Screening robust water infrastructure investments and their trade-offs under global change: A London Example

AbstractWe propose an approach for screening future infrastructure and demand management investments for large water supply systems subject to uncertain future conditions. The approach is demonstrated using the London water supply system. Promising portfolios of interventions (e.g., new supplies, water conservation schemes, etc.) that meet London’s estimated water supply demands in 2035 are shown to face significant trade-offs between financial, engineering and environmental measures of performance. Robust portfolios are identified by contrasting the multi-objective results attained for (1) historically observed baseline conditions versus (2) future global change scenarios. An ensemble of global change scenarios is computed using climate change impacted hydrological flows, plausible water demands, environmentally motivated abstraction reductions, and future energy prices. The proposed multi-scenario trade-off analysis screens for robust investments that provide benefits over a wide range of futures, including those with little change. Our results suggest that 60 percent of intervention portfolios identified as Pareto optimal under historical conditions would fail under future scenarios considered relevant by stakeholders. Those that are able to maintain good performance under historical conditions can no longer be considered to perform optimally under future scenarios. The individual investment options differ significantly in their ability to cope with varying conditions. Visualizing the individual infrastructure and demand management interventions implemented in the Pareto optimal portfolios in multi-dimensional space aids the exploration of how the interventions affect the robustness and performance of the system

Few smooth d-polytopes with n lattice points

We prove that, for fixed n there exist only finitely many embeddings of Q-factorial toric varieties X into P^n that are induced by a complete linear system. The proof is based on a combinatorial result that for fixed nonnegative integers d and n, there are only finitely many smooth d-polytopes with n lattice points. We also enumerate all smooth 3-polytopes with at most 12 lattice points. In fact, it is sufficient to bound the singularities and the number of lattice points on edges to prove finiteness.Comment: 20+2 pages; major revision: new author, new structure, new result

Using multivariate regression trees and multiobjective tradeoff sets to reveal fundamental insights about water resources systems

This paper presents the use of Multivariate Regression Trees (MRTs) to analyze Multiobjective Evolutionary Algorithm (MOEA) tradeoff sets generated from a long-term water utility planning problem. MOEAs produce large sets of non-dominated solutions, where each solution represents an observation of how multiple predictor variables (decision levers) impact performance in multiple response variables (objectives). Because they explicitly accommodate multiple response variables, MRTs can preserve the relationships between objectives revealed through MOEA-assisted optimization. We generated MRTs for two tradeoff sets that resulted from optimizing the Eldorado Utility planning problem under two climate change scenarios. A single MRT helped identify the subset of core planning decisions that led to preferred performance and demonstrated how decision preferences impacted performance in different objectives. Comparing MRTs from two scenarios revealed decisions that performed well across scenarios. The systematic and repeatable MRT approach can help water managers understand large, high-dimensional tradeoff sets and prompt additional promising analyses. Highlights &bull; MOEA tradeoff sets contain information that can be hard to extract heuristically&bull; MRTs offer an unbiased, repeatable method to analyze MOEA tradeoff sets&bull; MRTs can reveal core planning decisions that perform well across future scenarios</p

Testing the potential of Multiobjective Evolutionary Algorithms (MOEAs) with Colorado water managers

Multiobjective Evolutionary Algorithms (MOEAs) generate quantitative information about performance relationships between a system&rsquo;s potentially conflicting objectives (termed tradeoffs). Research applications have suggested that evaluating tradeoffs can enhance long term water utility planning, but no studies have formally engaged with practitioners to assess their perceptions of tradeoffs generated by MOEAs. This article examines how practitioners interact with MOEA tradeoffs and reports their ideas for how their agencies could use MOEA results. We hosted a group of Colorado water managers at a charrette, or structured investigatory workshop, where they directly interacted with tradeoffs, discussed how they used the information, and linked their workshop experiences to opportunities for MOEAs to enhance their agencies&rsquo; planning processes. We found that while managers approached tradeoff analyses differently, they all sought to understand relationships between decisions and performance. Managers&rsquo; feedback about processing tradeoffs as well as opportunities and challenges for real-world applications suggest promising future research directions.</p

Testing the potential of Multiobjective Evolutionary Algorithms (MOEAs) with Colorado water managers

Highlights: &bull; Structured workshop effectively provided managers with hands-on tradeoff experience&bull; Interactive MOEA tradeoffs aided in creation of decision dominance structure&bull; Increasing tradeoff info often resulted in revised and divergent portfolio choices&bull; Managers suggested opportunities and challenges to using MOEAs for planning Abstract: Multiobjective Evolutionary Algorithms (MOEAs) generate quantitative information about performance relationships between a system&rsquo;s potentially conflicting objectives (termed tradeoffs). Research applications have suggested that evaluating tradeoffs can enhance long term water utility planning, but no studies have formally engaged with practitioners to assess their perceptions of tradeoffs generated by MOEAs. This article examines how practitioners interact with MOEA tradeoffs and reports their ideas for how their agencies could use MOEA results. We hosted a group of Colorado water managers at a charrette, or structured investigatory workshop, where they directly interacted with tradeoffs, discussed how they used the information, and linked their workshop experiences to opportunities for MOEAs to enhance their agencies&rsquo; planning processes. Among other interesting results, we found that managers&rsquo; portfolio preferences diverged as tradeoff information increased and that structured information about the relationships between decision levers and performance would be beneficial for interpreting tradeoffs.</p

Parasol: an open source, interactive parallel coordinates library for multi-objective decision making

Highlights- We introduce Parasol, an open source visualization library- Parallel coordinates (PC) are well-suited for environmental decision making- Parasol provides building blocks for constructing PC-based web apps- Web apps are easily shared and promote interactive data visualization Abstract This paper introduces Parasol- an open source, interactive visualization library to support the development of web applications for multi-objective decision making. Multi-objective optimization is a popular way to explore competing objectives in environmental management problems. Interactive visualizations allow stakeholders to explore and gain insights about the large, high-dimensional datasets produced by multi-objective optimization. Among visualization methods, parallel coordinates are well-suited for this task. However, current software and open source libraries have limited support for these plots. The Parasol library described in this work provides developers with the building blocks to create sharable, interactive parallel coordinates web applications. Moreover, by incorporating state of the art clutter reduction techniques- "such as clustering, linking, brushing, marking, and bundling- Parasol improves upon traditional parallel coordinates visualizations. We demonstrate the benefit of such features through simple examples and by exploring a real-world water resources problem commonly used in multi-objective optimization literature.</p