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While research on constrained optimization using evolutionary algorithms has been actively pursued, it has had to face the problem that the ability to solve multi-modal problems, which have many local solutions within a feasible region, is insufficient, that the ability to solve problems with equality constraints is inadequate, and that the stability and efficiency of searches is low. We proposed the epsivDE, defined by applying the epsiv constrained method to a differential evolution (DE). DE is a simple, fast and stable population based search algorithm that is robust to multi-modal problems. The epsivDE is improved to solve problems with many equality constraints by introducing a gradient-based mutation that finds feasible point using the gradient of constraints at an infeasible point. Also the epsivDE is improved to find feasible solutions faster by introducing elitism where more feasible points are preserved as feasible elites. The improved epsivDE realizes stable and efficient searches that can solve multi-modal problems and those with equality constraints. The advantage of the epsivDE is shown by applying it to twenty four constrained problems of various types.