A multi-objective hyper-heuristic algorithm based on adaptive epsilon-greedy selection

AbstractA variety of meta-heuristics have shown promising performance for solving multi-objective optimization problems (MOPs). However, existing meta-heuristics may have the best performance on particular MOPs, but may not perform well on the other MOPs. To improve the cross-domain ability, this paper presents a multi-objective hyper-heuristic algorithm based on adaptive epsilon-greedy selection (HH_EG) for solving MOPs. To select and combine low-level heuristics (LLHs) during the evolutionary procedure, this paper also proposes an adaptive epsilon-greedy selection strategy. The proposed hyper-heuristic can solve problems from varied domains by simply changing LLHs without redesigning the high-level strategy. Meanwhile, HH_EG does not need to tune parameters, and is easy to be integrated with various performance indicators. We test HH_EG on the classical DTLZ test suite, the IMOP test suite, the many-objective MaF test suite, and a test suite of a real-world multi-objective problem. Experimental results show the effectiveness of HH_EG in combining the advantages of each LLH and solving cross-domain problems.

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Comparative Analysis of Selection Hyper-Heuristics for Real-World Multi-Objective Optimization Problems

Applied Sciences ◽

10.3390/app11199153 ◽

2021 ◽

Vol 11 (19) ◽

pp. 9153

Author(s):

Vinicius Renan de Carvalho ◽

Ender Özcan ◽

Jaime Simão Sichman

Keyword(s):

Real World ◽

Optimization Problem ◽

Optimization Problems ◽

Exact Algorithms ◽

Mathematical Function ◽

Multi Objective Optimization ◽

Algorithm Selection ◽

Multi Objective ◽

Cross Domain ◽

Domain Performance

As exact algorithms are unfeasible to solve real optimization problems, due to their computational complexity, meta-heuristics are usually used to solve them. However, choosing a meta-heuristic to solve a particular optimization problem is a non-trivial task, and often requires a time-consuming trial and error process. Hyper-heuristics, which are heuristics to choose heuristics, have been proposed as a means to both simplify and improve algorithm selection or configuration for optimization problems. This paper novel presents a novel cross-domain evaluation for multi-objective optimization: we investigate how four state-of-the-art online hyper-heuristics with different characteristics perform in order to find solutions for eighteen real-world multi-objective optimization problems. These hyper-heuristics were designed in previous studies and tackle the algorithm selection problem from different perspectives: Election-Based, based on Reinforcement Learning and based on a mathematical function. All studied hyper-heuristics control a set of five Multi-Objective Evolutionary Algorithms (MOEAs) as Low-Level (meta-)Heuristics (LLHs) while finding solutions for the optimization problem. To our knowledge, this work is the first to deal conjointly with the following issues: (i) selection of meta-heuristics instead of simple operators (ii) focus on multi-objective optimization problems, (iii) experiments on real world problems and not just function benchmarks. In our experiments, we computed, for each algorithm execution, Hypervolume and IGD+ and compared the results considering the Kruskal–Wallis statistical test. Furthermore, we ranked all the tested algorithms considering three different Friedman Rankings to summarize the cross-domain analysis. Our results showed that hyper-heuristics have a better cross-domain performance than single meta-heuristics, which makes them excellent candidates for solving new multi-objective optimization problems.

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A Set Based Newton Method for the Averaged Hausdorff Distance for Multi-Objective Reference Set Problems

Mathematics ◽

10.3390/math8101822 ◽

2020 ◽

Vol 8 (10) ◽

pp. 1822

Author(s):

Lourdes Uribe ◽

Johan M Bogoya ◽

Andrés Vargas ◽

Adriana Lara ◽

Günter Rudolph ◽

...

Keyword(s):

Hausdorff Distance ◽

Performance Indicators ◽

Pareto Front ◽

Optimization Problems ◽

Benchmark Problems ◽

Multi Objective Optimization ◽

Multi Objective ◽

Reference Set ◽

Common Task ◽

Objective Reference

Multi-objective optimization problems (MOPs) naturally arise in many applications. Since for such problems one can expect an entire set of optimal solutions, a common task in set based multi-objective optimization is to compute N solutions along the Pareto set/front of a given MOP. In this work, we propose and discuss the set based Newton methods for the performance indicators Generational Distance (GD), Inverted Generational Distance (IGD), and the averaged Hausdorff distance Δp for reference set problems for unconstrained MOPs. The methods hence directly utilize the set based scalarization problems that are induced by these indicators and manipulate all N candidate solutions in each iteration. We demonstrate the applicability of the methods on several benchmark problems, and also show how the reference set approach can be used in a bootstrap manner to compute Pareto front approximations in certain cases.

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