Disjunctive programming

A disjunctive program is a special type of MINLP problem whose constraints include the condition that exactly one of several sets of constraints must be satisfied (Raman and Grossmann, 1994). Defining v as the logical exclusive or operator and Y as logical variables (whose values are true or false), an example of a disjunctive program, taken from Lee and Grossman (2000), is... 

A generalized disjunctive program (GDP) may be formulated as an MINLP, with binary variables yt replacing the logical variables Yt. The most common formulation is called the big-M approach because it uses a large positive constant denoted by M to relax or enforce the constraints. This formulation of the preceding example follows ... 

Lee, S. and I. E. Grossmann. New Algorithms for Nonlinear Generalized Disjunctive Programming. In press, Comput Chem Engr. 

J.A. Caballero I.E. Grossmann, 2001, Generalized disjunctive programming model for the optimal synthesis of thermally linked distillation columns,, Industrial Engineering Chemistry Research 40 (10) 2260-2274... 

H. Yeomans and I. Grossmann. Optimal design of complex distillation columns using rigorous tray-by-tray disjunctive programming models. Ind. Eng. Chem. Res., 39(ll) 4326-4335, 2000. 

Yeomans H, Grossmann IE. Disjunctive programming models for the optimal design of distillation columns and separation sequences. Ind Eng Chem Res 2000 39 1637. 

Yeomans, H. and Grossmann, I.E. (1999). Nonlinear disjunctive programming models for the synthesis of heat integrated distillation sequences. Comput. Chem. Eng., 23, 1135-1151. 

When the nonlinear discrete optimization problem is formulated as the generalized disjunctive program in (DPI), one can develop a corresponding logic-based branch-and-bound method. The basic difference is that the branching is performed... 

Balas, E. Disjunctive Programming and a Hierarchy of Relaxations for Discrete Optimization Problems, SIAM J. Alg. Disc. Methods 6, 466-486 (1985). 

Genetic algorithms Annealing techniques Dynamic programming Collocation methods Stochastic optimisation Agent-based computations Disjunctive programming Tabu search... 

GDP (Raman and Grossmann, 1994) is an extension of disjunctive programming (Balas, 1979) that provides an alternate way of modeling (MILP) and (MINLP) problems. The general formulation of a (GDP) is as follows ... 

Balas E. 1985. Disjunctive programming and a hierarchy of relaxations for discrete optimization problems, SIAM J. Alg. Discrete Methods, 6, 466-486. 

Lee S. and Grossmann l.E. 2000. New algorithms for nonlinear generalized disjunctive programming, Comput. Chem. Eng., 24, 2125-2141. 

Sawaya N.W. and Grossmann I.E. 2004. A cutting plane method for solving linear-generalized disjunctive programming problems (submitted). 

The third set of constraints is often ctilled the disjunctive arc constraints and represent the fact that some ordering must exist among operations of different jobs that are processed on the same machine. Because of these constraints, this problem is sometimes referred to as the disjunctive programming problem. 

Therefore, the disjunctive programming formulation can be presented as follows ... 

Lee, S., Grossmann, I.E. Global optimization of nonlinear generalized disjunctive programming with bilinear equality constraints Applications to process networks. Comput. Chem. Eng. 27, 1557-1575 (2003)... 

Disjunctive programming model and a rolling horizon algorithm for optimal multiperiod capacity expansion in a multiproduct batch plant... 

Garcfa-Ayala, G., Rios-Mercado, R.Z., and Chacdn-Mondragdn, O.L. (2012) A disjunctive programming model and a rolling horizon algorithm for optimal multiperiod capacity expansion in a multiproduct batch plant. Computers Chemical Engineering, 46,29-38. 

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