Implicit Enumeration with Generalized Upper Bounds

A number of planning problems can be formulated as (0–1)-programs where all variables can be grouped into special ordered sets or generalized upper bounds. An implicit enumeration algorithm was developed and implemented for this class of problems. The generalized upper bounds are handled implicitly. Only non-zero elements of the large but sparse constraint matrix are stored explicitly and chained row-wise and column-wise. The storage structure allows for very efficient testing of partial solutions. Preliminary numerical results indicate that even large-scale problems can be solved efficiently.