Computationally Expensive Multi-objective Optimization Algorithm

A Computationally Expensive Multi-objective Optimization Algorithm is a Computationally Expensive Algorithm that can optimized by a multiobjective optimization method.

• Example(s):
  • an unoptimized algorithm involving black box functions.
  • computational fluid dynamics simulations utilizing finite element algorithms.
  • …
• Counter-Example(s):
  • an Heuristic Algorithm,
  • PAMELI Algorithm (Cuervo et al., 2021),
  • SOCEMO Algorithm (Muller, 2017),
  • a Swarm Intelligence Algorithm,
  • a Tabu Search Algorithm,
  • a Simulated Annealing Algorithm,
  • a Genetic Algorithm,
  • Artificial Neural Networks,
  • Support Vector Machines.
• See: Computational Complexity Theory, Exponential Algorithm, NP-hard, Cost Model, Multi-objective Optimization Problem, Evolutionary Algorithm, Pareto Optimal Front.

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References

2021

• (Cuervo et al., 2021) ⇒ Santiago Cuervo, Miguel Melgarejo, Angie Blanco-Canon, Laura Reyes-Fajardo, and Sergio Rojas-Galeano (2021). "PAMELI: A Meta-Algorithm for Computationally Expensive Multi-Objective Optimization Problems". arXiv preprint arXiv:2103.10736.
  • QUOTE: We present an algorithm for multi-objective optimization of computationally expensive problems (...)

    We synthesize these ideas in our proposed algorithm for multi-objective optimization, called Pareto set Approximation by Meta-Exploration of Landscape Identifiers (PAMELI). The pseudocode of PAMELI is presented in Algorithm 1 and Fig. 2 illustrates its components and the relations between them.

2019

• (Chugh et al., 2019) ⇒ Tinkle Chugh, Karthik Sindhya, Jussi Hakanen, and Kaisa Miettinen (2019). "A Survey On Handling Computationally Expensive Multiobjective Optimization Problems with Evolutionary Algorithms". In: Soft Computing, 23(9), 3137-3166. DOI:10.1007/s00500-017-2965-0.
  • QUOTE: In many problems, explicit formulations of objective or constraint functions are not known and such functions are called black box functions. Usually, problems involving such functions need a long time to be solved e.g. problems involving computational fluid dynamics simulations utilizing finite element algorithms take substantial time to obtain one solution. These are examples of problems that we refer to as computationally expensive multiobjective optimization problems.

2017

• (Muller, 2017) ⇒ Juliane Muller (2017). "SOCEMO: Surrogate Optimization of Computationally Expensive Multiobjective Problems". In: INFORMS Journal on Computing 29(4):581-596. DOI:10.1287/ijoc.2017.0749.
  • QUOTE: We present the algorithm SOCEMO for optimization problems that have multiple conflicting computationally expensive black-box objective functions. The computational expense arising from the objective function evaluations considerably restricts the number of evaluations that can be done to find Pareto-optimal solutions. Frequently used multiobjective optimization methods are based on evolutionary strategies and generally require a prohibitively large number of function evaluations to find a good approximation of the Pareto front. SOCEMO, in contrast, employs surrogate models to approximate the expensive objective functions.

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