The work presents evidence from experiments that attempt to combine optimization technologies of different qualities and advantages. The evidence is illustrated in relevance to the design problem of heat exchanger networks (HEN). The HEN problem has been addressed separately by Pinch technology, mathematical programming, and stochastic optimization. Pinch methods account for conceptual principles driven by an overall understanding of the problem. Mathematical programming applications have spanned across the entire spectrum of formulations and include LP, MILP, NLP, and MINLP problems. Stochastic optimization is presented mostly in the form of simulated annealing and genetic algorithms. Considered in isolation, the different optimization methods are both blessed and baffled in that they simultaneously enable and disable particular features. The paper presents scientific experiments as a paradigm for the development of an integrated methodology with a purpose to restrain limitations, compound merits and produce a syncretism of complimentary venues for synthesis and optimization.