Continuous optimisation

What we can help you with

How should a system be designed or operated to achieve the best possible performance within given constraints? Continuous optimisation addresses these questions when decision variables can vary continuously, such as injection rates, pressures, material properties or geometric parameters.

We specialise in problems where objective functions and constraints are evaluated using a simulator. We can help you:

• Formulate optimisation problems with appropriate decision variables, objectives and constraints.
• Connect existing simulators to gradient-based optimisation methods.
• Develop and adapt methods for design, operational planning and optimal control.
• Reduce computational cost through adjoint methods, model reduction and reuse of computational results.
• Account for uncertain model parameters and assess the robustness of proposed solutions.
• Estimate model parameters from observations by formulating and solving inverse problems.

Do you have a model or simulation workflow you would like to use for optimisation? Contact our Applied Computational Science research group.

When every evaluation requires a simulation

In simulation-based optimisation, evaluating even a single candidate solution can be expensive. A change in design or control may require solving a large, time-dependent system of equations again. Both the number of simulations and the information obtained from each run therefore matter.

We exploit model structure to compute how results depend on the decision variables. Differentiable simulation and sensitivity analysis provide gradients that guide the optimisation algorithm. Adjoint methods are particularly useful when there are many decision variables and few objective functions.

We also work on the interface between the simulator and the optimisation method: how variables are scaled, how constraints are represented, and how failed simulations or inexact computations are handled during the search.

Design, operation and optimal control

Decision variables may describe a fixed design or vary throughout an operating period. In optimal control, for example, the aim is to determine a schedule of control inputs that influences how the system evolves. Constraints may apply both to the controls themselves and to states computed by the simulator.

Our experience includes production optimisation and injection control in reservoirs. These problems combine long-term objectives with limits on rates, pressures and capacity. They illustrate a challenge shared by many dynamic systems: decisions made early in the process affect the options available later.

We develop computational methods for investigating these relationships systematically. Objectives, time horizons and constraints are defined in collaboration with specialists who understand the application.

Model calibration and inverse problems

Optimisation can also be used to identify model parameters that provide the best agreement with observations. The objective function then measures the mismatch between simulated and observed quantities, potentially including additional terms representing prior knowledge or desired properties of the solution.

We work on gradient-based calibration of simulation models and use sensitivities to understand which parameters the data can constrain. Different parameter combinations may produce similar agreement with observations. Regularisation, parameterisation and the choice of data are therefore important parts of the problem formulation.

Optimisation under uncertainty

A solution that performs well for one model may perform less well when model parameters or operating conditions change. We work on optimisation that accounts for multiple scenarios or model realisations.

Depending on the application, the objective may be to improve expected performance, reduce risk or maintain acceptable outcomes across scenarios. This increases computational demand and makes efficient sensitivity computations, parallel execution and simplified models particularly valuable.

We examine how uncertainty affects the proposed solution and explore the trade-offs between performance and robustness.

Efficient methods and verifiable results

Successful optimisation requires more than an algorithm. Scaling, parameterisation, initial guesses and numerical accuracy influence both progress and the final result. We adapt the method and computational approach to the structure of the problem and the cost of evaluating the model.

Reduced-order models can accelerate the exploration of alternatives, while more detailed simulators are used to check promising solutions. Computational accuracy can also be adjusted during optimisation, directing resources where they provide the greatest benefit.

Many simulation-based problems are non-convex and may have multiple local optima. We therefore assess results in terms of convergence, constraint satisfaction and sensitivity to the starting point and model assumptions. The aim is to obtain a solution that is numerically well founded and relevant to the decision at hand.

From numerical methods to practical applications

Our strength lies in combining optimisation, numerical methods and simulator development. We can work across the full computational process, from model formulation and gradient computation to the optimisation algorithm and assessment of the results.

We collaborate both on developing new methods and on adapting existing simulation tools to specific optimisation tasks. A collaboration can begin with a focused study or form part of the long-term development of models and software.