Knowledge Discovery Process for Blackbox Optimization
Traditional simulationbased optimization (SBO) approaches usually require predefined objective functions which directly describe the influence of all simulation input parameters on the specified simulation objectives (denoted as model behavior). Optimization toolsets, use these objective functions (e.g. ordinary differential equations) in order to find a local or global minimum which satisfies given constraints. As a consequence of the increasing complexity of stateoftheart simulations within virtual testbeds, such objective functions are not always available. Even more, there are many technical complex systems whose longterm behavior can not be described by a set of equations (e.g. the behavior of autonomous systems in changing environments). This kind of SBO problem is called blackbox simulation problem because the objective functions are unknown to both: the simulation engineer and consequently optimization toolset. There is already a huge number of computational methods for solving multiobjective optimization problems (MOPs) which usually do not consider the generation of vast amounts of simulation model behavior results that can be derived from a knowledge discovery process (KDP) in simulations. Usually, the traditional approaches use heuristics of the unknown objective functions for their algorithms. However, these approaches converge much better to local or global minima when they are enhanced with additional information about the MOP. We propose for this purpose an approximation of the complete simulation model behavior.
In contrast to stateoftheart approaches, which are not able to automatically analyze blackbox MOPs in simulations, our approach automatically builds an active model between simulation input and simulation objectives. This approximation of the simulation model behavior directly leads to an approximation of the feasible design space (FDS) of the simulation model configuration space for a Pareto based MOO.

Our automatic knowledge discovery process: first, causal relations between simulation input parameters and simulation objectives are revealed. Second, simulation data farming is efficiently conducted in order to approximate the unknown objective functions and the FDS. These approximations are used in order to compute Pareto gradient information and solution. 
It uncovers unknown causal relations in large parameter sets between simulation input and model behavior which are assumed to be unknown nonlinear objective functions. In detail, it approximates objective functions (resp. the FDS) in arbitrary deterministic and stochastic blackbox simulations as Bspline surfaces. It computes a Pareto gradient from this FDS approximation for concave, convex or interrupted Pareto fronts. In addition it is capable of computing an optimal solution from this FDS approximation via our hierarchical multiagentsystem (MAS) approach.

The goal of our approach is to accurately approximate the unknown objective functions in order to formulate a FDS. Our approach conducts a dimensionality reduction of the high dimensional input space down to threedimensional and twodimensional representations of the unknown ojective functions for precise approximation. The gained knowledge about the unknown objective functions is then aggregated back to the high dimensional input space via our Bspline surfaces and FDS approximation. 
As our approach is completely automatic, it does not need any supervision from simulation experts. Another advantage of our approach is its performance. It gains its efficiency from a novel splinebased sampling of the parameter space in combination with a novel forestbased simulation dataflow analysis. Another main advantage of our approach is that our Bspline surface based FDS approximation evaluation is computationally very fast and replaces costly simulation evaluations which are usually required. Consequently, our approach also delivers a performance boost when computing a solution for the given MOP. Furthermore, our approach is very generic. It can be easily incorporated into existing SBO approaches which already use a KDP. Even more, the computed Pareto solutions are close to the Pareto front for both, deterministic and stochastic simulations. Another advantage of our approach are the provided optimization strategies. These strategies can be used by stateoftheart MOO solvers in order to investigate a larger bandwidth of the simulated model behavior.

BSpline surface representation of the threedimensional space constructed by simulation input parameter C, simulation time T and objective function space O. 
In order to utilize our proposed FDS approximation for computing an optimal simulaton model configuration solution, we developed a highly parallel optimization system based on our waitfree data management. The optimization system proposed here is based on a hierarchical MAS which aims at dynamically tuning all given input configuration parameters with respect to the approximated FDS, which is retrieved from our KDP. Such hierarchical MAS have already proven their feasibility for solving MOP. Our main idea is that every agent introduces a partwise modelling singleobjective optimization (SOO) and multiobjective optimization (MOO) constraints per input parameter) of the problem and its behaviour and communication to other agents is used to solve the global (MOO) problem. Instead of using a costly evolutionary approach, our MAS directly utilizes our costefficient FDS approximation and can converge much quicker to the solution.
Our MAS is composed of several agent organizations. Each of these organizations aims at optimizing a subset of configuration parameters for one or more simulation objectives, each one represented by our FDS approximation. These agent organizations are defined per specified simulation objective and consist of a hierarchy of two agent types: objective and negotiationagents. For each identified input parameter, one objectiveagent is defined. The goal of every defined objectiveagent is to maximize or minimize every attached simulation objective under Pareto constraints. Several optimization constraints arise because of the underlying MOP. Therefore, a negotiationagent is defined for every specified objective. The goal of every negotiation agent is to manage requests between the objectiveagents in order to satisfy the existing multiobjective constraints between the objectiveagents. Our MAS is based upon our ECS based, waitfree, massively parallel data management approach. Consequently, all agents can communicate and exchange data very quickly, increasing the overall performance of the optimization process. Additionally, agents can be added and removed at runtime to the optimization system without the need of restarting the optimization run because it utilizes the ECS pattern.

Our MAS based optimization approach for a mixed objective problem statement (one multiobjective objective (beta) and two singleobjective problems (alpha, gamma) with three input parameters): Each agent organization optimizes the parameter set for one objective. Negotiation agents handle requests between the objectiveagents in order to effectively find the optimal parameter configuration. 
Results

Our GDS approach outperforms its competitors for approximation error (left) and overall sampling rate of the input space (right). 

Evaluation of one of our use case studies: Our agents are directly initialized at the singleobjective solution and converge fast to the multiobjective solution for a given multiobjective optimization problem. 
Publications
GDS: Gradient based Density Spline Surfaces for Multiobjective Optimization Arbitrary Simulations, ACM SIGSIM PADS 2017, Singapore, May 24  26, 2017Intelligent Realtime 3D Simulations, ACM SIGSIM PADS 2016, Banff, May 15  18, 2017
Knowledge Discovery for Pareto based Multiobjective Optimization in Simulation, ACM SIGSIM PADS 2016, Banff, May 15  18, 2017
Multi Agent System Optimization in Virtual Vehicle Testbeds, EAI SIMUtools, Athens, Greece, Portland, August 24  26, 2015