Discrete decision process

A. Solution Space Representation—Discrete Decision Process.555... 

The combinatorial problem is represented by a discrete decision process (DDP) (Ibaraki, 1978) where the underlying information in the problem is captured by an explicit state-space model (Nilsson, 1980). 

The first step in solving a combinatorial optimization problem is to model the solution space itself. Such a model should be declarative in character, if it is to be independent of the characteristics of the specific algorithm that will be used to find the solution within the solution space. The model we have adopted for the scheduling of flowshop operations is the discrete decision process (DDP) introduced originally by Karp and Held (1967). As defined by Ibaraki (1978) a DDP, Y, is a triple (.S,S,/) with its elements defined as follows ... 

If g(x) satisfies these conditions, we can use the following lower-bound elimination criterion to terminate the solution of a discrete decision process, T(y). 

Definition. A dominance relation, D, is a partial ordering of the partial solutions of the discrete decision processes in X, which satisfies the following three properties for any partial solutions, x and y. 

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