1. " Design and analysis of optimization algorithms ", including the following topics:
- Design of approximate algorithms ( e.g. FPTAS, PTAS, rounding methods, primal-dual methods, ...)
- Design of stochastic algorithms ( e.g. Monte Carlo algorithms, Las Vegas algorithms, ...)
- Partial enumeration algorithms ( e.g. Branch and Bound algorithms, Dynamic programming algorithms, Divide and Conquer algorithms, Decomposition algorithms, ...)
- Gardient-based search algorithms for unconstrained nonlinear problems ( e.g. Newton, Golden section, Broyden, BFGS, Conjugate directions, SQP, ...)
- Non gradient-based search algorithms for unconstrained nonlinear problems ( e.g. Fibonacci, Three points, ...)
- Algorithms for constraied LP/ NLP problems ( e.g. Simplex, Elipsoid, Active set, Frank-Wolfe, ...)
- Algorithms for multi-objective problems ( e.g. EMOAs, Geoffrion, ...)
- Algorithms for multi-criteria decision making problems ( e.g. Non-interactive methods, interactive methods, Goal seeking, ...)
- Greedy and Local search algorithms
- Hybrid algorithms
- Parallel algorithms
- Heuristic algorithms ( e.g. Hyper-heuristics, Meta-heuristics, ...)
2. " Combinatorial optimization and Computational complexity ", including the following topics:
- Analyzing complexity class of new optimization problems
- Run time coplexity analysis of algorithms (e.g. Worst/ average/ best case analysis, recursive analysis, ...)
- Improving the time/ space complexity of algorithms
- Integer programming modeling of real problems ( e.g. Linearization methods, Cutting planes, Decompositions, Hybrid algorithms such as B&C, B&P, C&B, ... )
3. " Graph theory ", including the following topics:
- Network optimization ( e.g. Modeling problems as network flows, developing new algorithms for capacitated networks, ...)
- Modeling facility location/ sequencing/ scheduling/ line balancing/ distribution/ assignment/ allocation/ production planning/ ... as problems in graph theory such as shortest path/ Hamiltonian path/ Hamiltonian cycle/ Eulerian circuit/ network flows/ graph coloring/ ...
- application of graphs as data structure