Multi-objective combinatorial optimization problems in transportation and defense systems

Multi-objective Optimization problems arise in many applications; hence, solving them efficiently is important for decision makers. A common procedure to solve such problems is to generate the exact set of Pareto efficient solutions. However, if the problem is combinatorial, generating the exact set of Pareto efficient solutions can be challenging. This dissertation is dedicated to Multi-objective Combinatorial Optimization problems and their applications in system of systems architecting and railroad track inspection scheduling. In particular, multi-objective system of systems architecting problems with system flexibility and performance improvement funds have been investigated. Efficient solution methods are proposed and evaluated for not only the system of systems architecting problems, but also a generic multi-objective set covering problem. Additionally, a bi-objective track inspection scheduling problem is introduced for an automated ultrasonic inspection vehicle. Exact and approximation methods are discussed for this bi-objective track inspection scheduling problem --Abstract, page iii

System of Systems Architecting Problems: Definitions, Formulations, and Analysis

The system of systems architecting has many applications in transportation, healthcare, and defense systems design. This study first presents a short review of system of systems definitions. We then focus on capability-based system of systems architecting. In particular, capability-based system of systems architecting problems with various settings, including system flexibility, fund allocation, operational restrictions, and system structures, are presented as Multi-Objective Nonlinear Integer Programming problems. Relevant solution methods to analyze these problems are also discussed

Multiobjective System of Systems Architecting with Performance Improvement Funds

A System of Systems architecting problem aims to determine a selection of systems, which are capable of providing a set of desired capabilities. A SoS architect usually has multiple objectives in generating efficient architectures such as minimization of the total cost and maximization the overall performance of the SoS. This study formulates a biobjective SoS architecting problem with these two objectives. Here, we consider that, by allocating funds to the systems, the SoS architect can improve the performance of the capabilities the systems can provide. The resulting architecting problem is a biobjective mixed-integer linear programming model. Specifically, the system selection decisions are binary while the fund allocation decisions are continuous. We first discuss the application of the adaptive epsilon-constraint method as an exact method for solving this model. Then, we propose an evolutionary method and compare its performance with the exact method. Finally, a numerical study demonstrates the benefits of fund allocation in the SoS architecting process

Combining Max-Min and Max-Max Approaches for Robust SoS Architecting

A System of Systems (SoS) architecting problem requires creating a selection of systems in order to provide a set of capabilities. SoS architecting finds many applications in military/defense projects. In this paper, we study a multi-objective SoS architecting problem, where the cost of the architecture is minimized while its performance is maximized. The cost of the architecture is the summation of the costs of the systems to be included in the SoS. Similarly, the performance of the architecture is defined as the sum of the performance of the capabilities, where the performance of a capability is the sum of the selected systems\u27 contributions towards its performance. Here, nevertheless, the performance of a system in providing a capability is not known with certainty. To model this uncertainty, we assume that the performance of a system for providing a capability has lower and upper bounds and subject to complete uncertainty, i.e., no information is available about the probability distribution of the performance values. To solve the resulting multi-objective SoS architecting problem with uncertainty, we propose and compare three robust approaches: max-min, max-max, and max-mid. We apply these methods on a military example and numerically compare the results of the different approaches

Mapping 123 million neonatal, infant and child deaths between 2000 and 2017

Since 2000, many countries have achieved considerable success in improving child survival, but localized progress remains unclear. To inform efforts towards United Nations Sustainable Development Goal 3.2—to end preventable child deaths by 2030—we need consistently estimated data at the subnational level regarding child mortality rates and trends. Here we quantified, for the period 2000–2017, the subnational variation in mortality rates and number of deaths of neonates, infants and children under 5 years of age within 99 low- and middle-income countries using a geostatistical survival model. We estimated that 32% of children under 5 in these countries lived in districts that had attained rates of 25 or fewer child deaths per 1,000 live births by 2017, and that 58% of child deaths between 2000 and 2017 in these countries could have been averted in the absence of geographical inequality. This study enables the identification of high-mortality clusters, patterns of progress and geographical inequalities to inform appropriate investments and implementations that will help to improve the health of all populations

Global, regional, and national cancer incidence, mortality, years of life lost, years lived with disability, and disability-Adjusted life-years for 29 cancer groups, 1990 to 2017 : A systematic analysis for the global burden of disease study

Importance: Cancer and other noncommunicable diseases (NCDs) are now widely recognized as a threat to global development. The latest United Nations high-level meeting on NCDs reaffirmed this observation and also highlighted the slow progress in meeting the 2011 Political Declaration on the Prevention and Control of Noncommunicable Diseases and the third Sustainable Development Goal. Lack of situational analyses, priority setting, and budgeting have been identified as major obstacles in achieving these goals. All of these have in common that they require information on the local cancer epidemiology. The Global Burden of Disease (GBD) study is uniquely poised to provide these crucial data. Objective: To describe cancer burden for 29 cancer groups in 195 countries from 1990 through 2017 to provide data needed for cancer control planning. Evidence Review: We used the GBD study estimation methods to describe cancer incidence, mortality, years lived with disability, years of life lost, and disability-Adjusted life-years (DALYs). Results are presented at the national level as well as by Socio-demographic Index (SDI), a composite indicator of income, educational attainment, and total fertility rate. We also analyzed the influence of the epidemiological vs the demographic transition on cancer incidence. Findings: In 2017, there were 24.5 million incident cancer cases worldwide (16.8 million without nonmelanoma skin cancer [NMSC]) and 9.6 million cancer deaths. The majority of cancer DALYs came from years of life lost (97%), and only 3% came from years lived with disability. The odds of developing cancer were the lowest in the low SDI quintile (1 in 7) and the highest in the high SDI quintile (1 in 2) for both sexes. In 2017, the most common incident cancers in men were NMSC (4.3 million incident cases); tracheal, bronchus, and lung (TBL) cancer (1.5 million incident cases); and prostate cancer (1.3 million incident cases). The most common causes of cancer deaths and DALYs for men were TBL cancer (1.3 million deaths and 28.4 million DALYs), liver cancer (572000 deaths and 15.2 million DALYs), and stomach cancer (542000 deaths and 12.2 million DALYs). For women in 2017, the most common incident cancers were NMSC (3.3 million incident cases), breast cancer (1.9 million incident cases), and colorectal cancer (819000 incident cases). The leading causes of cancer deaths and DALYs for women were breast cancer (601000 deaths and 17.4 million DALYs), TBL cancer (596000 deaths and 12.6 million DALYs), and colorectal cancer (414000 deaths and 8.3 million DALYs). Conclusions and Relevance: The national epidemiological profiles of cancer burden in the GBD study show large heterogeneities, which are a reflection of different exposures to risk factors, economic settings, lifestyles, and access to care and screening. The GBD study can be used by policy makers and other stakeholders to develop and improve national and local cancer control in order to achieve the global targets and improve equity in cancer care. © 2019 American Medical Association. All rights reserved.Peer reviewe

Mapping local patterns of childhood overweight and wasting in low- and middle-income countries between 2000 and 2017

A double burden of malnutrition occurs when individuals, household members or communities experience both undernutrition and overweight. Here, we show geospatial estimates of overweight and wasting prevalence among children under 5 years of age in 105 low- and middle-income countries (LMICs) from 2000 to 2017 and aggregate these to policy-relevant administrative units. Wasting decreased overall across LMICs between 2000 and 2017, from 8.4% (62.3 (55.1–70.8) million) to 6.4% (58.3 (47.6–70.7) million), but is predicted to remain above the World Health Organization’s Global Nutrition Target of <5% in over half of LMICs by 2025. Prevalence of overweight increased from 5.2% (30 (22.8–38.5) million) in 2000 to 6.0% (55.5 (44.8–67.9) million) children aged under 5 years in 2017. Areas most affected by double burden of malnutrition were located in Indonesia, Thailand, southeastern China, Botswana, Cameroon and central Nigeria. Our estimates provide a new perspective to researchers, policy makers and public health agencies in their efforts to address this global childhood syndemic

Set-Based Min-Max and Min-Min Robustness for Multi-Objective Robust Optimization

Min-max and min-min robustness are two extreme approaches discussed for single-objective robust optimization problems. Recently, multi-objective robust optimization problems are studied and robust Pareto efficiency definitions have been proposed. In particular, the set-based min-max robust efficiency defined for multi-objective robust optimization problems is analogous to the min-max robust optimality definition for single-objective robust optimization problems. In this study, we define the set-based min-min robust efficiency in addition to the existing definition of the min-max robust efficiency for multi-objective robust optimization problems. We discuss a method to determine the set of set-based min-max robust efficient solutions and propose an evolutionary algorithm to approximate this set. Furthermore, a modification of the algorithm is discussed to approximate the set of set-based min-min robust Pareto efficient solutions. The outcomes based on the two robust efficiency, i.e., set-based min-max and set-based min-min, are compared using numerical examples. Our results show that set-based min-min robust efficiency can be used by optimistic decision makers and can be combined with set-based min-max robust efficiency to model the preferences of the decision makers, who are not ultimately pessimistic

Track Inspection Planning and Risk Measurement Analysis

This project models track inspection operations on a railroad network and discusses how the inspection results can be used to measure the risk of failure on the tracks. In particular, the inspection times of the tracks, inspection frequency of the tracks, and times between consecutive inspections on the same tracks should be considered for scheduling inspections on the railroad tracks. Furthermore, an inspection plan should schedule inspections considering the characteristics of different tracks. Therefore, it is important to schedule track inspections such that the potential defects are captured as much as possible within minimum times to increase safety. The project formulates a mathematical optimization problem for the track inspection planning considering the practical settings of track inspection operations such as inspection times, inspection frequencies required, time between consecutive inspections, and importance of distinct tracks. The two objectives simultaneously captured in this model are minimization of total inspection times and maximization of the weighted inspections. An efficient solution method is proposed for solving this model. The solution method is compared to a scheduling procedure, which can be used in absence of the findings in this project, on a set of railroad track networks of different sizes. Based on the comparison, the solution method proposed proves to find improved inspection schedules regardless of the railroad network size. A review of the techniques on how to use the inspection results to measure risk of failure is provided

A Decomposition Approach for Bi-Objective Mixed-Integer Linear Programming Problems

In this study, we analyze solution methods for approximating the Pareto front of bi-objective mixed-integer linear programming problems. First of all, we discuss a two-stage evolutionary algorithm. Given the values for the integer variables, the second stage of the two-stage evolution algorithm generates the values for the continuous variables of the corresponding Pareto efficient solutions. Then, the corresponding Pareto efficient solutions of integer variables are compared in the first-stage of the two-stage evolutionary algorithm to determine the Pareto efficient integer solutions. These stages are repeated within an evolutionary heuristic structure to approximate the Pareto front. Secondly, we propose a decomposition approach to separate the integral part of the feasible region of the problem. The decomposition approach separates the problem into sub-problems, each of which has an additional constraint, and approximates the Pareto fronts of the sub-problems using the two-stage evolutionary algorithm discussed. Then, using the sub-problem Pareto fronts, the Pareto front of the main problem is approximated. A numerical study is conducted to compare the two-stage evolutionary algorithm with the decomposition approach, which uses the two-stage evolutionary algorithm