## 3 Multi-Objective Optimization Algorithms
### Optimized multi-Objective Particle Swarm Optimization (OMOPSO)
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**Comparison Criteria** & **GA, NSGA-II, and SPEA2** & **PSO and OMOPSO** & **SSO and MOSFET** & **MAs (Hybrid GAs)** \\ \hline Type of procedure & Discrete procedures & Continuous procedures & Continuous procedures & Hybrid procedures \\ \hline Type of a metaphor & [PERSON]’s theory of evolution applied to biology, which simulates the construction of chromosome and its evolution. & Social interaction, which simulates the movement of birds flock while searching for food. & Natural fertilization procedure, which simulates the motility of sperm swarm through the fertilization procedure. & [PERSON]’s theory of natural evolution that simulates the construction of chromosome and its evolution as well as it uses [PERSON]’s notion of a meme. \\ \hline Solutions need ranking and selection & Solutions will be ranked through the evaluations. Selection operator will filter out the population. Routlet wheel selection is an example of selection operator in GA. & Solutions will not be ranked through the evaluations. There is no selection operation. & Solutions will not be ranked through the evaluations. There is no selection operator with filter out the population. Roulette wheel selection \\ \hline Use crossover operation & Use different types of crossover operations such as Simulated Binary Crossover (SBO). & Do not use crossover operations. & Do not use crossover operations. & Use different types of crossover operations such as Simulated Binary Crossover (SBO). \\ \hline Use mutation operation & Use different types of mutation such as polynomial mutation. & OMOPSO uses different types of mutation such as uniform mutation and non-uniform mutation on the second part, and also it does not apply any mutation on the third part of the swarm. & MOSFET divides the swarm into three equal parts, after that, performs uniform mutation on the first part and non-uniform mutation on the second part, and also it does not apply any mutation on the third part of the swarm. & Use different types of mutation such as polynomial mutation. \\ \hline Influence of population size or swarm size on solution time & Exponential & Linear & Linear & Exponential \\ \hline Population affected by best solution & Deal with each individual independently. & Use the solution of swarm leader (best solution) to add it for other individual solutions. & Use the best solution (the value of winner) as a reference value for other members in the swarm to adjust their velocities. & Use local search to improve the results. \\ \hline Average fitness value cannot get worse & Average fitness will not be worse because the individual will be ranked from the best to the worse. The best individuals will be reserved for next step while the worst will be eliminated. & Average fitness will not be worse because the voters because the voters will be the winner will use the voters. The best solution is added to all other velocities in the swarm. & Average fitness will not be worse because the individual will be ranked from the best to the worse. The best individuals will be reserved for next step while the worst will be eliminated. & Average fitness will not be worse because the individual will be ranked from the best to the worse. The best individuals will be reserved for next step while the worst will be eliminated. \\ \hline Convergence & Less than PSO, OMOPSO, SSO, and MOSFET. & More than GA, NSGA-II, and SPEA2. & More than GA, PSO, NSGA-II, OMOPSO, and SPEA2. & More than GAs. \\ \hline Ability to find good solution and explanation related to the Pareto front more than SPEA2. & NGA-II finds good solution and approximation related to the Pareto front more than SPEA2. & OMOPSO finds good solution solution and approximation related to the Pareto front more than the Pareto front more than OMOPSO, SPEA2 and NSGA-II. & MOSFP finds good solution and approximation related to the Pareto front more than OMOPSO, SPEA2 and NSGA-II. & MOSFET finds good solution and approximation related to the Pareto front more than OMOPSO, SPEA2 and NSGA-II. \\ \hline \hline \end{tabular}
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