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Operations Research, Systems Engineering and Industrial Engineering

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2020

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Articles 31 - 60 of 1932

Full-Text Articles in Engineering

Automatic Discovery Method Of Dynamic Job Shop Dispatching Rules Based On Hyper-Heuristic Genetic Programming, Suyu Zhang, Wang Yan, Zhicheng Ji Dec 2020

Automatic Discovery Method Of Dynamic Job Shop Dispatching Rules Based On Hyper-Heuristic Genetic Programming, Suyu Zhang, Wang Yan, Zhicheng Ji

Journal of System Simulation

Abstract: The dynamic job shop has the uncertainty of resource state and the randomness of tasks,so it is difficult to find the common dispatching rules applicable to a variety of complex production scenarios.A method for automatic discovery of dynamic shop dispatching rules based on Hyper-Heuristic genetic programming is proposed,with makespan and average weighted tardiness as the optimization goals,is improved by using the automatic discovery of machine sequencing rules and the dynamic adaptability of workshop scheduling under different production scenarios.Through the semantic analysis of dispatching rules,the function of terminators on different optimization objectives is analyzed.The experiment result shows that …


Scenario Analysis Of Downtown One-Way Street Conversions In Lincoln, Nebraska: A Case Study For Downtown Livability And Pedestrian Safety, Terrence Lage Dec 2020

Scenario Analysis Of Downtown One-Way Street Conversions In Lincoln, Nebraska: A Case Study For Downtown Livability And Pedestrian Safety, Terrence Lage

Community and Regional Planning Program: Theses and Student Projects

An era of downtown street design benefiting the automobile has become over designed for the movement of volumes of traffic in many North American cities. Since the 1950s, the primary focus of planners and traffic engineers has been to address the growing problem of traffic congestion caused by the suburban traveler coming into and out of downtown. The solution was retrofitting the original two-way street grid into a network of wide and straight multi-lane one-way corridors. This design successfully moved volumes of traffic through downtown streets but induced behavior to favor the automobile instead of design that favors active mobility …


Size And Cost Reduction Of The Antenna 3000, Mario Mignott, Austin Deaver, Josh Madaris Dec 2020

Size And Cost Reduction Of The Antenna 3000, Mario Mignott, Austin Deaver, Josh Madaris

Senior Design Project For Engineers

For our senior design project, we have partnered with Compass Technology Group to improve its Antenna 3000 manufacturing process. The Antenna we are working on is not actually called this, but due to NDA regulations, we will disguise it as the Antenna 3000. This will include finding a way to minimize material costs and labor hours involved to assemble this product together. Our minimum success criteria will be to reduce both the manufacturing time and materials' cost by 20%. Our primary approach to solving this problem will be to implement Lean Six Sigma practices such as the DMAIC principle.

Using …


Supplier Ranking System And Its Effect On The Reliability Of The Supply Chain, Farshad Rabib Dec 2020

Supplier Ranking System And Its Effect On The Reliability Of The Supply Chain, Farshad Rabib

Doctoral Dissertations

Today, due to the growing use of social media and an increase in the number of

A HITS with a solution in PageRank (Massimo, 2011) sharing their opinions globally, customers can review products and services in many novel ways. However, since most reviewers lack in-depth technical knowledge, the true picture concerning product quality remains unclear. Furthermore, although product defects may come from the supplier side, making it responsible for repair cost, it is ultimately the manufacturer whose name is damaged when such defects are revealed. In this context, we need to revisit the cost vs. quality equations. Observations of customer …


Operational Decision-Making In Healthcare Using Control Charts, Rohan More Dec 2020

Operational Decision-Making In Healthcare Using Control Charts, Rohan More

Master's Theses

The primary objective of this thesis was to design a framework supplemented with guidelines for the healthcare managers to select an appropriate type of control chart for operational decision-making. A systematic literature review was conducted to gauge the extent to which control charts were being used in a healthcare setting for clinical decision making and operational decision-making purposes. The findings showed that the application of control charts was almost equal for the clinical decision-making sector and the operational decision-making sector. On further analysis, the ability of control charts to function as a standalone tool was affirmed by the vast majority …


Math Models And Heuristic Methods For Constructing Fair Political Districts, Roya Ghorashi Dec 2020

Math Models And Heuristic Methods For Constructing Fair Political Districts, Roya Ghorashi

Theses and Dissertations

Political parties’ attempts to manipulate district boundaries in order to gain political advantages in the election system lead to huge inefficiency and unfair election results. Previously some studies have developed methods for forming political districts considering various factors such as population equality, compactness, and contiguity; but only a few recent studies have considered political fairness as an objective for redistricting political map.This study attempts to find a solution to draw political districts using political fairness as a factor in addition to integrity, population equality, contiguity, and compactness of the districts in order to prevent gerrymandering. In this research, we introduce …


A Parametric Evaluation Of Iot Applications To Freight Transportation Using Model-Based Systems Engineering, Paul George Crawford Dec 2020

A Parametric Evaluation Of Iot Applications To Freight Transportation Using Model-Based Systems Engineering, Paul George Crawford

Theses and Dissertations

Industrial Internet of Things or IIoT consists of computing and communication at the operational edge of a value chain. Applications span manufacturing, energy, and transportation, among others. In the transportation context, IIoT translates to connected vehicle architecture and ITS applications. Current trends in communication allow more applications and devices to contribute to functions traditionally allocated to transportation ITS infrastructure. This poses challenges to design engineers to prototype emerging technologies in the existing transportation context and reduce integration, validation, and time to market. Model-based systems engineering is crucial step for IIoT deployment since it allows for a feature-rich digital representation of …


Development Of A Deformation-Based Structural Health System With Contactless Sensors And Machine Learning For Health Characterization And Failure Prediction, Juan Camilo Avendano Arbelaez Dec 2020

Development Of A Deformation-Based Structural Health System With Contactless Sensors And Machine Learning For Health Characterization And Failure Prediction, Juan Camilo Avendano Arbelaez

Theses and Dissertations

This dissertation presents the design and development of a structural health monitoring (SHM) system specifically tailored for transportation infrastructure components, such as bridges. The proposed system collects data by using contactless sensors and performs health characterization and failure prediction. It is capable of simulating multiple load conditions on structures, identifying possible failure points, and detecting and predicting failure scenarios. Both hardware and software implementations of a model of a bridge were performed as a pilot project in order to validate the proposed system. Computer simulation in ANSYS and the application of gradient boosting neural networks were performed to produce a …


A Mathematical Approach To Paint Production Process Optimization, Ching-Ya Chuang Dec 2020

A Mathematical Approach To Paint Production Process Optimization, Ching-Ya Chuang

Theses and Dissertations

As the global paint market steadily grows, finding the most effective processing model to increase production capacity will be the best way to enhance competitiveness. Therefore, this study proposes two production environments commonly used in the paint industry: build-to-order (BTO) and the variation of a configuration-to-order (CTO), called group production, to schedule paint production. Mixed-Integer Linear Program (MILP) was solved using genetic algorithms (GA) to analyze two production environments with various products, different set-up times, and different average demand for each product. The models determine the number of batches, the size and product of each batch, and the batch sequence …


Systems Thinking In Engineering Design: Differences In Expert Vs. Novice And Relationship To Personality Traits, Yuzhen Luo Dec 2020

Systems Thinking In Engineering Design: Differences In Expert Vs. Novice And Relationship To Personality Traits, Yuzhen Luo

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Systems thinking is the ability to see the big picture and the related elements when designing, and how these relationships form the big picture. In engineering design, systems thinking is valuable to both industry, as well as engineering education. As such, it creates opportunities for researchers to better understand systems thinking of both professional engineers in industry, who are assumed to be the experts, and engineering students in higher education, who are assumed to be the novices. The purpose of this study was to compare and identify the differences between expert and novice systems thinking in engineering design. Additionally, the …


Bullwhip Effect Of A Closed Leep Supply Chain With And Without Information Sharing Of Customer Demand, Jui-Hsin Hsu Dec 2020

Bullwhip Effect Of A Closed Leep Supply Chain With And Without Information Sharing Of Customer Demand, Jui-Hsin Hsu

Theses and Dissertations

In recent years, companies have become interested in a closed-loop supply chain that is concerned with the recovery pipeline. The expenses of a company can be influenced by large inventories and backlogs due to the bullwhip effect in the supply chain. Previous literature has shown that the bullwhip effect can be decreased by a reverse supply chain. This paper develops a closed-loop supply chain including seven echelons for recovery of end-of-life products. The model considers the order-up-to inventory policy and the exponential smoothing forecasting with a trend method in the system to assist in determining the ordering quantities. The best …


ℓ-Ctp: Utilizing Multiple Agents To Find Efficient Routes In Disrupted Networks, Andrew Alseth Dec 2020

ℓ-Ctp: Utilizing Multiple Agents To Find Efficient Routes In Disrupted Networks, Andrew Alseth

Graduate Theses and Dissertations

Recent hurricane seasons have demonstrated the need for more effective methods of coping with flooding of roadways. A key complaint of logistics managers is the lack of knowledge when developing routes for vehicles attempting to navigate through areas which may be flooded. In particular, it can be difficult to re-route large vehicles upon encountering a flooded roadway. We utilize the Canadian Traveller’s Problem (CTP) to construct an online framework for utilizing multiple vehicles to discover low-cost paths through networks with failed edges unknown to one or more agents a priori. This thesis demonstrates the following results: first, we develop the …


Optimal Collaborative Path Planning For Unmanned Surface Vehicles Carried By A Parent Boat Along A Planned Route, Ari Carisza Graha Prasetia, I-Lin Wang, Aldy Gunawan Dec 2020

Optimal Collaborative Path Planning For Unmanned Surface Vehicles Carried By A Parent Boat Along A Planned Route, Ari Carisza Graha Prasetia, I-Lin Wang, Aldy Gunawan

Research Collection School Of Computing and Information Systems

In this paper, an effective mechanism using a fleet of unmanned surface vehicles (USVs) carried by a parent boat (PB) is proposed to complete search or scientific tasks over multiple target water areas within a shorter time . Specifically, multiple USVs can be launched from the PB to conduct such operations simultaneously, and each USV can return to the PB for battery recharging or swapping and data collection in order to continue missions in a more extended range. The PB itself follows a planned route with a flexible schedule taking into consideration locational constraints or collision avoidance in a real-world …


The Effects Of Aircraft Use And Available Repar Spares On Aircraft Sortie Generaiton: A Long-Duration Logistical Wargaming Simulationtool, Nathaniel M. Choo Dec 2020

The Effects Of Aircraft Use And Available Repar Spares On Aircraft Sortie Generaiton: A Long-Duration Logistical Wargaming Simulationtool, Nathaniel M. Choo

Theses and Dissertations

A long-duration logistical wargame simulation tool that can provide quick insights into the daily aircraft availability and the daily number of missions accomplished for a variety of operational scenarios is developed. This simulation tool is designed to be a stepwise wargaming support tool for adjudication within long-duration logistical wargames and provides the user many capabilities including, but not limited to, the ability to have multiple bases and types of aircraft. Additionally, the user has the ability to control types of part failures, control parts availability, control maintenance capabilities, and control number of mission scheduled. Finally, the user can account for …


Using Interacting Multiple Model Filters To Indicate Program Risk, Amy Sunshine Smith-Carroll Dec 2020

Using Interacting Multiple Model Filters To Indicate Program Risk, Amy Sunshine Smith-Carroll

Engineering Management & Systems Engineering Theses & Dissertations

Technology development has increased exponentially. Program managers are pushed to accelerate development. There are many resources available to program managers that enable acceleration, such as: additional resources in the form of funding, people and technology. There are also negative impacts to acceleration, such as: inclusion, inexperience program managers, and communication. This research seeks to identify the limit to which a program or project can be accelerated before the program manager begins to accept an unacceptable amount of pre-determined risk.

This research will utilize estimation algorithms used by sensor systems to estimate the current and future state of objects in space. …


Continuous Integration/Continuous Delivery Pipeline For Air Force Distributed Common Ground System (Af Dcgs), Carolyn W. Fuller Dec 2020

Continuous Integration/Continuous Delivery Pipeline For Air Force Distributed Common Ground System (Af Dcgs), Carolyn W. Fuller

Theses and Dissertations

AF DCGS has a recognized need to improve speed of delivery for modification and sustainment of the weapon system. Given that the program office implemented a Continuous Integration/Continuous Delivery (CI/CD) process for the sole purpose of delivering capability to the field faster, there is a need to measure and report the pipeline throughput. This research conducts an independent evaluation of the newly implemented pipeline within AF DCGS’s existing integration and test laboratories. Actual project data from the agile development work environments is studied and hypothesis tests are conducted to substantiate that the CI/CD pipeline improved the speed of delivery. The …


Designing An Autonomous Goods-To-Person Order Picking System: From Storage To Pick., Mina Shekari Ashgzari Dec 2020

Designing An Autonomous Goods-To-Person Order Picking System: From Storage To Pick., Mina Shekari Ashgzari

Electronic Theses and Dissertations

In recent years, there has been an increased growth in e-commerce, which is a special case of a business-to-customer model. Among all the operations for fulfilling online orders, order picking has been the concern of many researchers and practitioners in the field of warehousing and material handling. This is due to very different technical assumptions and service expectations for online retailers compared to the case of business-to-business models. The most fundamental change in order processing, imposed by business-to-customer models, is shipping individual items or “eaches,” instead of cases and pallets, which is typical of business-to-business models. As a result, the …


Parametric Study Of Residual Stresses In Wire And Arc Additive Manufactured Parts, Hisham Khaled Jamil Abusalma Dec 2020

Parametric Study Of Residual Stresses In Wire And Arc Additive Manufactured Parts, Hisham Khaled Jamil Abusalma

Mechanical & Aerospace Engineering Theses & Dissertations

Wire and Arc Additive Manufacturing (WAAM) is a cost-effective additive manufacturing process due to its capability to fabricate large metal parts with high deposition rate and low equipment cost. Although this method is gaining popularity in manufacturing industry, more research is needed to understand process parameters’ effects on residual stress (RS) distribution and part distortion. As such, a 3D thermo-elastic-plastic transient model was established in ABAQUS and employed to investigate the effect of process parameters such as the torch speed, the deposition power and the interlayer dwell time on RS distribution and distortion in WAAM part. The numerical model utilized …


Comparison Of Classification Algorithms And Undersampling Methods On Employee Churn Prediction: A Case Study Of A Tech Company, Heather Cooper Dec 2020

Comparison Of Classification Algorithms And Undersampling Methods On Employee Churn Prediction: A Case Study Of A Tech Company, Heather Cooper

Master's Theses

Churn prediction is a common data mining problem that many companies face across industries. More commonly, customer churn has been studied extensively within the telecommunications industry where there is low customer retention due to high market competition. Similar to customer churn, employee churn is very costly to a company and by not deploying proper risk mitigation strategies, profits cannot be maximized, and valuable employees may leave the company. The cost to replace an employee is exponentially higher than finding a replacement, so it is in any company’s best interest to prioritize employee retention.

This research combines machine learning techniques with …


An Investigation On The Effectiveness Of A Problem Structuring Method In A Group Decision-Making Process, Ying Thaviphoke Dec 2020

An Investigation On The Effectiveness Of A Problem Structuring Method In A Group Decision-Making Process, Ying Thaviphoke

Engineering Management & Systems Engineering Theses & Dissertations

There is no shortage of methods to address messy problems. A messy problem is a system of problems with multiple stakeholders who may hold different views of what is feasible or desirable. Decision-makers in a messy problem are prone to committing an error – especially the Type III error. One of the ways to mitigate the chance of committing the error in a messy problem is to reach a group consensus. Problem Structuring Methods (PSM) are the collections of participatory modeling methods that aim to tackle a messy problem. Despite the positive reports, literature indicates some challenges and criticisms of …


Improvement Of Light Intensity And Efficiency Of N-Zno/Nio/P-Gan Heterojunction-Based White Light Emitting Diodes Using Micro-/Nanolens Array, Apurba Adhikary, Md Shamim Ahsan, Md Mahbub Hossain, Md Bipul Hossain, S. H. Shah Newaz, Farid Ahmed, Ik-Bu Sohn Nov 2020

Improvement Of Light Intensity And Efficiency Of N-Zno/Nio/P-Gan Heterojunction-Based White Light Emitting Diodes Using Micro-/Nanolens Array, Apurba Adhikary, Md Shamim Ahsan, Md Mahbub Hossain, Md Bipul Hossain, S. H. Shah Newaz, Farid Ahmed, Ik-Bu Sohn

Manufacturing & Industrial Engineering Faculty Publications and Presentations

Our study proposes a technique to enhance light extraction efficiency of light emitting diodes (LEDs) by incorporating various micro-/nanolens arrays (MNLAs) on the substrate layer, which in turn increases the external quantum efficiency (EQE) of the LEDs. To simulate the LEDs, we utilized the finite difference time domain method. To achieve a white LED, we inserted a thin layer of NiO at the interface between the n-type ZnO and the p-type GaN. The basic n-ZnO/NiO/p-GaN heterojunction-based LED exhibited an EQE of 10.99% where the effective refractive index of the LED structure was 1.48. The EQE was further increased by engraving …


Demystifying Artificial Intelligence Based Digital Twins In Manufacturing- A Bibliometric Analysis Of Trends And Techniques, Satish Kumar, Shruti Patil, Arunkumar Bongale, Ketan Kotecha, Anup Kumar M. Bongale, Pooja Kamat Nov 2020

Demystifying Artificial Intelligence Based Digital Twins In Manufacturing- A Bibliometric Analysis Of Trends And Techniques, Satish Kumar, Shruti Patil, Arunkumar Bongale, Ketan Kotecha, Anup Kumar M. Bongale, Pooja Kamat

Library Philosophy and Practice (e-journal)

Nowadays, data is considered as a new life force for operations of physical systems in various domains such as manufacturing, healthcare, transportations, etc. However, the hugely generated data, which mirrors the working essence of the product life cycle, is still underutilised. Digital Twin (DT), a collective representation of active and passive captured data, is a virtual counterpart of the physical resources that could help prevent effective preventive maintenance in any applied domain. Currently, lots of research is going on about the applicability of digital twin in smart IOT based manufacturing industry 4.0 environment. Still, it lacks a formal study, which …


Influence Of Fiberboard Container Design On Compression Bulge Displacement, Koushik Saha, Shane Messner, John Dizon, Nirav Chhajed, Jay Singh Nov 2020

Influence Of Fiberboard Container Design On Compression Bulge Displacement, Koushik Saha, Shane Messner, John Dizon, Nirav Chhajed, Jay Singh

Journal of Applied Packaging Research

Bulge effect is the out-of-plane displacement of a panel of a corrugated fiberboard box from its original position. This bulge effect often is the result of excessive weight being placed on a box that rests at the bottom of a palletized load. Panels that are out-of-plane reduce the stacking strength of the box and can result in damage to products inside the containers. This study was designed to find the influence of fiberboard container design on its bulging performance when under compression. The objective of the study was to determine if change in height of a regular slotted container will …


Optimal Scheduling And Decision Making Method For Dynamic Flexible Job Shop, Wang Yan, Ding Yu Nov 2020

Optimal Scheduling And Decision Making Method For Dynamic Flexible Job Shop, Wang Yan, Ding Yu

Journal of System Simulation

Abstract: For multi-objective dynamic flexible job-shop scheduling, an improved multi-objective differential evolution algorithm is proposed. The adaptive cross-mutation operator is introduced into the differential evolution algorithm to improve its global search capability. The fast non-dominated sorting method based on immunological principles is introduced to improve the quality of the solution set in the selection and sorting. An improved TOPSIS-G1-EVM comprehensive decision-making method is proposed. The comprehensive weight of G1-EVM is calculated by Nash equilibrium theory. The comprehensive weight and TOPSIS evaluation system are combined to evaluate each dispatching scheme. The experimental results show that the optimal scheduling algorithm is superior …


Research On Configurable Simulation Integration Technology For Equipment Software, Yuanyuan Wang, Yuxin Duan, Guangzhao Song Nov 2020

Research On Configurable Simulation Integration Technology For Equipment Software, Yuanyuan Wang, Yuxin Duan, Guangzhao Song

Journal of System Simulation

Abstract: The problems of the traditional distributed digital simulation system are analyzed. The method of constructing the digital simulation system based on the equipment software is studied. The configurable simulation integration middleware is designed. The overall structure of the configurable middleware is designed and the design ideas of each module are briefly summarized. An example of a digital simulation system with networked transformation of equipment shows that the middleware can be effectively and flexibly configured and can provide support for constructing digital simulation system with software, which can be promoted and used in other simulation systems.


Effect Of New Titanium Alloy On Biomechanical Behavior Of Dental Implant, Jiwu Zhang, Qiguo Rong Nov 2020

Effect Of New Titanium Alloy On Biomechanical Behavior Of Dental Implant, Jiwu Zhang, Qiguo Rong

Journal of System Simulation

Abstract: Titanium alloy materials have excellent mechanical properties, chemical stability and biocompatibility, and have become the main raw materials for implants. However, the biomechanical compatibility of medical titanium alloys still needs to be improved in order to meet the long-term safety and functionality of patient's clinical treatment requirement. New medical titanium alloy materials with high strength and low modulus play an important role in reducing the loosening and shedding of implants caused by stress shielding. The effects of new medical titanium alloy materials and traditional medical titanium alloy materials on implant structure and stress distribution of jaw are compared and …


Fast 3d Medical Image Registration Based On Geometric Feature Invariants, Juping Gu, Tianyu Cheng, Jianping Wang, Hua Liang, Fengshen Zhao, Jiang Ling Nov 2020

Fast 3d Medical Image Registration Based On Geometric Feature Invariants, Juping Gu, Tianyu Cheng, Jianping Wang, Hua Liang, Fengshen Zhao, Jiang Ling

Journal of System Simulation

Abstract: Aiming at the of large amount of computational data and low registration efficiency in 3D cranial medical image registration, a fast registration method based on geometric feature space constraints is proposed. The algorithm extracts three-dimensional contour point clusters, and proposes a feature construction method based on the optimal fitting ring of point clusters. The feature rings and the centroids of each layer are used as feature quantities, and the fast registration is completed by using Iterative Closest Point (ICP) method. The experimental results show that the method has less computation amount, high satisfactory registration accuracy and much faster registration …


A Pmbldc Motor Measurement And Control System Available For Zynq Hardware-In-The-Loop Simulation, Zhiguo Zhou, Jiaen Sun, Jiabao Yu, Xuehua Zhou Nov 2020

A Pmbldc Motor Measurement And Control System Available For Zynq Hardware-In-The-Loop Simulation, Zhiguo Zhou, Jiaen Sun, Jiabao Yu, Xuehua Zhou

Journal of System Simulation

Abstract: In order to solve the modeling of permanent magnet brushless dc(PMBLDC) motor, it is difficult to modify the control algorithm, inconvenient to add and remove the closed loop, and has poor real-time measurement and control capability. Based on hall sensor position detection algorithm and PID control algorithm, combined with piecewise linear method to generate PWM waveform, Simulink graphical modeling platform is used, and a new closed-loop measurement and control method is proposed. A sudden load and sudden speed simulation are carried out to verify the established PMBLDC motor measurement and control system. The simulation results show that the system …


Research On Dynamic Flexible Job Shop Scheduling Problem Based On Dynamic Interaction Layer, Zhang Xiang, Wang Yan, Zhicheng Ji Nov 2020

Research On Dynamic Flexible Job Shop Scheduling Problem Based On Dynamic Interaction Layer, Zhang Xiang, Wang Yan, Zhicheng Ji

Journal of System Simulation

Abstract: In order to quickly response to the unforeseen circumstances in flexible job shop, a dynamic flexible job shop scheduling model is constructed, which takes the overall production time and the completion time of emergency orders as the optimization objectives. For the model, a dynamic interaction layer (DIL) model, which has a better performance on DFJSP, is proposed to replace the scroll window. Particle swarm genetic hybrid algorithm (PSGA) is designed to combine the particle swarm optimization algorithm with the genetic algorithm to enhance the ability of local search. Aiming at the unexpected urgent orders in flexible job shop, …


Research On Multi-Objective Optimization Method Based On Model, Jianjun Liu, Guangya Si, Yanzheng Wang, Dachuan He Nov 2020

Research On Multi-Objective Optimization Method Based On Model, Jianjun Liu, Guangya Si, Yanzheng Wang, Dachuan He

Journal of System Simulation

Abstract: There is a model-based algorithm for the optimization of multiple objective functions by means of black-box evaluation is proposed. The algorithm iteratively generates candidate solutions from a mixture distribution over the solution space and updates the mixture distribution based on the sampled solutions’ domination count, such that the future search is biased towards the set of Pareto optimal solutions. The proposed algorithm seeks to find a mixture distribution on the solution space so that each component of the mixture distribution is a degenerate distribution centered at a Pareto optimal solution and each estimated Pareto optimal solution is uniformly spread …