# Combined Simulation-Optimization

Combined simulation-optimization (CSO) is employed for a variety of hydrological control problems, and has proven to be beneficial for demanding, complex problems that are difficult to unravel by trial-and-error methods or by manual tuning alone. CSO involves mathematically solving an objective function that states the management goal(s). The objective function assimilates model predictions and thus usually is not expressed in closed form. Accordingly, an external optimization algorithm is applied to automatically arrive at the optimal solution while complying with a given set of constraints.

Combined simulation-optimization (CSO) is employed for a variety of hydrological control problems, and has proven to be beneficial for demanding, complex problems that are difficult to unravel by trial-and-error methods or by manual tuning alone. CSO involves mathematically solving an objective function that states the management goal(s). The objective function assimilates model predictions and thus usually is not expressed in closed form. Accordingly, an external optimization algorithm is applied to automatically arrive at the optimal solution while complying with a given set of constraints.

My focus is on the use of evolution strategies, optimization under uncertainty, and a broad range of application cases from water resource management to geothermal borefield optimization.

Hydrogeological CSO problems have certain characteristic features in common – (i) they are always unique, often non-convex and thus need robust solvers, (ii) they often use costly simulation routines which may limit the applicability of computationally intense procedures, (iii) they have to deal with uncertainty, (iv) they include multiple objectives and (v) mostly close-optimal or at least improved solutions are searched for instead of one exact global optimum. Taking courses in soft computing during my PhD studies I was infected by an enthusiasm for evolutionary algorithms for solving demanding CSO problems. I stimulated the use of evolution strategies as an alternative to established algorithms in our discipline. Around a decade ago, I introduced Niko Hansen’s CMA-ES for hydrogeological optimization and control problems, which is currently among the most widely used heuristics worldwide.

My major focus is on including predictive model uncertainty in CSO. We introduced “stack ordering”, a computationally efficient technique for solving such stochastic optimization problems. Uncertainty or inaccuracy is represented by multiple model variants of equal probability. In principle, all possible model variants or parameter realizations for each objective function evaluation would have to be computed, which is often not feasible. Instead, only a few variants are probabilistically sampled, but at the expense of noise introduced in the formulation. The originally heuristic probabilistic sampling rule is now formulated in a Bayesian learning framework. Through this, model variants which are most critical (e.g. due to severe constraint violation) are learned during the evolutionary search, ranked and preferably sampled. As a result, highly reliable solutions are found for complex freshwater and remediation problems with computational savings of >95%. Current work focuses on worst case, as well as reduced reliability-based optimization, and its application to real irrigation problems.

The rigorous optimization of borehole heat exchanger (BHE) fields is a highlight of our work. These BHEs are vertical installations of often more than 100s of meter depth and the most common devices of shallow geothermal energy production. For providing high energy demand and exploiting a big volume of the ground, a field of simultaneously operating multiple BHEs is suggested. We demonstrated by CSO in a series of papers, how optimal arrangement and strategic individual BHE operation can improve the overall system’s performance. The patented technique is applicable to heating and cooling cases, and mitigates local temperature decline in the ground.