Probability-based black-box branch-and-bound optimization for biofuel system design
We are developing new ways of producing sustainable biofuels from non-food-competitive biomass feedstocks grown in Canada, such as switchgrass, forestry bi-products, and other forms of lignocellulose. However, in order to produce enough biofuels for transformative change to our nations energy infrastructure, there are many systems issues in the supply chain and chemical processing which must be overcome. To address this, we are currently developing semicontinuous approaches to producing biofuels such as biobutanol (gasoline and ethanol substitute) and bio-dimethyl-ether (diesel substitute) to overcome these challenges at lower costs.
Although the semicontinuous approach has significant promise, it is incredibly complex, and as such traditional approaches to process design no longer apply. Although attempts at designing the process can be made by hand, a formal mathematical optimization technique is required to determine the key process parameters. Batch sizes, distillation parameters, heat duties, flow rates, transition behavior, controller tuning parameters, set-points, and many other parameters must be determined simultaneously in order to discover a configuration which achieves quality, sustainability, and profitability constraints. However, this is a significant challenge due to the high dimensionality of the problem and the character of the computer models on which our analyses are based. As such, we have found that existing optimization solvers (specifically, those which solve the class of problems known as black-box) are wholly inadequate for our needs.
Therefore, in order to assist in our work in biofuels process, we propose the development of a new optimization algorithm which is suitable not only for our particular biofuels problem, but for a large class of black-box optimization problems. The proposed approach is to combine well known stochastic solvers such as particle swarm optimization (PSO) or differential evolution with branch-and-bound techniques that systematically reduce the size of the problem to improve convergence toward a global optimum.
Branch-and-bound techniques work by systematically dividing the optimization problems search space into regions, and mathematically proving that the global optimum cannot be in one region or another, thus eliminating it from consideration. However, branch-and-bound requires explicit knowledge of the model equations in order to do this, which are unavailable for our problem and other black-box problems. Therefore, we propose a new probability-based algorithm gets around the problem of requiring explicit knowledge of model equations by creating implicit, approximations of the model using the knowledge gained by particle swarm optimization runs.
With this technique, we cannot completely eliminate one region of the search space, but should be able to estimate the probability that the global optimum should exist in one region or another. For black-box problems, this should be significantly faster and more likely to converge upon a true global optimum than the current state-of-the-art.
