Analítica prescriptiva / Investigación operativa / Optimización combinatoria / Programación entera
- Greedy: Solución a mano
- Travelling Salesman Problem: At each step of the journey, visit the nearest unvisited city.
- Knapsack: Sort items in decreasing order of value per weight (V/W), then insert them into the sack in that order until there is no space.
- Global techinques: Techniques that are guaranteed to find the optimal solution if you give the enough time.
- Dynamic Programming (DP) (backtracking, branch & bound)
- Constraint Programming (CP)
- Linear Programming (LP)
- Programación lineal continua: Simplex
- Programación lineal entera (discreta): Simplex Lineal Entero
- Mixed Integer Programming (MIP)
- Continuous math, Linear algebra,...
- Local Search (LS): Scale very well with problems of large size (may not give you the best solution).
- Tabu Search: Past moves or solutions are prohibited (tabu)
- Simulated Annealing: Random at the beggining, deterministic at the end.
- Hybrids: best of Global and Local.
| Tecnicas | Puntos Fuertes |
|---|---|
 |
 |
- CP: How much it prunes?
- LS: What are the sequence of solutions? How fast it goes down?
- LP, MIP: What is the relaxation? how good is it?
- Es muy rápido de checkear si la solucion propuesta es correcta.
- Si sabes resolver un problema NP-Completo, sabes resolverlos todos.
- Existe el mito de que se resuelven con coste exponencial.
- Feasibily Problems: Any solution meeting all the criteria is acceptable.
- Optimization Problems: Find the best solution that satisfies the criteria.
DP=Dynamic Programming, CP=Constraint Programming, MIP=Mixed Integer Programming
| Problem | My solution | OR Tools Doc |
|---|---|---|
| Cryptarithmetic | CP | doc |
| N queens | CP | doc |
| Sudoku | DP, CP | |
| Graph Coloring | CP | |
| Employee Scheduling | CP | doc |
| The Job Shop | CP | doc |
| Routing problem | Description | OR-Tools |
|---|---|---|
| Traveling Salesman Problem (TSP) | Visit all locations once and come back to the starting location. | link |
| Vehicle Routing Problem (VRP) | A generalisation of the TSP with multiple vehicles. | link |
| VRP with capacity constraints | Vehicles have maximum capacities for the items they can carry. | link |
| VRP with Pickups and Deliveries | Each vehicle picks up items at some locations and drops them off at others. | link |
| VRP with time windows | Vehicles must visit the locations in specified time intervals. | link |
| VRP with resource constraints | Load and unload vehicles at the depot (the starting point). | link |
| VRP with dropped visits | When you must pay a penalty for unvisited locations. | link |
| Dijkstra shortest path | Find the shortest path between 2 locations (ej. Google Map finding route) |
- Knapsack (Problema de la mochila)
- Relajación Lagrangeana (empresa eléctrica, arrancar o parar una central térmica)
- Constraint programming
- Turnos de Madrid
- problema de asignación de turnos
- Procesos de aprovisonamiento, inventario...
- Cuánto envío del almacén a la tienda
-
Traducir el problema de negocio a un problema de optimización Identificar Variables de decisión.
- Hora que empieza.
- Hora que acaba.
- Tarea que hace en el minuto 3
- Tarea que hace en el minuto 4
-
Normalemete se acaban con muchas soluciones que igualan la mejor función objetivo
- Recomendable: Añadir funciones objetivo secundarias hasta que queden pocas soluciones e idelamente una unica solucion. Ejemplo de turnos
Funcion pricipal: Encajar horarios Fucion Scundaria: Que esten más contentos con su horario
- COURSE: https://www.coursera.org/learn/discrete-optimization
- BOOK: Competitive Programming 4 by Steven Halim, Felix Halim
- https://www.coursera.org/learn/delivery-problem
- https://www.gestiondeoperaciones.net
- https://medium.com/@AlainChabrier/scheduling-with-constraint-programming-35a23839e25c
- Twit de @JFPuget recommendos for learing MILP:
- Read the Model Building in Mathematical Programming book
- Read the tesis of @AchterbergT If you want to know about how MILP are solved
- cmu-comp-or: A series of tutorials for conducting computational experiments with optimization solvers by @rkimura47
| Year | Competition | Description |
|---|---|---|
| 2012 | Traveling Santa Problem | Traveling salesman |
| 2014 | Helping Santa's Helpers | Job Scheduling |
| 2015 | Santa's Stolen Sleigh | Routing |
| 2016 | Santa's Uncertain Bags | |
| 2017 | Santa Gift Matching Challenge | Maximize child-gift happiness |
| 2018 | Traveling Santa 2 | Traveling salesman on prime paths |
| 2019 | Revenge of the Accountants | Minimizing his workshop costs |
| 2019 | Santa's Workshop Tour 2019 | |
| 2021 | The Merry Movie Montage | Optimize television programming |
- Hash Code
- Hash Code Kaggle Archive: Drone Delivery: Can you help coordinate the drone delivery supply chain?
- Hash Code Kaggle Archive: Photo Slideshow Optimization: Optimizing a photo album from Hash Code 2019
- ROADEF: Bastante complicada.
Para Constraint Programming sin dudarlo Choco Solver.
| Library | Languaje | Price |
|---|---|---|
| OR-Tools (Google) | C++ (APIs: Java, Python, & .NET) | Open Source |
| CHOCO | Java | Open Source |
| JACOP | Java | Open Source |
| Gecode | C++ | Free |
| ILog | Binary | Free with academic license |
| MiniZinc / G12 | Binary | Free for students |
Para Mixed Integer Programming no hay nada open source y bueno. Pero CPLEX, de IBM, tiene una versión community limitada por tamaño de problema.
| Library | Languaje | Price |
|---|---|---|
| GLPK | C | Open Source |
| LPSolve | C | Open Source |
| BCP | C++ | Open Source |
| CBC | C++ | Open Source |
| CPLEX (IBM) | Binary | Free with academic license |
| Gurobi | Binary | Free with academic license |
| SCIP | Binary | Free for academic use |
Revisar PuLP
| Library | Languaje | Price |
|---|---|---|
| CLP | C++ | Open Source |
| SimplexSolver | Java | Open Source |
Para Local Search Optaplanner.
| Library | Languaje | Price |
|---|---|---|
| OptaPlanner | Java | Open Source |
| Local Solver | Binary | Free with academic license |
| Library | Languaje | Price |
|---|---|---|
| cryptominisat | C++ | Open Source |
| Glucose | C | Open Source |
| Lingeling | C | Open Source |
| UBCSAT | C | Open Source |
| MiniSat | Binary | Free |
| Library | Languaje | Price |
|---|---|---|
| SCIP | Binary | Free for academic use |
https://kristerw.github.io/2022/11/01/verifying-optimizations/