, depth-averaged models (lubrication and shallow water type models) are derived for 3D (three-dimensional) multi-regime flows on non-flat inclined topographies with varying basal slipperiness. Starting from the Navier–Stokes equations, two flow regimes corresponding to different balances between shear and pressure forces are presented. Flow models corresponding to these regimes are calculated as perturbations of the zeroth-order solutions. The classical reference models in the literature are recovered by considering their respective cases on a flat-inclined surface. In the second regime case, a pressure term is non-negligible. Mathematically, it leads to a corrective term to the classical regime equations. Flow solutions of the two regimes are compared; the difference appears in particular in the vicinity of sharp changes of slopes. Nonetheless, both regime models are compared with experiments and are found to be in good agreement. Furthermore, numerical examples are shown to illustrate the robustness of the present shallow water models to simulate viscoplastic flows in 3D and over an inclined topography with local perturbations in basal elevation and basal slipperiness. The derived models are adequate for direct (engineering and geophysical) applications to real-world flow problems presenting Herschel–Bulkley rheology like lava and mud flows.

Solving the project scheduling problem with dependent resource constraints

ABSTRACT Most resource-constrained project scheduling problems consider resources that are independent of the job processing sequence. However, solving project scheduling problems in some industrial manufacturing is challenging because the required resources depend on the job processing sequence in existing scheduling approaches. To address this issue, this paper proposes a dependent resource-constrained project scheduling problem formulated with two types of models: a conceptual model and a binary integer programming model. The performance of four proposed algorithms – binary integer programming, reduced subproblem of the binary integer programming, job sequence assignment, and job as early as possible – is tested on 68 combinations of numerical simulation experiments. The computational results show that the job as early as possible algorithm can find a better approximate solution for solving real-world problems. This achievement aids project managers in generating activity schedules and finding the approximate minimum makespan for a project with dependent resource constraints.

From Single-Objective to Bi-Objective Maximum Satisfiability Solving

The declarative approach is key to efficiently finding optimal solutions to various types of NP-hard real-world combinatorial optimization problems. Most work on practical declarative solvers—ranging from classical integer programming to finite-domain constraint optimization and maximum satisfiability (MaxSAT)—has focused on optimization under a single objective; fewer advances have been made towards efficient declarative techniques for multi-objective optimization problems. Motivated by significant recent advances in practical solvers for MaxSAT, in this work we develop BiOptSat, an exact declarative approach for finding Pareto-optimal solutions to bi-objective optimization problems, with propositional logic as the underlying constraint language. BiOptSat can be viewed as an instantiation of the lexicographic method. The approach makes use of a single Boolean satisfiability solver that is incrementally employed throughout the entire search procedure, allowing for finding a single Pareto-optimal solution, finding one representative solution for each non-dominated point, and enumerating all Pareto-optimal solutions. We detail several algorithmic instantiations of BiOptSat, each building on recent algorithms proposed for single-objective MaxSAT. We empirically evaluate the instantiations compared to recently-proposed alternative approaches to multi-objective MaxSAT solving on several real-world domains from the literature, showing the practical benefits of our approach.

Skin Cancer Diagnosis With Multi-Level Classification

Skin cancer arises from the uncontrolled proliferation of abnormal skin cells, primarily triggered by exposure to the harmful ultraviolet (UV) rays of the sun and the utilization of UV tanning beds. This condition poses a heightened risk due to its potential to progress into blood cancer and lead to rapid fatality. Extensive research efforts have been dedicated to advancing the treatment of this perilous ailment. This paper presents a system designed for the examination and diagnosis of pigmented skin lesions and melanoma. The system incorporates a supervised classification algorithm that combines Convolutional Neural Network (CNN) and Deep Neural Network (DNN) architectures with feature extraction techniques. It operates in two distinct stages: the initial stage classifies images into two categories, namely benign or malignant, while the subsequent stage further categorizes the images into one of three classes: basal cell carcinomas, squamous cell carcinomas, or melanoma. Consequently, the comprehensive system addresses four classes, namely benign, basal cell carcinomas, squamous cell carcinomas, and melanoma. This work contributes to the system's design in three significant ways. Firstly, it implements multiple iterations to select the most optimal images, resulting in the highest classification accuracy. Secondly, it employs various statistical methods to identify the most pertinent features, thereby enhancing the classifier's accuracy by focusing on the most informative features for the classification task. Lastly, a two-stage classification approach is implemented, employing two distinct classifiers at different levels within the overall system. Despite the inherent complexity of the real-world problem, the overall system attains a commendable level of classification accuracy. Following rigorous experimentation, the study identifies the top three models. Each approach culminates in a classifier for each stage. The first approach, utilizing a deep learning classifier, achieves an accuracy of 81.82% in the initial cancer discrimination stage and 58.33% in the subsequent stage. The second approach, employing a machine learning classifier, attains an accuracy of 74.63% in the first stage and 64.41% in the second stage. The third approach, utilizing a linear regression classifier, achieves an accuracy of 98% in the first stage and 90% in the second stage. These results underscore the significance of feature selection in influencing model accuracy and suggest the potential for further optimization.

Evolutionary Constrained Multiobjective Optimization: Scalable High-Dimensional Constraint Benchmarks and Algorithm

Evolutionary constrained multiobjective optimization has received extensive attention and research in the past two decades, and a lot of benchmarks have been proposed to test the effect of the constrained multiobjective evolutionary algorithms (CMOEAs). Specially, the constraint functions are highly correlated with the objective values, which makes the features of constraints too monotonic and differ from the properties of the real-world problems. Accordingly, previous CMOEAs cannot solve real-world problems well, which generally involve decision space constraints with multi-modal/non-linear features. Therefore, we propose a new benchmark framework and design a suite of new test functions with scalable high-dimensional decision space constraints. To be specific, different high-dimensional constraint functions and mixed linkages in variables are considered to be close to realistic features. In this framework, several parameter interfaces are provided, so that users can easily adjust the parameters to obtain the variant functions and test the generalization performance of the algorithms. Different types of existing CMOEAs are employed to test the use of the proposed test functions, and the results show that they are easy to fall into local feasible regions. Therefore, we improve one evolutionary multitasking-based CMOEA to better handle these problems, in which a new search algorithm is designed to enhance the search abilities of populations. Compared with the existing CMOEAs, the proposed CMOEA presents better performance.

AutoTQA: Towards Autonomous Tabular Question Answering through Multi-Agent Large Language Models

With the growing significance of data analysis, several studies aim to provide precise answers to users' natural language questions from tables, a task referred to as tabular question answering (TQA). The state-of-the-art TQA approaches are limited to handling only single-table questions. However, real-world TQA problems are inherently complex and frequently involve multiple tables, which poses challenges in directly extending single-table TQA designs to handle multiple tables, primarily due to the limited extensibility of the majority of single-table TQA methods. This paper proposes AutoTQA, a novel Auto nomous T abular Q uestion A nswering framework that employs multi-agent large language models (LLMs) across multiple tables from various systems (e.g., TiDB, BigQuery). AutoTQA comprises five agents: the User , responsible for receiving the user's natural language inquiry; the Planner , tasked with creating an execution plan for the user's inquiry; the Engineer , responsible for executing the plan step-by-step; the Executor , provides various execution environments (e.g., text-to-SQL) to fulfill specific tasks assigned by the Engineer ; and the Critic , responsible for judging whether to complete the user's natural language inquiry and identifying gaps between the current results and initial tasks. To facilitate the interaction between different agents, we have also devised agent scheduling algorithms. Furthermore, we have developed LinguFlow, an open-source, low-code visual programming tool, to quickly build and debug LLM-based applications, and to accelerate the creation of various external tools and execution environments. We also implemented a series of data connectors, which allows AutoTQA to access various tables from multiple systems. Extensive experiments show that AutoTQA delivers outstanding performance on four representative datasets.

Integer programming using a single atom

Integer programming (IP), as the name suggests is an integer-variable-based approach commonly used to formulate real-world optimization problems with constraints. Currently, quantum algorithms reformulate the IP into an unconstrained form through the use of binary variables, which is an indirect and resource-consuming way of solving it. We develop an algorithm that maps and solves an IP problem in its original form to any quantum system possessing a large number of accessible internal degrees of freedom that are controlled with sufficient accuracy. This work leverages the principle of superposition to solve the optimization problem. Using a single Rydberg atom as an example, we associate the integer values to electronic states belonging to different manifolds and implement a selective superposition of different states to solve the full IP problem. The optimal solution is found within a few microseconds for prototypical IP problems with up to eight variables and four constraints. This also includes non-linear IP problems, which are usually harder to solve with classical algorithms when compared to their linear counterparts. Our algorithm for solving IP is benchmarked by a well-known classical algorithm (branch and bound) in terms of the number of steps needed for convergence to the solution. This approach carries the potential to improve the solutions obtained for larger-size problems using hybrid quantum–classical algorithms.

Population diversity control based differential evolution algorithm using fuzzy system for noisy multi-objective optimization problems

The objective measurements of the real-world optimization problems are mostly subject to noise which occurs due to several reasons like human measurement or environmental factors. The performance of the optimization algorithm gets affected if the effect of noise is higher than the negligible limit. The previous noise handling optimization algorithms use a large population size or multiple sampling at same region which increases the total count of function evaluations, and few methods work for a particular problem type. To address the above challenges, a Differential Evolution based Noise handling Optimization algorithm (NDE) to solve and optimize noisy bi-objective optimization problems is proposed. NDE is a Differential Evolution (DE) based optimization algorithm where the strategies for trial vector generation and the control parameters of DE algorithm are self-adapted using fuzzy inference system to improve the population diversity along the evolution process. In NDE, explicit averaging based method for denoising is used when the noise level is higher than negligible limit. Extending noise handling method enhances the performance of the optimization algorithm in solving real world optimization problems. To improve the convergence characteristics of the proposed algorithm, a restricted local search procedure is proposed. The performance of NDE algorithm is experimented using DTLZ and WFG problems, which are benchmark bi-objective optimization problems. The obtained results are compared with other SOTA algorithm using modified Inverted Generational Distance and Hypervolume performance metrics, from which it is confirmed that the proposed NDE algorithm is better in solving noisy bi-objective problems when compared to the other methods. To further strengthen the claim, statistical tests are conducted using the Wilcoxon and Friedman rank tests, and the proposed NDE algorithm shows significance over the other algorithms rejecting the null hypothesis.