  Optimization is a critical tool for addressing a broad range of human and
technical problems. However, the paradox of advanced optimization techniques is
that they have maximum utility for problems in which the relationship between
the structure of the problem and the ultimate solution is the most obscure. The
existence of solution with limited insight contrasts with techniques that have
been developed for a broad range of engineering problems where integral
transform techniques yield solutions and insight in tandem. Here, we present a
``Pareto-Laplace'' integral transform framework that can be applied to problems
typically studied via optimization. We show that the framework admits related
geometric, statistical, and physical representations that provide new forms of
insight into relationships between objectives and outcomes. We argue that some
known approaches are special cases of this framework, and point to a broad
range of problems for further application.
