Scalable multi-objective optimization test problems

By Kalyanmoy Deb, Lothar Thiele, Marco Laumanns, Eckart Zitzler. Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600), 2002

1,711 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/e2f4c72965231d9f7ff8fe92d518a00165735c1f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Yaochu Jin
2. Ran Cheng
3. Xing-yi Zhang
4. Ye Tian
5. Hisao Ishibuchi
6. Xin Yao
7. Gary G. Yen
8. Kalyanmoy Deb

In Computational Theory and Mathematics

1. Yaochu Jin
2. Ran Cheng
3. Xing-yi Zhang
4. Ye Tian
5. Kalyanmoy Deb
6. Gary G. Yen
7. Xin Yao
8. Hisao Ishibuchi

Citations in the corpus

• A Tutorial on Evolutionary Multiobjective Optimization (2004, background): “There are different problem difficulties that make these goals hard to achieve as discussed in detail in [6, 9 ]; accordingly various design variants have been suggested for different types of problems, and we will briefly summarize the main variants in this section.”
• A Scalable Multi-objective Test Problem Toolkit (2005, methodology): “Related by authorship to Deb’s toolkit are the DTLZ test problems [4, 8], which, unlike the majority of multi-objective problems, are scalable objectivewise.”
• SMS-EMOA: Multiobjective selection based on dominated hypervolume (2007, background): “For DTLZ4, ten runs are executed and five for all other DTLZ and ZDT functions.”
• Reducing the run-time complexity of multiobjective EAs: The NSGA-II and other algorithms (2003, methodology): “• The DTLZ1 benchmark from [ 11 ] was used, since it is a standard multiobjective benchmark and since it is scalable (any number of objectives can be used).”
• A faster algorithm for calculating hypervolume (2006, methodology): “For each front, we generated mathematically a representative set of 10 000 points from the (known) Pareto optimal set.”
• A survey on multi-objective evolutionary algorithms for many-objective problems (2014, methodology): “[57]werethefirsttousetheDTLZsuite [25]tocomparetheperformanceofthreeMOEAsinamany-objectivecontext.”
• Borg: An Auto-Adaptive Many-Objective Evolutionary Computing Framework (2013, methodology): “ǫ-MOEA (Deb et al., 2002b) and ǫ-NSGA-II (Kollat and Reed, 2006) are two popular algorithms using ǫ-dominance included in this study.”
• MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition (2007, methodology): “We use five widely used bi-objective ZDT test instances [33] and two 3-objective instances [ 34 ] in comparing MOEA/D with NSGA-II [16], one of the most successful nondecomposition MOEAs.”
• Evaluating the -Domination Based Multi-Objective Evolutionary Algorithm for a Quick Computation of Pareto-Optimal Solutions (2005, methodology): “Here, we concentrate on the 12-variable DTLZ3 test problem, which has a large number of local Pareto-optimal fronts and one global front (Deb et al., 2002b).”
• Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization (2020, methodology): “1 Additional Synethetic Benchmarks We include two additional synthetic benchmarks: a Constrained Branin-Currin problem [6] and the additional commonly used disk constraint (d = 2,M = 2, V = 1) [28, 40], and the DTLZ2 problem from the MO literature [14] (d = 6,M = 2).”
• Omni-optimizer: A generic evolutionary algorithm for single and multi-objective optimization (2008, methodology): “For all these problems, we use a population of size 100, except in OSY and DTLZ4, where we use a population size of 200 and 300, respectively.”
• Multiobjective optimization Test Instances for the CEC 2009 Special Session and Competition (2009, methodology): “D p p p = p : the penalty value To overcome the shortcomings of the DTLZ test functions for which the global optimum lies on the lower bound, or in the center of the search range, we extend the lower bound zmin by d.”
• Multiobjective Optimization Problems With Complicated Pareto Sets, MOEA/D and NSGA-II (2009, methodology): “For example, the PSs of the ZDT test instances [19] with two objectives are part of a line segment defined by and the PSs of the DTLZ test instances [20] with three objectives are subsets of There is no reason that real world problems have such simple PSs. 2 Observing these oversimplified PSs in the…”
• A competitive mechanism based multi-objective particle swarm optimizer with fast convergence (2018, methodology): “A total of 21 benchmark MOPs from three test suits, ZDT [52], DTLZ [8] and WFG [13] are used to evaluate the performance of the algorithms, where ZDT1 to ZDT4 and ZDT6 are bi-objective problems and two-/three-objective DTLZ and WFG test problems are considered.”
• 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.”
• A MOPSO Algorithm Based Exclusively on Pareto Dominance Concepts (2005, methodology): “We compared the efficiency of the global guide selection methods on standard test problems DTLZ1–DTLZ3 [13], whose definitions for three objectives are provided in Table 1.”