Efficient symbolic multi-objective design space exploration

Nowadays many design space exploration tools are based on Multi-Objective Evolutionary Algorithms (MOEAs). Beside the advantages of MOEAs, there is one important drawback as MOEAs might fail in design spaces containing only a few feasible solutions or as they are often afflicted with premature convergence, i.e., the same design points are revisited again and again. Exact methods, especially Pseudo Boolean solvers (PB solvers) seem to be a solution. However, as typical design spaces are multi-objective, there is a need for multi-objective PB solvers. In this paper, we will formalize the problem of design space exploration as multi-objective 0-1 ILP. We will propose (1) a heuristic approach based on PB solvers and (2) a complete multi-objective PB solver based on a backtracking algorithm that incorporates the non-dominance relation from multi-objective optimization and is restricted to linear objective functions. First results from applying our novel multi-objective PB solver to synthetic problems will show its effectiveness in small sized design spaces as well as in large design spaces only containing a few feasible solutions. For non-linear and large problems, the proposed heuristic approach is outperforming common MOEA approaches. Finally, a real world example from the automotive area will emphasize the efficiency of the proposed algorithms.