Presenting my research at INFORMS Annual Meeting, Nashville, Tennessee, 2016.
Risk-Averse Stochastic Optimization
The concept of Risk Parity (RP) for a financial portfolio has been proposed by Qian  in 2005. Here the goal is to create a portfolio of diversified financial assets, such that each asset equally contributes to the total portfolio variance. In this research, we provide corresponding mathematical definitions necessary to a straightforward generalization of Risk Parity by selecting a coherent measure of risk in place of variance. We also demonstrate that a careful analysis is required. We then develop a nonlinear convex optimization problem for obtaining Conditional-Value-at-Risk (CVaR)-based risk parity model, and present results of two case studies illustrating its properties. Finally, we also outline a two-stage risk-reward-diversification framework aimed at combining the advantages of both risk parity and standard risk-reward optimization.
Finance (Portfolio Optimization)
Financial portfolio selection is widely used to test risk-averse stochastic optimization models. For this case study, the data is collected through Yahoo Finance for assets in S\&P 500 index. Fifty assets with highest average return were selected for the historical close price from September 2005 through October 2015. We aim to demonstrate that in the presence of heavy-tailed distributions of losses CVaR-RP provides a robust and efficient diversification tool. Experimental results show the better performance and higher quality diversification by employing CVaR-RP model. On the one hand, CVaR-RP gives slight preference to higher average returns, on the other, this preference is not significant. It may be concluded that the observed improvement in performance is primarily due to better diversification rather than better quality of individual assets.
Insurance (Flood insurance claims)
The study is based on a real dataset which contains flood insurance claims for 67 counties of the State of Florida from 1980 to 2006 (355 months). The decision-making problem considered in this study is selecting a distribution of a resource over all of the counties so that the overall exposure to flood risk, as measured by flood insurance claims, is minimized. The proposed CVaR-RP method produces a higher expected return and Sharpe ratio and lower
standard deviation, indicating that a higher quality diversication is attained. A lower expected loss and lower variance achieved by CVaR-RP model show that in this case, the achieved diversification is "more robust" or that the resource distribution is better protected from the risks.
Routing / Logistics / Supply Chain (Hazardous material transportation)
The simplest type of the hazardous materials (hazmats) transportation routing problem deals with an origin and a destination and one type of hazmat to be shipped. Thus, a single route will be chosen as the optimal solution for the problem based on minimizing related risk. At the same time, using the single optimal path repeatedly over time increases the risk for the population that lives in the surrounding areas. Hence, one might be interested in finding a fair distribution of hazmats in the transportation network to guarantee the equal risk contribution of each route to the total risk, which is well-aligned with our proposed two-stage stochastic optimization framework.
In this context, considering a pair of origin-destination, a number of routes to transport the hazmats from origin to the destination will be selected as the decisions of the first stage. Then, the optimal distribution of hazmats will be chosen based on RP condition in the second stage.
Data Analytics and Visualization
Centralized Open-Access Rehabilitation Database for Stroke (SCOAR) is a tool that stroke therapy researchers can use to understand the relationships among variables better, efficiently share data, generate hypotheses, and streamline clinical trial design. To prepare SCOAR, 2,892 titles and 514 manuscripts screened by full text, leaving 215 RCTs in the database. There is 489 independent group representing 12,847 patients. The collected data contains papers from 1981 to early 2016. The goal is to organize a database to allow researchers to add their studies to the database to have constant information architecture. SCOAR is a living database, however, and data are continuously extracted from publications and uploaded into the database. The SCOAR dataset is extracted by Dr. Lohse and his colleagues .
In this research, using stroke rehabilitation as an example, we demonstrate that organizing RCTs around core experimental data advances scientific understanding beyond common bibliometric methods. This organization highlights sources of systematic variability in the outcomes of RCTs, which in turn provides insights for practitioners and identifies opportunities for future research. In this regard, we developed a website with interactive data visualizations.
The SCOAR website (http://www.auburn.edu/~nzm0030) allows users to visualize some of the complex relationships among the variables in the SCOAR dataset. Furthermore, these visualizations are interactive, allowing users to filter the data in each visualization, allowing them to ask their own unique questions. The website is a powerful platform that enables researchers/ practitioners to review and monitor the trends in various aspects of stroke rehabilitation.
The visualizations were arranged around three main research questions that are broadly applicable to scientific research:
1. Is there substantial bias in a field?
By collating summary statistics from different experimental studies, which can be further filtered by study characteristics, it is easy to see publication bias across a field (or sub-field).
2. What are the common experimental parameters and how do they vary?
Cross-indexing common study parameters with experimental outcomes allow researchers to quickly and easily visualize relationships in a field. These visualizations are useful for summarizing past research and thus inform future research (i.e., better planning, power analyses, etc.).
3. What interventions are most effective and for whom?
Cross-indexing common study parameters with outcome measures enable knowledge translation on a large scale. In stroke rehabilitation, for instance, the SCOAR database allows users to plot dose-response curves for therapy broadly (using all outcomes), for specific outcomes (e.g., upper extremity versus lower extremity) or for specific groups of participants (e.g., younger to older, severely impaired to minimally impaired).
The outcomes of this research are an interactive website and a journal paper:
Mohabbati-Kalejahi et al., Streamlining science with structured data archives: insights from stroke rehabilitation, Sientometrics, 113 (2), 969-983, 2017 (Abstract)
My multidisciplinary research has been recognized by Auburn University Graduate School as the winner of the 2018 ‘Frank Sturm Memorial Fellowship’.
Truck Routing & Scheduling Problem
The rapid growth of today’s competitive marketplace enforces companies to provide a comprehensive coverage of customers' demand with efficient utilization of scarce resources. They need to employ new methods to decrease operating costs and improve productivity.
In this research, Truck Routing and Scheduling problem is studied. There is a limited number of trucks and several customers in different locations. Each customer has a specific due date. Trucks have a limited capacity, and each product has a particular volume (size). The problem aims to optimally assign the orders to the trucks based on the limited number of vehicles and their capacities, and find the optimal sequence of deliveries based on the due date. This problem has broad applications in many industries, especially for shipping companies.
In this research, a mixed integer linear programming (MILP) model is proposed for scheduling the transportation of goods to the customers with the objective of minimizing the maximum lateness. Since the research problem is shown to be NP-hard, a metaheuristic algorithm based on Scatter Search is applied to solve the problem. A parameter tuning based on the design of experiments and TOPSIS is employed to find the best set of parameters for the proposed algorithm. Random test problems are generated in different sizes to evaluate the efficiency of the MILP model and the proposed metaheuristic algorithm. Computational results show that both approaches have promising results.
Synchronization of BRT Routes Scheduling Considering Real Conditions
In this research, a decision support system is introduced for Bus Rapid Transport (BRT) scheduling problem with considering synchronization of transfer points. Assume there is a road network, and there are several BRT routes in this network. Each route has a specific origin and destination and some stations in between. The routes are sharing some stations in between, which we refer to them as transfer points. Passengers can change their BRT routes in transfer points. The aim of this research is to schedule all the BRT routes in the network in a way that minimize headways, stop time of buses in each station, total travel time, customers’ wait time, and waste time of buses in routes (e.g. stopping at traffic lights; and accordingly, maximize the service level).
Two mixed integer programming models were developed and used in this research, first is scheduling the BRTs considering real conditions, second is the integration of the scheduling in transfer points. The proposed scheduling problem aims to eliminate waiting time of passengers in stations as well as the waste time of buses behind red lights. Also, efficient scheduling of BRT system results in an integrated balancing of scheduled buses in all stations and improving service level by employing the waste time of buses in previous stations, to increase stopping time in some other stations and pick up more passengers. The following picture shows the BRT System and its isolated route in the road network.
The outcome of this research is an integrated timetable for five different BRT routes in Tehran metropolis.
A solution for 8×8 problem.
The outcomes of this research are two journal papers, a book chapter, and two conference proceedings.
Mohabbati-Kalejahi, N., Akbaripour, H. and Masehian, E., "Basic and Hybrid Imperialist Competitive Algorithms for Solving the Non-attacking and Nondominating n-Queens Problems", Studies in Computational Intelligence (SCI) published by Springer, 2012. (Abstract) Link
Masehian, E., Akbaripour, H., Mohabbati-Kalejahi, N., "Solving the n-Queens Problem using a Tuned Hybrid Imperialist Competitive Algorithm (HICA)", The International Arab Journal of Information Technology, vol. 11 No. 6, November 2014. (Abstract)
Masehian E., Akbaripour H., Mohabbati-Kalejahi N., "Landscape Analysis and Efficient Metaheuristics for Solving the n-Queens Problem", Computational Optimization and Applications, Springer, vol. 55 No. 3, pp: 735-764, 2013. (Abstract)
"Basic and Hybrid Imperialist Competitive Algorithms for Solving the N-Queens Problem", In Proceedings of the 4th International Joint Conference on Computational Intelligence, Barcelona, Spain, pp: 87-95, 2012.
"A Hybrid Heuristic with TOPSIS-based Parameter Tuning for Solving the N-Queens Problem", 8th International Conference of Industrial Engineering, Tehran, Iran, 2012.
The objective of the classic n-queens problem is to place n non-attacking queens on a n×n chessboard by considering the chess rules. The problem is a well-known combinatorial optimization problem in Artificial Intelligence. It has several real-world applications that indicates the reason for the wide interest in this well-known problem: practical task scheduling and assignment, computer resource, management (deadlock prevention and register allocation), VLSI testing, traffic control, communication system design, robot placement for maximum sensor coverage, permutation problems, parallel memory storage schemes, complete mapping problems, constraint satisfaction, and other physics, computer science and industrial applications [Erbas et al. 1992; Segundo 2011; Sosic and Gu 1994].
In this research we studied two different problems: non-attacking n-queens problem in which the goal is to place n queens on a n×n chessboard such that no two queens are in the same row, column, or diagonal; second is the non-dominating n-queens problem in which n queens are placed on a n×n chessboard such that the number of non-attacked squares is maximized.
For a 20×20 problem, the size of the solution space is about 24E+17 which is a very large number. We developed different single-solution-based and population-based metaheuristics to find the solution of the problem in a very efficient time. We compared the performance of the proposed methods on different sizes of the problem (up to 2000) considering three major criteria: Fitness Function Evaluation (FFE), Normalized Convergence Curve Area (NCCA), and run time. We also conducted the landscape analysis of the problem space. To find out what type of metaheuristics is suitable for a specific problem, the landscape of the problem’s search space should be analyzed. In designing a metaheuristic for an optimization problem, the properties of the problem’s landscape influence the effectiveness of the metaheuristic for a given instance. These properties are types of solution representation, neighborhood, and the objective function, which completely defines the landscape of a problem. Depending on the shape of the landscape, specific types of search methods will be more effective.
Combinatorial Optimization: n-queens problem