Optimisation: The Science of Taking Better Decisions

OPTIMISATION

Solving an optimisation problem is about finding solutions that satisfy constraints. One is often interested in the best solutions.

Overview

Solving an optimisation problem is about finding solutions that satisfy constraints. One is often interested in the best solutions.

A solution might be an allocation of resources (say a personnel roster, with work regulations and employee preferences as constraints), a packing (say of containers), a plan, a set of routes (say of vehicles in logistics, or of dataflows in a communication network), a schedule (say a school timetable), or a plan for energy usage (say for the charging of electric buses).

The challenge is to find good solutions fast. Our research focuses on identifying new and efficient optimisation models and methods, often driven by real-world applications.

  • Constraint programming (CP) is an AI approach to optimisation: modelling languages, high-level constraints, high-level types for decision variables, symmetry breaking
  • Local search (LS): modelling languages, search languages, solver design, autonomous search
  • Mathematical optimisation (MP): efficient mathematical modelling, linear programming (LP), mixed integer (linear) programming (MIP)
  • Propositional satisfiability (SAT) and Satisfiability modulo theories (SMT): trustworthy and verified solvers, proofs and certificates, competitions and evaluations
  • Surrogate-based optimisation and Bayesian optimisation (SBO): scalable acquisition functions/sampling algorithms, multi-objective and constrained black-box optimisation, optimisation of multi-fidelity (simulation-based) objective functions, evolutionary optimisation, etc
  • Applied optimisation: air traffic management; resource allocation in networks and mobile communications; cutting patterns for sawmills; software testing, analysis, and verification; vehicle routing for waste management; vehicle routing for winter road maintenance; charging of electric buses; expectation-maximisation (EM) for hidden Markov models; etc

  • 1DL442: Combinatorial Optimisation and Constraint Programming (10 credits) (slides): CP, LS
  • 1DL451: Modelling for Combinatorial Optimisation (5 credits) (slides): CP, LS, MP, SAT, SMT
  • 1DL481: Algorithms and Data Structures III (5 credits): LS, MP, SAT, SMT
  • 1RT242: Applied Systems Analysis (5 credits): LP, MIP
  • 1TD184: [Continuous] Optimisation (5 credits): MP
  • Numerical Optimisation (PhD course): PDE-constrained optimisation, multi-objective and model-based optimisation

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