Two new jumping gene (JG) adaptations of the binary-coded, elitist non-dominated sorting genetic algorithm, NSGA-II are developed. Three benchmark problems are first solved to compare the performance of these adaptations with the earlier JG adaptations of NSGA-II. Single- and multi-objective optimal design of a shell and tube heat exchanger is then carried out using the new sJG (specific JG) adaptation of NSGA-II. The optimal design of the shell and tube heat exchanger (HX) is carried out using a compact formulation of the Bell-Delaware method, coupled with NSGA-II-sJG. Some of the decision variables are continuous, while the others are discrete. The number of binaries used for coding each of these is different. Two multi-objective problems are solved. In the first problem, the cooling water is returned to its source after use, without cooling. The total (annualized) cost and the amount of cooling water required, are minimized simultaneously. in the second problem, it is assumed that the cooling water is recycled to the HX after it is cooled in a cooling tower (which is not being designed). In this, the total (annualized) cost of the heat exchanger (including that of the cooling tower), and the amount of cooling water needed, are minimized. A Pareto set of non-dominated solutions is obtained for both these problems. (c) 2007 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.