## Past Students

I was the co-supervisor of one internship student at the University of Adelaide. His research project (Prof. Nigel Bean was the co-supervisor of) aimed to solve a multi-criteria optimization problem on a weighted graph-case study.

During my lecturing position at Azad University of Qazvin, I supervised more than 10 undergraduate final projects, mainly in the area of optimisation and discrete-event system simulation.

## Current Students

I was the co-supervisor of one PhD student at Flinders University (2012-2016). His PhD research (Prof. Jerzy Filar was the principal supervisor of) aimed to design random walk algorithms for the Hamiltonian cycle problem.

Since 2016, I have been the principal supervisor of one PhD student at the University of Newcastle. His PhD research (Dr Mojtaba Heydar is the co-supervisor of) aims to develop novel forecasting models for a food industry in Australia

Since 2015, I have been the principal supervisor of one PhD student at the University of Newcastle. His PhD research (Prof. Rick Middleton is the co-supervisor of) aims to optimise the supply chain models for a food industry in Australia.

## Prospective Students

I can supervise honours/PhD students working on one of the following research projects. There is also one PhD-scholarship available. If you are interested, please send me your latest CV.

• Consider a population infected by a virus. This intrusive virus spreads out very quickly and the number of infected people is growing very fast. In order to control the growth of the number of infected people, firstly, we should construct a mathematical model to explain the growth of this population. Due to the high level of uncertainty, perhaps, a good mathematical model is a proper stochastic process. For this problem, a simple birth process can be a good choice to start. This process has a parameter, namely the birth rate, that is the rate in which people are infected. If the latter is known, all controlling procedure can be implemented. In reality, this parameter is indeed unknown. In order to estimate this unknown parameter, we have to take some observations from the population at some observation times. An intriguing question is that at what times those observations should be made? Presumably, a good choice for those observation times is finding them such that the total volume of information gained from the sample to estimate the unknown birth rate is maximized. A good tool to measure that information is the Fisher Information. In this project, we study the Fisher Information and try to find the optimal observation times both analytically and numerically.

• One of the central constructs in graph theory is the Hamiltonian cycle. Given a graph G on n nodes, a simple path that starts from one node, visits all nodes exactly once, and returns to the initial node is called a ‘Hamiltonian Cycle’ (HC). Accordingly, we can define the Hamiltonian cycle problem (HCP), a well-known problem in graph theory. Particularly, given a graph G, we are asked to determine whether it contains at least one HC or not. If G contains at least one HC, then the graph is called Hamiltonian and otherwise, it is called non-Hamiltonian. In spite of its simple appearance, the HCP is known to be an NP problem. Therefore, no one has yet found an efficient solution algorithm with polynomial complexity for HCP. The topic of ‘solving the HCP in an efficient time’ is being actively researched by top scientists around the world. We have already developed a random walk algorithm that performs very well for the HCP. We do believe that this algorithm shed new light on the famous P vs. NP problem. In this project we investigate the properties of this random walk algorithm by testing it on several random graphs and shall try to develop some of its theoretical properties.