Heuristics for Network Design with budget constraint

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The aim of this presentation is make a comprehensive overview about some heuristics able to suggest a sub optimal solution for network design under traffic uncertainty and budget constraint. The presentation will conclude with a rough investment risk analysis of a potential real investor.

Heuristics for Network Design under traffic uncertainty Luca Pizziniaco Politecnico di Milano A dvanced N etwork T echnologies Lab Supervised by : Prof. Edoardo Amaldi OR Group

Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

The Problem – Classical Approach ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

The Problem – Stochastic Approach ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Problem Overview ,[object Object],[object Object],P,D P,D P,D P,D Maximize

Investor Point of View ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

New Approach ,[object Object],[object Object],[object Object],[object Object],[object Object]

MIP Probabilistic Model ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

MIP Probabilistic Model (cont.) Expected Throughput Budget Constraint Balance Constraint

MIP Probabilistic Model (Cont.) Capacity Allocation Flow Limit Constraint

Problem Size ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Euristhical Approach ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Scenario Based Euristic ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Complexity : O(KS), where S = Algorithm Complexity for design a scenario

Links Based Euristic ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Complexity : O((C max -B)K-N 3 ), where C max -B = Maximum cost - Budget

Path Based Euristic ,[object Object],[object Object],[object Object],[object Object],[object Object],Complexity : O(N 2 ), since Djikstra is used to find paths for every demand d st - CONTROLLARE VERY FAST HEURISTIC

A first Result ,[object Object],[object Object],[object Object],[object Object]

A First Result (cont.) Expected Throughput Budget Heuristic 2 - 3 give very close results Heuristic 1 is worst when budget is low

CPU Time Comparison ,[object Object],[object Object],[object Object],Eu2 Eu1 Eu3 Budget CPU Time

Heuristics Quality ,[object Object],Optimal ,[object Object]

The Scrooge Investor ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Improvements ,[object Object],Low slope Similar TP values Different B Values Medium/High slope Different TP values Similar B Values Heuristic 2 Heuristic 3 Heuristics Moves Continue to move until derivative reach a certain value Throughput Budget

Some modification ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Rusults ,[object Object],[object Object]

Investments Analysis RES9 Increase the budget means increase the revenue and the investments risks Low Budget High Budget Throughput Probability

Conclusion ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Alea Iacta Est ,[object Object],[object Object]

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Heuristics for Network Design with budget constraint

1. Heuristics for Network Design under traffic uncertainty Luca Pizziniaco Politecnico di Milano A dvanced N etwork T echnologies Lab Supervised by : Prof. Edoardo Amaldi OR Group

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9. MIP Probabilistic Model (cont.) Expected Throughput Budget Constraint Balance Constraint

10. MIP Probabilistic Model (Cont.) Capacity Allocation Flow Limit Constraint

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17. A First Result (cont.) Expected Throughput Budget Heuristic 2 - 3 give very close results Heuristic 1 is worst when budget is low

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24. Investments Analysis RES9 Increase the budget means increase the revenue and the investments risks Low Budget High Budget Throughput Probability

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