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Append description of Lex and Pareto

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Jip J. Dekker 2021-02-25 14:29:20 +11:00
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chapters/6_incremental.tex
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@ -366,10 +366,31 @@ on. We can model this strategy restarts as such:
\highlightfile{assets/mzn/6_lex_minimize.mzn}
Another optimisation
The lexicographic objective changes the objective at each stage in the
evaluation. Initially the stage is 1. Otherwise is we have an UNSAT result, then
the last stage has been completed (proved optimal). We increase the stage by one
if we have stages to go otherwise we finish. Otherwise if the last all was SAT
we maintain the same stage, and store the objective value (for this stage) in
the \mzninline{best} array. For normal computation we fix all the earlier stage
variables to their best value. If we are not in the first run for a stage we add
the branch and bound cut to try to find better solutions. Finally we set the
objective to be the objective for the current stage.
There is not always a clear order of importance for different objectives in a
problem. In these cases we might instead look for a number of diverse solutions
and allow the user to pick the most acceptable options. The following fragment
shows a \gls{meta-search} for the pareto optimality of a pair of objectives:
\highlightfile{assets/mzn/6_pareto_optimal.mzn}
In this implementation we keep track of the number of solutions found so far
using \mzninline{nsol}. There is a maximum number we can handle
(\mzninline{ms}). At the start the number of solutions is 0. If we find no
solutions we finish the entire search. Otherwise we record that we have one more
solution. We store the solution values in \mzninline{s1} and \mzninline{s2}
arrays. Before each restart we add constraints removing pareto dominated
solutions, based on each previous solution.
\section{Compilation of Meta-Search Specifications}
\label{sec:6-solver-extension}