In this paper, four simulated annealing based multiobjective algorithms—SMOSA, UMOSA, PSA and WMOSA have been used to solve multiobjective optimization of constrained problems with varying degree of complexity along with a new PDMOSA algorithm. PDMOSA algorithm uses a strategy of Pareto dominant based fitness in the acceptance criteria of simulated annealing and is improved. In all algorithms, the current solution explores its neighborhoods in a way similar to that of classical simulated annealing. The performance and computational cost for all algorithms have been studied. All algorithms are found to be quite robust with algorithmic parameters and are capable of generating a large number of well diversified Pareto-optimal solutions. The quality and diversification of Pareto-optimal solutions generated by all algorithms are found to be problem specific. The computational cost is least by WMOSA and is followed by PDMOSA. The algorithms are simple to formulate and require reasonable computational time. Hence, the simultaneous use of all algorithms is suggested to obtain a wider spectrum of efficient solutions.