Robust optimization examples
The robust optimization examples in this directory are described in the whitepaper Robust Optimization with Xpress (file robustwp.pdf or online).
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| Introductory examples: Defining robust constraints, uncertainty sets, nominal values
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| Type: |
Programming |
| Rating: |
3 (intermediate) |
| Description: |
Introductory examples from the whitepaper 'Robust Optimization with Xpress'. Topics covered by the examples:
- Price of robustness: cost_of_robustness.mos (calculating the cost of having uncertainty in the model)
- Working with nominal values:
nominalvalue_0base.mos (simple robust model without nominal values);
nominalvalue_2base.mos (simple robust model with a nominal valued uncertain);
nominalvalue_none.mos (uncertainty as an addition to a coefficient);
nominalvalue_rule2.mos (using uncertains with nominal value as coefficients);
nominalvalue_shift1.mos (basic version without nominal values);
nominalvalue_shift2.mos (defining nominal values);
nominalvalue_shift3.mos (substituting the effect of the nominal values);
nominalvalue_simple.mos (uncertainty as a coefficient)
- Overlapping uncertainty:
overlapping_cardinality.mos (cardinality constraint with overlapping
uncertainty sets);
overlapping_polyhedral.mos, overlapping_polyhedral2.mos (polyhedral uncertainty set with overlapping use in
robust constraints)
- Working with scenarios:
scenario_simple.mos (simple robust optimization model with scenario based
uncertainty);
scenario_simple_deterministic.mos (deterministic version of the simple
scenario problem)
- Special cases:
careful_equalities.mos (robust problem with equality constraint);
careful_unbounded_uncertain.mos (robust problem with an unbounded uncertain)
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| File(s): |
cost_of_robustness.mos, nominalvalue_0base.mos, nominalvalue_2base.mos, nominalvalue_none.mos, nominalvalue_rule2.mos, nominalvalue_shift1.mos, nominalvalue_shift2.mos, nominalvalue_shift3.mos, nominalvalue_simple.mos, overlapping_cardinality.mos, overlapping_polyhedral.mos, overlapping_polyhedral2.mos, scenario_simple.mos, scenario_simple_deterministic.mos, careful_equalities.mos, careful_unbounded_uncertain.mos |
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| Robust formulations of the single knapsack problem: Types of uncertainty sets
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| Robust portfolio optimization: 'ellipsoid' uncertainty set, retrieving the worst value of an uncertain
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| Type: |
Portfolio optimization |
| Rating: |
3 (intermediate) |
| Description: |
Robust single period portfolio allocation with uncertain variability of share prices formulated as 'ellipsoid' uncertainty.
The example also shows how
to quantify the robustness of a solution using
Monte-Carlo simulation.
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| File(s): |
021folio_robust.mos |
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| Security constrained robust unit commitment: 'scenario' and 'cardinality' uncertainty sets
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| Production planning under demand uncertainty: 'scenario' and polyhedral uncertainty sets
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| Type: |
Production planning |
| Rating: |
3 (intermediate) |
| Description: |
Planning the production of several types of drinking glasses for the next N weeks subject to uncertain demand (formulated
via scenarios) or uncertain resource capacity limits (polyhedral uncertainty).
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| File(s): |
c2glass_robust.mos |
| Data file(s): |
c2glass_scen.dat |
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| Production planning under energy supply uncertainty: polyhedral uncertainty set
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| Type: |
Production planning |
| Rating: |
3 (intermediate) |
| Description: |
Plan the production of liquid nitrogen and liquid oxygen for
the next N periods subject to an Interruptible Load
Contract (ILC) for the power supply. Formulation using a polyhedral uncertainty set.
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| File(s): |
prodplan_robust.mos |
| Data file(s): |
prodplan_robust.dat |
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| Robust shortest path: 'cardinality' uncertainty set
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| Type: |
Network fow |
| Rating: |
2 (easy-medium) |
| Description: |
Determine the shortest path through a road network subject to uncertain travel times caused by road works (formulated as a
'cardinality' uncertainty set).
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| File(s): |
roadworks.mos, roadworks_graph.mos |
| Data file(s): |
roads_9.dat |
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| Robust network optimization for VPN design: polyhedral uncertainty set
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| Type: |
Network design |
| Rating: |
3 (intermediate) |
| Description: |
Designing a telecommunication network with uncertain demand, formulated via polyhedral uncertainty sets. This problem is a
particular case of a multi-commodity network
flow problems, with the important addition of the uncertainty in
the traffic demands.
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| File(s): |
vpn_design.mos |
| Data file(s): |
vpn_data.dat |
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