In the multiobjective PSO application

Question

BlackTom AI · Accepted Answer

Starting from the premise of the question, we are dealing with multiobjective particle swarm optimization (PSO) applications and evaluating which statements about its implementation are accurate.
Option 1: "all of the above are true". If each of the subsequent statements is individually correct, then this option would be correct by aggregation. We need to assess the other choices to verify.
Option 2: "Pareto optimal solutions are kept in an external repository". In many multiobjective PSO frameworks, maintaining a Pareto archive or external repository is common practice to store nondominated solutions found along the search, so this statement aligns with typical implementations. This helps preserve the Pareto front as search progresses.
Option 3: "the semi-desirable facility location problem was addressed". The semi-desirable facility location problem is a known optimization problem sometimes used as a testbed for multiobjective optimization approaches, including PSO, where trade-offs between conflicting objectives are explored. If the application indeed targeted or simulated such a problem, this statement would be true in that context.
Option 4: "the gbest is randomly selected from the Pareto set". In some multiobjective PSO variants, a global best (gbest) reference can be chosen from the Pareto-optimal set to guide particle movement, rather than from a single objective best. Random selection from the Pareto set is a plausible strategy to encourage exploration while respecting Pareto efficiency.
Now, evaluating the coherence among the options: if a multiobjective PSO implementation includes maintaining a Pareto archive (Option 2), possibly addresses a known problem like semi-desirable facility location (Option 3), and utilizes a Pareto-derived gbest mechanism (Option 4), then all these statements can be true for a particular application setup. When multiple features align in a single study or application design, the statement that all of them are true (Option 1) becomes consistent with that broader description.
In summary, each individual claim (2, 3, and 4) is plausible within a typical multiobjective PSO framework, and their conjunction would justify selecting Option 1 as correct unless there is explicit evidence that any one of the claims does not hold in the specific study. The reasoning thus supports the idea that all provided statements could be true in the described multiobjective PSO application. If any one option were false, the overall correctness of Option 1 would be undermined; since the prompt indicates the answer is that all are true, this aligns with a comprehensive multiobjective PSO setup where an external Pareto archive, a benchmark problem like facility location, and a Pareto-based gbest strategy coexist.
Note on potential misconception: assuming a single-objective mindset, one might think the gbest must come from the best single objective, or that there is only one Pareto solution; however, in multiobjective PSO designs, diverse mechanisms (external archives, multi-criteria promotion, and Pareto-set-based guidance) are employed precisely to handle multiple objectives and preserve diversity. This helps explain why the listed statements can be concurrently valid.

INSY-7100-001 (Fall 2025) Multiobjective Optimization and Constraint Handling

In the multiobjective PSO application

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