Marriage & Optimization

An interesting analogy formulated in my mind yesterday between Marriage and Optimization. Specifically, Love Marriage::Gradient Based Optimization and Arranged Marriage::Heuristic Optimization.

Optimization is a mathematical technique for finding the optimum solution of a function. There are two major methods of doing it viz. Gradient based optimization where in the derivative information of the objective function is used to approach the optimum solution and heuristic (stochastic) optimization wherein a more stochastic approach is used for reaching the optimum. Survival of the fittest is the solution strategy for Heuristic Optimization (like Genetic Algorithms). There is a higher probability of achieving a global optimum in Heuristic optimization while in Derivative based optimization its highly possible that you get stuck at a local optimum. In other words it highly depends on from what point you start your optimization for Derivative based optimization. Derivative based methods require fewer objective function evaluations since they use derivative information as opposed to Heuristic Optimization.

Before a love marriage, the lovers test out the chemistry (use derivative information) between themselves and arrive at the conclusion or marriage (optimum). In an arranged marriage the bride(groom) is selected at random (Heuristics). Of course its not entirely random because the family etc is known but the chemistry and compatibility between the two are unknown. The solution is kept feasible by the patrika matching exercise (constraints satisfied). Love marriages are quicker once love is initiated (faster optimization), while Arranged Marriages may take time (more bride(groom) evaluations). Arranged Marriages work wonders since Global Optimum is highly probable. Love Marriages work too since its still an Optimum (Was a Global missed?) :)