Rigorous finite-time guarantees for optimization on continuous domains by simulated annealing

Simulated annealing is a popular method for approaching the solution of a global optimization problem. Existing results on its performance apply to discrete combinatorial optimization where the optimization variables can assume only a finite set of possible values. We introduce a new general formulation of simulated annealing which allows one to guarantee finite-time performance in the optimization of functions of continuous variables. The results hold universally for any optimization problem on a bounded domain and establish a connection between simulated annealing and up-to-date theory of convergence of Markov chain Monte Carlo methods on continuous domains. This work is inspired by the concept of finite-time learning with known accuracy and confidence developed in statistical learning theory.

Fundamentals and Challenges

An improved understanding of lean fuel turbulent premixed flames must play a central role in the fundamental science of these new concepts.

Simulated Annealing: Rigorous finite-time guarantees for optimization on continuous domains

Simulated annealing is a popular method for approaching the solution of a global optimization problem. Existing results on its performance apply to discrete combinatorial optimization where the optimization variables can assume only a finite set of possible values. We introduce a new general formulation of simulated annealing which allows one to guarantee finite-time performance in the optimization of functions of continuous variables. The results hold universally for any optimization problem on a bounded domain and establish a connection between simulated annealing and up-to-date theory of convergence of Markov chain Monte Carlo methods on continuous domains. This work is inspired by the concept of finite-time learning with known accuracy and confidence developed in statistical learning theory.

Engineering Fundamentals of Energy Efficiency

Using energy more efficiently is essential if carbon emissions are to be reduced. According to the International Energy Agency (IEA), energy efficiency improvements represent the largest and least costly savings in carbon emissions, even when compared with renewables, nuclear power and carbon capture and storage. Yet, how should future priorities be directed? Should efforts be focused on light bulbs or diesel engines, insulating houses or improving coal-fired power stations? Previous attempts to assess energy efficiency options provide a useful snapshot for directing short-term responses, but are limited to only known technologies developed under current economic conditions. Tomorrow's economic drivers are not easy to forecast, and new technical solutions often present in a disruptive manner. Fortunately, the theoretical and practical efficiency limits do not vary with time, allowing the uncertainty of economic forecasts to be avoided and the potential of yet to be discovered efficient designs to be captured. This research aims to provide a rational basis for assessing all future developments in energy efficiency. The global fow of energy through technical devices is traced from fuels to final services, and presented as an energy map to convey visually the scale of energy use. An important distinction is made between conversion devices, which upgrade energy into more useable forms, and passive systems, from which energy is lost as low temperature heat, in exchange for final services. Theoretical efficiency limits are calculated for conversion devices using exergy analysis, and show a 89% potential reduction in energy use. Efforts should be focused on improving the efficiency of, in relative order: biomass burners, refrigeration systems, gas burners and petrol engines. For passive systems, practical utilisation limits are calculated based on engineering models, and demonstrate energy savings of 73% are achievable. Significant gains are found in technical solutions that increase the thermal insulation of building fabrics and reduce the mass of vehicles. The result of this work is a consistent basis for comparing efficiency options, that can enable future technical research and energy policy to be directed towards the actions that will make the most difference.