Simulated Annealing with Penalization for University Course - - PowerPoint PPT Presentation

Simulated Annealing with Penalization for University Course Timetabling

Edon Gashi & Kadri Sylejmani Faculty of Electrical and Computer Engineering University of Prishtina, Kosovo

Overview

• Solution model
• Operators
• Evaluation
• Simulated Annealing
• Penalization
• Random walks

Solution model

• Solutions are complete

○ Variables are always assigned ○ Infeasible combinations possible

• Three types of penalties
• Soft penalty

○ ITC19 solution score

• Hard penalty

○ Conflict between classes ○ Unavailable rooms ○ Unsatisfied required constraints

• Class overflow penalty

○ Easier to satisfy

Mutations & Operators

• Mutations

○ Class – Time change ○ Class – Room change ○ Student – Course – Configuration change (when ph = 0)

• High performance

○ Structural sharing ○ Delta evaluation

• Neighborhood operator

○ 50% chance for 1 mutation ○ 50% chance for 1–3 mutations

• Initial solution

○ Variables set to 1 of 3 lowest soft penalty assignments

Evaluation – Search Penalty

Evaluation – FSTUN

Wolfgang Wenzel and Kay Hamacher Stochastic tunneling approach for global minimization

• f complex potential energy landscapes. Physical Review Letters 82.15 (1999): 3003.

Simulated Annealing

• Lundy and Mees cooling schedule*

* Miranda Lundy and Alistair Mees Convergence of an annealing algorithm. Mathematical programming 34.1 (1986): 111-124.

• Times out after a while
• Penalize and increase temperature

Penalization

Random walks

• Penalization may fail with large distribution constraints
• Focus on persistently unsatisfied constraints
• Hill climb with random walk operator
• Return to regular search after timeout

Summary

• Fast
• Problem agnostic
• Good overall results
• Two-phase approach limits search space

○ Poor results for some problems

• Open source github.com/edongashi/itc-2019