A review of multiobjective test problems and a scalable test problem toolkit

By Simon Huband, Philip Hingston, L. Barone, Lyndon While. IEEE Transactions on Evolutionary Computation, 2006

1,974 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/344052ba1f58dddeb583fc5fefd2f2bff744215a

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Citations in the corpus

Evolutionary Large-Scale Multi-Objective Optimization: A Survey (2021, neutral): “Table 4 summarizes the features of the benchmark LSMOPs in five widely used artificial test suites, including ZDT [226], DTLZ [35], WFG [71], LSMOP [26], and SMOP [171].”
Direct Multisearch for Multiobjective Optimization (2011, background): “To illustrate how Algorithm 3.1 works, we will now describe in detail its application to problem SP1 [24], defined by: min F (x) ≡ ( (x1 − 1)2 + (x1 − x2)2, (x1 − x2)2 + (x2 − 3)2 ) s.t. − 1 ≤ x1 ≤ 5, − 1 ≤ x2 ≤ 5.”
Multiple Populations for Multiple Objectives: A Coevolutionary Technique for Solving Multiobjective Optimization Problems (2013, background): “Various test problems have been proposed to evaluate the multiobjective optimization algorithms in the literature [49].”
A competitive mechanism based multi-objective particle swarm optimizer with fast convergence (2018, methodology): “For bi-objective problems, the number of decision variables is set to 30 in ZDT1 to ZDT3, to 10 in ZDT4 and ZDT6, to 6 in DTLZ1, to 21 in DTLZ7, to 11 in DTLZ2 to DTLZ6 and all WFG problems.”
A survey on multi-objective evolutionary algorithms for many-objective problems (2014, methodology): “Other test suites used for scalability analysis are the WFG toolkit [39], the CEC 2009 competition problems [105], and a set of problems based on a framework for continuous many-objective test problems with arbitrarily prescribed Pareto set shapes describedin[91];thelasttwoinonlyonework.”
A Grid-Based Evolutionary Algorithm for Many-Objective Optimization (2013, background): “Digital Object Identifier 10.1109/TEVC.2012.2227145 I N THE REAL world, it is not uncommon to face a problemwith several objectives to be met simultaneously, which is known as a multiobjective optimization problem (MOP).”
A New Dominance Relation-Based Evolutionary Algorithm for Many-Objective Optimization (2016, methodology): “As for all WFG problems, unless otherwise stated, the number of decision variables is set to 24 and the position-related parameter is set to m − 1 according to [54] and [73].”
A Classification-Based Surrogate-Assisted Evolutionary Algorithm for Expensive Many-Objective Optimization (2019, methodology): “We also compared the algorithms on the WFG test suite [71], MaF test suite [72], and a car cab design problem [11].”
Decomposition of a Multiobjective Optimization Problem Into a Number of Simple Multiobjective Subproblems (2014, methodology): “The following modified ZDT and DTLZ instances are used [21].”
HypE: An Algorithm for Fast Hypervolume-Based Many-Objective Optimization (2011, positive): “HypE was compared to various state-of-the-art MOEAs with regard to the hy-pervolume indicator values of the generated Pareto-set approximations—on the DTLZ (Deb et al., 2005), the WFG (Huband et al., 2006), and the knapsack (Zitzler and Thiele, 1999) testproblem suites.”
jMetal: A Java framework for multi-objective optimization (2011, positive): “A rich set of test problems including: – Problem families: Zitzler–Deb–Thiele (ZDT) [26], Deb– Thiele–Laumanns–Zitzler (DTLZ) [27], Walking-Fish-Group (WFG) test problems [28]), CEC2009 (unconstrained problems) [29], and the Li-Zhang benchmark [17].”
Fuzzy-Based Pareto Optimality for Many-Objective Evolutionary Algorithms (2014, methodology): “These problem characteristics are summarized in Table II [21].”
A Knee Point-Driven Evolutionary Algorithm for Many-Objective Optimization (2015, methodology): “The parameters of these problems are set as suggested in [55], which are listed in Table VII.”
Benchmark Problems and Performance Indicators for Search of Knee Points in Multiobjective Optimization (2020, methodology): “One unique property of the WFG test suite [48], [49] is that the Pareto front of the test problems can be specified, similar to the idea reported in [50].”
An Evolutionary Algorithm for Large-Scale Sparse Multiobjective Optimization Problems (2020, methodology): “…on testing the performance of algorithms in ﬁnding sparse Pareto optimal solutions, three simple Pareto fronts (i.e., sets of shape functions) taken from DTLZ [58] and WFG [60] are adopted in SMOP1–SMOP8, namely, the linear Pareto front, the convex Pareto front, and the concave Pareto front.”
An easy-to-use real-world multi-objective optimization problem suite (2020, methodology): “For details, refer to [10, 13].”
Multiobjective optimization Test Instances for the CEC 2009 Special Session and Competition (2009, methodology): “Table 1: Properties of the test functions [5]”
Preference-Inspired Coevolutionary Algorithms for Many-Objective Optimization (2013, background): “From [45], the Pareto-front shape WFG4–9 is part of a hyperellipse with radii ri = 2 × i, i = 1, 2, .”
Objective Reduction in Many-Objective Optimization: Linear and Nonlinear Algorithms (2013, background): “The authors [32] categorized the problem variables as either the “distance” variables (changing which results in comparable solutions) or the “position” variables (changing which results in incomparable solutions).”
Balancing Convergence and Diversity in Decomposition-Based Many-Objective Optimizers (2016, methodology): “For comparison purposes, we use the test problems from DTLZ [53] and WFG [54] test suites.”