## A survey of recent developments in multiobjective optimization.(English)Zbl 1146.90060

Summary: Multiobjective Optimization (MO) has many applications in such fields as the Internet, finance, biomedicine, management science, game theory and engineering. However, solving MO problems is not an easy task. Searching for all Pareto optimal solutions is expensive and a time consuming process because there are usually exponentially large (or infinite) Pareto optimal solutions. Even for simple problems determining whether a point belongs to the Pareto set is $$\mathcal{NP}$$-hard. In this paper, we discuss recent developments in MO. These include optimality conditions, applications, global optimization techniques, the new concept of epsilon Pareto optimal solution, and heuristics.

### MSC:

 90C29 Multi-objective and goal programming

### Keywords:

Pareto optimality; duality; generalized convexity

Knapsack
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