Portfolio Management with Heuristic Optimization consist of two parts. The first part (Foundations) deals with the foundations of portfolio optimization, its assumptions, approaches and the limitations when "traditional" optimization techniques are to be applied. In addition, the basic concepts of several heuristic optimization techniques are presented along with examples of how to implement them for financial optimization problems. The second part (Applications and Contributions) consists of five chapters, covering different problems in financial optimization: the effectsof (linear, proportional and combined) transaction costs together with integer constraints and limitations on the initital endowment to be invested; the diversification in small portfolios; the effect of cardinality constraints on the Markowitz efficient line; the effects (and hidden risks) of Value-at-Risk when used the relevant risk constraint; the problem factor selection for the Arbitrage Pricing Theory.