Using a computational weld mechanics (CWM) frame-work for exploring a design space, a recent direct-search algorithm from Kolda, Lewis and Torczon is modified to use a least-square approximation to improve the method of following a path to the minimum in the algorithm. To compare the original and modified algorithms, a CWM optimization problem on a 152 × 1220 × 12.5 mm bar of Aluminum 5052-H32 to minimize the weld distortion mitigated by a side heating technique is solved. The CWM optimization problem is to find the best point in the space of side heater design parameters: power, heated area, longitudinal and transverse distance from the weld such that the final distortion is as low as possible (minimized). This CWM optimization problem is constrained to keep the stress level generated by the side heaters, in the elastic region to avoid adding an additional permanent plastic strain to the bar. The number of iterations, size of design of experiments (DOE) matrix required and CPU time to find the minimum for the two algorithms are compared.