Best choices over discrete possibilities.
Answer five questions about Discrete Optimization and get instant feedback.
Score you try to make as small or as large as possible
In discrete optimization, the objective can mix several goals, like minimizing cost plus a penalty for late delivery, so solutions that break rules become less attractive.
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The knapsack problem captures choosing the most value under a strict capacity limit.
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The traveling salesman problem asks for the shortest tour visiting each location once.
What can never improve the best value in a minimization problem?
In a minimization model, adding constraints only shrinks the feasible set, so the optimum can stay the same or get worse, and it can even make the problem infeasible.
Replacing an integer variable by a real variable in an interval, often to get a useful bound
In integer programming, the LP relaxation's optimal value is a bound, and the ratio or difference to the best integer solution, the integrality gap, predicts how hard the instance may be.
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