In this paper, a round-table group optimization (RTGO) algorithm is presented. RTGO is a simple metaheuristic framework using the insights of research on group creativity. In a cooperative group, the agents work in iterative sessions to search innovative ideas in a common problem landscape. Each agent has one base idea stored in its individual memory, and one social idea fed by a round-table group support mechanism in each session. The idea combination and improvement processes are respectively realized by using a recombination search (XS) strategy and a local search (LS) strategy, to build on the base and social ideas. RTGO is then implemented for solving two difficult sequencing problems, i.e., the flowshop scheduling problem and the quadratic assignment problem. The domain-specific LS strategies are adopted from existing algorithms, whereas a general XS class, called socially biased combination (SBX), is realized in a modular form. The performance of RTGO is then evaluated on commonly-used benchmark datasets. Good performance on different problems can be achieved by RTGO using appropriate SBX operators. Furthermore, RTGO is able to outperform some existing methods, including methods using the same LS strategies.