Trace-based methods for solving nonlinear global optimization and satisfiability problems

In this paper we present a method called NOVEL (Nonlinear Optimization via External Lead) for solving continuous and discrete global optimization problems. NOVEL addresses the balance between global search and local search, using a trace to aid in identifying promising regions before committing to local searches. We discuss NOVEL for solving continuous constrained optimization problems and show how it can be extended to solve constrained satisfaction and discrete satisfiability problems. We first transform the problem using Lagrange multipliers into an unconstrained version. Since a stable solution in a Lagrangian formulation only guarantees a local optimum satisfying the constraints, we propose a global search phase in which an aperiodic and bounded trace function is added to the search to first identify promising regions for local search. The trace generates an information-bearing trajectory from which good starting points are identified for further local searches. Taking only a small portion of the total search time, this elegant approach significantly reduces unnecessary local searches in regions leading to the same local optimum. We demonstrate the effectiveness of NOVEL on a collection of continuous optimization benchmark problems, finding the same or better solutions while satisfying the constraints. We extend NOVEL to discrete constraint satisfaction problems (CSPs) by showing an efficient transformation method for CSPs and the associated representation in finite-difference equations in NOVEL. We apply NOVEL to solve Boolean satisfiability instances in circuit fault detection and circuit synthesis applications, and show comparable performance when compared to the best existing method.