By J. N. Hooker (auth.), David L. Woodruff (eds.)

Computer technological know-how and Operations learn proceed to have a synergistic courting and this booklet - as part of the*Operations examine and laptop technological know-how Interface Series* - sits squarely within the heart of the confluence of those technical learn groups. The learn provided within the quantity is proof of the increasing frontiers of those intersecting disciplines and offers researchers and practitioners with new paintings within the parts of good judgment programming, stochastic optimization, heuristic seek and post-solution research for integer courses.

The bankruptcy themes span the spectrum of software point. many of the chapters are hugely utilized and others characterize paintings during which the appliance capability is barely starting. furthermore, each one bankruptcy includes expository fabric and experiences of the literature designed to augment the participation of the reader during this increasing interface.

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**Additional info for Advances in Computational and Stochastic Optimization, Logic Programming, and Heuristic Search: Interfaces in Computer Science and Operations Research**

**Example text**

The previously stated generality principle suggests that if we allow the or operator in constraints, then we should similarly allow AMPL's other boolean operators. To provide an example, here is how one real-world assignment model uses additional binary variables and constraints to enforce a requirement that prevents any person from being "isolated" in the solution. As specified in the initial part of the model (not shown here), there are number [i1, i2] people of rank il from site i2, and there is a set ROOM of meeting rooms; each person must be assigned to exactly one room.

AMPL already handles a variety of nonlinear expressions in the variables, however, by passing quite general expression trees to the solver. As a result, the changes required to accommodate new operators on variables - including and, or, not, and others to be proposed in this section - should be straightforward. The greater challenge will be to write AMPL's interfaces to different solvers, so as to convert the expression trees to whatever constraint representations the solvers require. A MODELING LANGUAGE FOR COMBINATORIAL OPTIMIZATION 39 More seriously, with the introduction of logical operators it becomes possible to specify a feasible region that is not closed, with the result that a continuous-valued objective may have an infimum (or supremum) but may not achieve a minimum (or maximum).

Thus our generality principle would suggest that the language should be extended by allowing subscripts to contain valid arithmetic expressions that also use variables. Then rather than evaluating all subscripts while generating a problem (as at present), AMPL will need to send subscript expressions involving variables to the solver, for evaluation within the optimization algorithm. This extension to the implementation is not expected to give rise to any fundamental difficulties, since the expressions to be allowed within subscripts are no more general than the expressions currently allowed elsewhere in constraints.