This study introduces the Borg multi-objective evolutionary algorithm (MOEA) for many-objective, multimodal optimization. The Borg MOEA combines [Formula: see text]-dominance, a measure of convergence speed named [Formula: see text]-progress, randomized restarts, and auto-adaptive multioperator recombination into a unified optimization framework. A comparative study on 33 instances of 18 test problems from the DTLZ, WFG, and CEC 2009 test suites demonstrates Borg meets or exceeds six state of the art MOEAs on the majority of the tested problems. The performance for each test problem is evaluated using a 1,000 point Latin hypercube sampling of each algorithm's feasible parameteri- zation space. The statistical performance of every sampled MOEA parameterization is evaluated using 50 replicate random seed trials. The Borg MOEA is not a single algorithm; instead it represents a class of algorithms whose operators are adaptively selected based on the problem. The adaptive discovery of key operators is of particular importance for benchmarking how variation operators enhance search for complex many-objective problems.
This study contributes a rigorous diagnostic assessment of state-of-theart multiobjective evolutionary algorithms (MOEAs) and highlights key advances that the water resources field can exploit to better discover the critical tradeoffs constraining our systems. This study provides the most comprehensive diagnostic assessment of MOEAs for water resources to date, exploiting more than 100,000 MOEA runs and trillions of design evaluations. The diagnostic assessment measures the effectiveness, efficiency, reliability, and controllability of ten benchmark MOEAs for a representative suite of water resources applications addressing rainfall-runoff calibration, long-term groundwater monitoring (LTM), and risk-based water supply portfolio planning. The suite of problems encompasses a range of challenging problem properties including (1) many-objective formulations with four or more objectives, (2) multi-modality (or false optima), (3) nonlinearity, (4) discreteness, (5) severe constraints, (6) stochastic objectives, and (7) nonseparability (also called epistasis). The applications are representative of the dominant problem classes that have shaped the history of MOEAs in water resources and that will be dominant foci in the future. Recommendations are provided for which modern MOEAs should serve as tools and benchmarks in the future water resources literature.
The growing popularity of multiobjective evolutionary algorithms (MOEAs) for solving many-objective problems warrants the careful investigation of their search controls and failure modes. This study contributes a new diagnostic assessment framework for rigorously evaluating the effectiveness, reliability, efficiency, and controllability of MOEAs as well as identifying their search controls and failure modes. The framework is demonstrated using the recently introduced Borg MOEA, [Formula: see text]-NSGA-II, [Formula: see text]-MOEA, IBEA, OMOPSO, GDE3, MOEA/D, SPEA2, and NSGA-II on 33 instances of 18 test problems from the DTLZ, WFG, and CEC 2009 test suites. The diagnostic framework exploits Sobol's variance decomposition to provide guidance on the algorithms’ non-separable, multi-parameter controls when performing a many-objective search. This study represents one of the most comprehensive empirical assessments of MOEAs ever completed.
The Borg MOEA is a self-adaptive multiobjective evolutionary algorithm capable of solving complex, many-objective environmental systems problems efficiently and reliably. Water and environmental resources problems pose significant computational challenges due to their potential for large Pareto optimal sets, the presence of disjoint Pareto-optimal regions that arise from discrete choices, multi-modal suboptimal regions, and expensive objective function calculations. This work develops two large-scale parallel implementations of the Borg MOEA, the master-slave and multi-master Borg MOEA, and applies them to a highly challenging risk-based water supply portfolio planning problem. The performance and scalability of both implementations are compared on up to 16384 processors. The multi-master Borg MOEA is shown to scale efficiently on tens of thousands of cores while dramatically improving the reliability of attaining high-quality solutions. Our results dramatically expand the scale and scope of complex environmental systems that can be addressed using manyobjective evolutionary optimization.
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