Derivative-free optimization aims at solving optimization problems that do not have an exploitable analytical structure (i.e. differentiability, convexity, and so on), that precludes the use of classical derivative-based techniques. Typical applications arise in engineering contexts involving numerical simulations/models of complex physical systems, whose structure cannot be exploited. With advances in computer science, the field of derivative-free optimization has taken considerable importance over the last two decades.

Direct search methods rely on sampling the objective function and take action solely based on those function values without gradient approximation or model building. They are a class of efficient and robust algorithms for solving such problems. Their extension to multiobjective optimization, where one looks to optimize multiple criteria simultaneously, has only begun in the last decade.

After introducing some main concepts of multiobjective optimization, we will give an overview of a state-of-the-art multiobjective direct search algorithm, DMulti-MADS, implemented in the Nomad software; and present some recent extensions, i.e., new heuristic search methods, and the handling of mixed-integer variables. Its performance will be illustrated on benchmarks and engineering problems.