This paper addresses constrained and optimal engineering problems solved using an adapted particle swarm optimization (PSO) algorithm. In fact, a specific constraint-handling mechanism is presented. It consists of a closeness evaluation of the solutions to the feasible region. The total constraints violation is introduced as an objective function to minimize. Interval arithmetic is used to normalize the total violations. The resulting objective problem is solved using a simple lexicographic method. The new algorithm is called CVI-PSO for constraint violation with interval arithmetic PSO. The paper provides numerous experimental results based on a well-known benchmark and comparisons with previously reported results. Finally, a case study of the optimal design of an electrical actuator with several model reformulations is detailed