# System-Level Reliability Based Design Optimization Using Agents

In my work, I have used a multi-agent system to solve a system-level reliability-based optimization problem, which considered three failure modes. This problem is formulated as:

In general, it is easier (and cheaper) to solve a problem where constraints fall on each of the *n *number of failure modes:

Each agent was formulated to solve the simplified problem that considered the failure of each failure mode. Surrogates (or meta-models) were used to aide in the search for the optimum risk allocations (the allowable probabilities of failure of the failure modes) that would result in a global optimum. By using different surrogates, each agent took its own view of the problem. Upon the completion of its task, the agent could share and receive information.

The ITPS was optimized for minimum mass with a constraint that the system probability of failure be less than or equal to 1.5%. Two agents were considered in this problem, *KRG* and *PRS*, which used kriging and polynomial response surfaces, respectively. Different levels of cooperation were considered:

- no cooperation (
*no sharing*) - mixed cooperation and privacy (
*KRG sharing*and*PRS sharing*) - full cooperation (
*full sharing*)

The figure below compares each through 15 iterations of the solution process.

**Learn more**: Villanueva, D., Le Riche, R., Picard, G., Haftka, R.T. (2011). "A Multi-Agent System Approach to Risk Allocation for Reliability Based Design

Optimization," 12th Annual Congress of the French National Society of Operations Research and Decision Science, Saint-Etienne, France (Abstract)