Numerous problems encountered in real life cannot be actually formulated as a single objective problem; hence the requirement of Multi-Objective Optimization (MOO) had arisen several years ago. Due to the complexities in such type of problems powerful heuristic techniques were needed, which has been strongly satisfied by Swarm Intelligence (SI) techniques. Particle Swarm Optimization (PSO) has been established in 1995 and became a very mature and most popular domain in SI. Multi-Objective PSO (MOPSO) established in 1999, has become an emerging field for solving MOOs with a large number of extensive literature, software, variants, codes and applications. This paper reviews all the applications of MOPSO in miscellaneous areas followed by the study on MOPSO variants in our next publication. An introduction to the key concepts in MOO is followed by the main body of review containing survey of existing work, organized by application area along with their multiple objectives, variants and further categorized variants.

The present study brings together the bene ts of the results of exergy, exergoeconomic, and exergoenvironmental analyses as well as optimization of a wasteto-energy power plant. First, exergoeconomic balance for each stream was calculated. To validate the current simulations, the actual data from the Amsterdam waste-to-energy power plant in working conditions were examined. Moreover, the behaviors of the in uential parameters in the objective functions were evaluated. In order to perform multi-objective optimization, Multi-Objective Particle-Swarm Optimization (MOPSO) algorithm was employed. To obtain the optimum operating conditions, 14 design parameters and 3 objective functions were taken into consideration, with the total cost rate, total exergy e ciency of the cycle, and environmental impacts as the objective functions. Finally, the TOPSIS decision-making method determined the optimum-operating conditions. The results of exergy analysis indicated that the most exergy destruction belonged to the incinerator unit at 66%. Instead, the pumps contributed the least in this  eld (approximately 1%). Under the in uence of the optimization process, the total exergy e ciency of the power plant increased from 30. 89% to 38. 9% at the total cost of 5188. 05 USD/hour. A comparison of the obtained results from the optimization procedure revealed that introducing optimum working condition would cause an increase in the exergy e ciency and a decrease in the exergy destruction among the components.

Financial optimization is one of the most attractive areas in decision-making under uncertainty. Portfolio selection problem is a classical financial problem but it relies on three restrictive assumptions. In this paper, we propose the multi-stage mean-semivariance-Skewness portfolio optimization problem under transaction cost. Solving the multi-stage portfolio optimization problem is very challenging due to nonlinearity of the problem. Having modeled the problem, both particle swarm optimization and multi objective particle swarm optimization (MOPSO) algorithm are utilized to solve the presented model. Finally, some numerical examples are given to illustrate the effectiveness of the proposed approach and the feasibility of the MOPSO algorithm.

The main problem of water resources planning is the inappropriate allocation between different consumers. Water allocation planning is a complex, multi-variable, and multi-constraint problem, which requires advanced optimization methods to be solved. Classical optimization methods are facing some limitations such as being trapped in local optimum points, and difficulties in handling different variables. In this paper two of these methods including particle swarm optimization, PSO and multiobjective non-dominated sorting genetic algorithms, NGGAII were explored and their efficiency in optimization water reservoir operation problems is compared. Dealing with the necessary of multiobjective programing accuracy, two single objective models was developed separately using PSO to verify the NSGAII results.