Evolutionary multiobjective optimization

Almost no engineering decision has a single optimal answer. When investing, more return usually means more risk; when designing a model, more accuracy usually costs more size. There is no single best solution: there is a frontier of trade-offs — the Pareto front — where no solution can improve on one objective without getting worse on another.

My original line studies how to discover that entire frontier with multiobjective evolutionary algorithms, using hypervolume-based indicators to guide the search. Part of my published work develops exactly these hypervolume-based methods.

Try it

The demo trains a real SMS-EMOA optimizer on a portfolio problem: choose assets to balance risk (standard deviation) and return, with a cardinality constraint (you can't hold 500 stocks, only a few). That constraint makes the problem non-convex — and that is exactly where classical exact methods fall short and evolutionary optimization shines.

First watch the convergence toward the frontier; then pick a solution by your investor profile: none is "the best", it depends on how much risk you accept.

The gap between the classical frontier (dashed line) and the solutions found is the cost of cardinality: the price, in return, of running a realistic, bounded portfolio.