This paper explores the use of a self-adaptive multipopulation elitist (SAMPE) Jaya algorithm for the economic optimization of shell-and-tube heat exchanger (STHE) design. Three different optimization problems of STHE are considered in this work. The same problems were earlier attempted by other researchers using genetic algorithm (GA), particle swarm optimization (PSO) algorithm, biogeography-based optimization (BBO), imperialist competitive algorithm (ICA), artificial bee colony (ABC), cuckoo-search algorithm (CSA), intelligence-tuned harmony search (ITHS), and cohort intelligence (CI) algorithm. The Jaya algorithm is a newly developed algorithm and it does not have any algorithmic-specific parameters to be tuned except the common control parameters of number of iterations and population size. The search mechanism of the Jaya algorithm is upgraded in this paper by using the multipopulation search scheme with the elitism. The SAMPE-Jaya algorithm is proposed in this paper to optimize the setup cost and operational cost of STHEs simultaneously. The performance of the proposed SAPME-Jaya algorithm is tested on four well-known constrained, ten unconstrained standard benchmark problems, and three STHE design optimization problems. The results of computational experiments proved the superiority of the proposed method over the latest reported methods used for the optimization of the same problems.