I am interested in solving challenging real-world optimization problems. Consequently, I am actively seeking for collaboration opportunities with industry. So, please do not hesitate to contact me if you have an interesting problem/idea.
I want to have some contributions in the field of Radiation Therapy.
So, I will soon start a research project on this topic with real data at the University of South Florida.
Radiation Therapy can be viewed as a multi-objective optimization problem since you ideally want to design
a treatment that delivers a uniform dose to the tumor and no dose at all to critical structures and normal tissue.
This is typically impossible. So, you need to violate some of the bounds given on the radiation dose delivered to the tumor,
critical structures and normal tissue (in the prescription). Consequently, you can think of each violation as a separate objective that you want to minimize.
vehicles scheduling problem under uncertainty
We are completing a study about repositioning autonomous vehicle in a shared mobility system.
We have developed a new exact algorithm that can solve this problem when there is uncertainty in data.
(Application:) Bi-objective mixed integer linear programming for managing building clusters with a shared electrical energy storage
Fairness and freedom are two important considerations that need to be taken into account
during operational planning of any shared facility among independent agents/players. On one
hand, imposing no limitation on using the facility may eventually cause the break of collaboration agreement between agents. On the other hand, imposing strict restrictions for using the facility may
destroy opportunities for taking advantage of the facility. In this study, we addressed this issue in the
context of building clusters with shared electrical energy storage and two buildings. We introduced
three energy storage sharing strategies including extreme free, extreme fair, and contract balance
strategies. By using bi-objective mixed integer programming techniques, we numerically showed
that the contract balance strategy is almost as fair as the extreme fair strategy but it is significantly
better than the extreme fair strategy, in terms of freedom.
(Application:) An integer linear programming formulation for removing nodes in a network to minimize the spread of influenza virus infections
We studied the spread of influenza virus infections on a (dynamic) network of people. We pre-
sented the first ILP formulation to minimize the spread of infections by removing nodes, which is equivalent to isolate infected people (or vaccinate the healthy people). The novelty of the formula-
tion comes from the fact that it incorporates many practical aspects of in
uenza spread. Moreover, several potential enhancement techniques to improve the formulation were also introduced and tested via computational study. In particular, it is shown that employing variable fixing and moderating big-M coefficients techniques can reduce the run time or the optimality gap.
(Application:) A Robust Optimization Approach for Solving Problems in Conservation Planning
In conservation planning, the data related to size, growth and diffusion of populations is
sparse, hard to collect and unreliable at best. If and when the data is readily available, it is
not of suffcient quantity to construct a probability distribution. In such a scenario, applying
deterministic or stochastic approaches to the problems in conservation planning either ignores
the uncertainty completely or assumes a distribution that does not accurately describe the nature
of uncertainty. To overcome theses drawbacks, we proposed a robust optimization approach
to problems in conservation planning. We explored two of the basic models in conservation planning
related to reserve selection and invasive species control to show the value of the robust
optimization. We conducted a computational study to demonstrate the efficacy of our proposed approach in
finding more applicable conservation planning strategies by considering the uncertainty in data
but making no assumption about its probability distribution.
(Algorithm:) A Feasibility Pump and Local Search Based Heuristic for Bi-objective Pure Integer Linear Programming
We presented a new heuristic algorithm for computing the approximate nondominated
frontier of any bi-objective pure integer linear program. The proposed algorithm uses the
underlying ideas of several exact/heuristic algorithms in the literature of both single and biobjective
integer linear programs including the perpendicular search method, the feasibility
pump heuristic, the local search approach, the weighted sum method. The feasibility pump
heuristic has been successfully used in the literature of single-objective optimization. Also,
the fact that the commercial exact single-objective optimization solvers (such as CPLEX)
are using it, shows that this heuristic can enhance the exact solution approaches. To
best of our knowledge, we are the first introducing a customized variant of this heuristic
for multi-objective optimization. We hope the simplicity and the efficacy of our method
encourage more researchers to work on the feasibility pump based heuristics for multiobjective
optimization, and possibly combining them with the exact solutions approaches
(to boost them) just like what happened in the world of single-objective optimization.
(Theory:) On the Existence of Ideal Solutions in Multi-objective 0-1 Integer Programs
We studied conditions under which the objective functions of a multi-objective 0-1 integer
linear program guarantee the existence of an ideal point, meaning the existence of a feasible
solution that simultaneously minimizes all objectives. In addition, we studied the complexity of
recognizing whether a set of objective functions satisfies these conditions: we showed that it is NP-hard,
but can be solved in pseudo-polynomial time. Few multi-objective 0-1 integer programs
have objectives satisfying the conditions for the existence of an ideal point, but the conditions
may be satisfied for a subset of the objective functions and/or be satisfied when the objective
functions are restricted to a subset of the variables. We illustrated how such occurrences can be
exploited to reduce the number of objective functions and/or to derive cuts in the space of the
decision variables. The following figures show how the projection of the LP-relaxation of a problem (in the criterion space) has improved (decreased) after using some of the techniques developed in our study.