APROS: Algorithmic Development Methodology for Discrete-Continuous Optimization Problems

APROS represents an algorithmic development procedure for classes of mathematical programming problems that involve some form of decomposition technique and require extensive communication of data between a set of subproblems whose sizes and structures may vary during the solution procedure. Examples include most classes of mixed-integer nonlinear programming problems and large-scale mixed-integer linear programming problems as well as a wide variety of algorithms for large-scale nonlinear and linear programming problems exhibiting special structure. APROS works through the General Algebraic Modeling System (GAMS) to provide exact syntactic statement of algorithmic solution procedures. APROS procedures are implemented through GAMS which is interfaced with nonlinear, linear and mixed-integer linear programming solvers to provide completely general automated implementations of many well known algorithms including the Generalized Benders Decomposition, the Outer Approximation/Equality Relaxation and Dantzig-Wolfe Decomposition. The flexibility of APROS and the highly procedural modeling language GAMS provide a means of obtaining quick solutions to difficult classes of problems by implementing a selected algorithm, and also provide a unique tool for developing, prototyping and experimenting with new algorithms. A description of the procedural components, features and setups is presented with emphasis on the generality of the techniques.