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.

In all cases accepted manuscripts should:  link to the formal publication via its DOI  bear a CC-BY-NC-ND license -this is easy to do, click here to find out how  if aggregated with other manuscripts, for example in a repository or other site, be shared in alignment with our hosting policy  not be added to or enhanced in any way to appear more like, or to substitute for, the published journal article AbstractThe development and application of evolutionary algorithms (EAs) and other metaheuristics for the optimisation of water resources systems has been an active research field for over two decades. Research to date has emphasized algorithmic improvements and individual applications in specific areas (e.g., model calibration, water distribution systems, groundwater management, river-basin planning and management, etc.). However, there has been limited synthesis between shared problem traits, common EA challenges, and needed advances across major applications. This paper clarifies the current status and future research directions for better solving key water resources problems using EAs. Advances in understanding fitness landscape properties and their effects on algorithm performance are critical. Future EA-based applications to real-world problems require a fundamental shift of focus towards improving problem formulations, understanding general theoretic frameworks for problem decompositions, major advances in EA computational efficiency, and most importantly aiding real decision-making in complex, uncertain application contexts.

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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.

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