The traditional approach to financial advice often relies on "risk-profiling" to determine the client's investment portfolio. This approach is based on a subjective questionnaire that tries to find out the level of fear that the client experiences in response to short-term variability in markets and investment returns. Investments that produce highly variable short-term returns (eg equities) are described as more "risky" than those producing more stable short-term returns (eg cash) and if the client is shown to be "risk averse" then they are directed to an investment portfolio that has more stable returns. But that is also typically a lower return portfolio over the long term, which is the typically the time-frame For most clients. In terms of real risk (i.e. chance of failing achieve goals), this approach is often actually counter-productive - it puts the client in riskier portfolios!
Portfolio optimisation seeks to model many (could be hundreds) of different portfolios for the client's financial future and compare all the results in terms of goals and risk and find the best one i.e. the one that maximises the client's goals at the level of confidence (or risk) they have chosen. For example, find the portfolio that produces the best retirement income and legacy for a client at their chosen confidence level of 90% (where confidence level is just another way of expressing risk (eg 90% confidence of achieving goals is another way of saying a 10% risk of failing to achieve goals). In financial advice, portfolio optimisation is most meaningful when it is combined with stochastic modelling.