### Radiation Therapy

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.
### Autonomous 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

### (Application:) An integer linear programming formulation for removing nodes in a network to minimize the spread of influenza virus infections

### (Application:) A Robust Optimization Approach for Solving Problems in Conservation Planning

### (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.