Pareto simulated annealing—a metaheuristic technique for multiple‐objective combinatorial optimization

Abstract

This paper presents a multiple-objective metaheuristic procedureÐPareto simulated annealing. The goal of the procedure is to find in a relatively short time a good approximation of the set of efficient solutions of a multipleobjective combinatorial optimization problem. The procedure uses a sample, of so-called generating solutions. Each solution explores its neighbourhood in a way similar to that of classical simulated annealing. Weights of the objectives, used for their local aggregation, are tuned in each iteration in order to assure a tendency for approaching the efficient solutions set while maintaining a uniform distribution of the generating solutions over this set. A computational experiment shows that the method is a better tool for approximating the efficient set than some previous proposals.

Tourism Service Scheduling in Smart City Based on Hybrid Genetic Algorithm Simulated Annealing Algorithm

“…In addition to the well-known traveling salesman issue, a smaller problem with two objectives was also solved using the approach. The technique performs well for minor issues, but with large problems, only limited parts of the Pareto front can be reached, as claimed by Czyzak and Jaszkiewicz [70].…”

Tourism Service Scheduling in Smart City Based on Hybrid Genetic Algorithm Simulated Annealing Algorithm

“…In addition to the well-known traveling salesman issue, a smaller problem with two objectives was also solved using the approach. The technique performs well for minor issues, but with large problems, only limited parts of the Pareto front can be reached, as claimed by Czyzak and Jaszkiewicz [70].…”

Performance assessment of multiobjective optimizers: an analysis and review

“…Independently of what definition of "outperformance" we use, it always should be compliant with the most general notion in terms of the -relation, i.e., the statement "algorithm a outperforms algorithm b" should also imply that the outcome A of the first method is better than the outcome B of the second method (A B). 1 More accurate assessments may be possible if preference information is given [9], however, most studies assume that additional knowledge is not available, i.e., all objectives are to be considered equally important.…”

“…• Existing unary indicators at best allow to infer that an approximation set is not worse than another, e.g., the distance indicator by Czyzak and Jaszkiewicz [1], the hypervolume indicator by Zitzler and Thiele [26], or the unary -indicator presented in this paper. However, with many unary indicators and also combinations of unary indicators no statement about the relation between the corresponding approximation sets can be made.…”

NSCSO: a novel multi-objective non-dominated sorting chicken swarm optimization algorithm

“…Generational distance (GD) has a simple design and good practicability and is suitable for comparison between multiple algorithms 52 . GD indicates the distance between the Pareto optimal solution derived by the algorithm and the true value, and its formula is shown in Eq.…”

“…Inverse generational distance (IGD) tests the comprehensive performance of the algorithm 52 . IGD uses the average distance from the solution point in the true value to the solution point found by the algorithm.…”

Tourism Service Scheduling in Smart City Based on Hybrid Genetic Algorithm Simulated Annealing Algorithm

“…In addition to the well-known traveling salesman issue, a smaller problem with two objectives was also solved using the approach. The technique performs well for minor issues, but with large problems, only limited parts of the Pareto front can be reached, as claimed by Czyzak and Jaszkiewicz [70].…”

Performance assessment of multiobjective optimizers: an analysis and review

“…Independently of what definition of "outperformance" we use, it always should be compliant with the most general notion in terms of the -relation, i.e., the statement "algorithm a outperforms algorithm b" should also imply that the outcome A of the first method is better than the outcome B of the second method (A B). 1 More accurate assessments may be possible if preference information is given [9], however, most studies assume that additional knowledge is not available, i.e., all objectives are to be considered equally important.…”

“…• Existing unary indicators at best allow to infer that an approximation set is not worse than another, e.g., the distance indicator by Czyzak and Jaszkiewicz [1], the hypervolume indicator by Zitzler and Thiele [26], or the unary -indicator presented in this paper. However, with many unary indicators and also combinations of unary indicators no statement about the relation between the corresponding approximation sets can be made.…”

NSCSO: a novel multi-objective non-dominated sorting chicken swarm optimization algorithm

“…Generational distance (GD) has a simple design and good practicability and is suitable for comparison between multiple algorithms 52 . GD indicates the distance between the Pareto optimal solution derived by the algorithm and the true value, and its formula is shown in Eq.…”

“…Inverse generational distance (IGD) tests the comprehensive performance of the algorithm 52 . IGD uses the average distance from the solution point in the true value to the solution point found by the algorithm.…”

Tourism Service Scheduling in Smart City Based on Hybrid Genetic Algorithm Simulated Annealing Algorithm

“…In addition to the well-known traveling salesman issue, a smaller problem with two objectives was also solved using the approach. The technique performs well for minor issues, but with large problems, only limited parts of the Pareto front can be reached, as claimed by Czyzak and Jaszkiewicz [70].…”

Performance assessment of multiobjective optimizers: an analysis and review

“…Independently of what definition of "outperformance" we use, it always should be compliant with the most general notion in terms of the -relation, i.e., the statement "algorithm a outperforms algorithm b" should also imply that the outcome A of the first method is better than the outcome B of the second method (A B). 1 More accurate assessments may be possible if preference information is given [9], however, most studies assume that additional knowledge is not available, i.e., all objectives are to be considered equally important.…”

“…• Existing unary indicators at best allow to infer that an approximation set is not worse than another, e.g., the distance indicator by Czyzak and Jaszkiewicz [1], the hypervolume indicator by Zitzler and Thiele [26], or the unary -indicator presented in this paper. However, with many unary indicators and also combinations of unary indicators no statement about the relation between the corresponding approximation sets can be made.…”

NSCSO: a novel multi-objective non-dominated sorting chicken swarm optimization algorithm

“…Generational distance (GD) has a simple design and good practicability and is suitable for comparison between multiple algorithms 52 . GD indicates the distance between the Pareto optimal solution derived by the algorithm and the true value, and its formula is shown in Eq.…”

“…Inverse generational distance (IGD) tests the comprehensive performance of the algorithm 52 . IGD uses the average distance from the solution point in the true value to the solution point found by the algorithm.…”