Welded cylindrical containers usually experience stress corrosion cracking (SCC) in the closure-weld area. Induction coil heating technique may be used to relieve the residual stresses from the closure-weld. This technique involves localized heating of the material by the surrounding coils. The material is then cooled to the room temperature by quenching. A two-dimensional axisymmetric finite element model is developed to study the effects of induction coil heating and subsequent quenching. The finite element results are validated through an experimental test. The parameters of the design are tuned to maximize the compressive stress within a layer of thickness from the outer surface that is equal to the long-term general corrosion of Alloy 22 (Appendix A). The problem is subject to geometrical and stress constraints. Two different solution methods are implemented for this purpose. First, an off-the-shelf optimization software is used to obtain an optimum solution. These results are not satisfactory because of the highly nonlinear nature of the problem. The paper proposes a novel alternative: the Successive Heuristic Quadratic Approximation (SHQA) technique. This algorithm combines successive quadratic approximation with an adaptive random search. Examples and discussion are included.