Assuring a global optimum by the use of an upper bound on the lower (dual) bound

Abstract Many structured engineering systems have several local cost optima which will often trap a conventional minimum seeking optimization algorithm. This paper presents an algorithm to establish, often quite quickly, whether the discovered optimum is global or local. The strategy is based on finding both a lower (dual) bound for the optimum of the structured system and an upper bound on this lower bound. The paper illustrates the effectiveness of the algorithm by applying it to three small heat exchanger network problems, a type of problem where one can demonstrate the local optima are indeed very common in the annualized network cost.