Efficiently Optimizing for Dendritic Connectivity on Tree-Structured Networks in a Multi-Objective Framework

Abstract

We provide an exact and approximation algorithm based on Dynamic Programming and an approximation algorithm based on Mixed Integer Programming for optimizing for the so-called dendritic connectivity on tree-structured networks in a multi-objective setting. Dendritic connectivity describes the degree of connectedness of a network. We consider different variants of dendritic connectivity to capture both network connectivity with respect to long and short-to-middle distances. Our work is motivated by a problem in computational sustainability concerning the evaluation of trade-offs in ecosystem services due to the proliferation of hydropower dams throughout the Amazon basin. In particular, we consider trade-offs between energy production and river connectivity. River fragmentation can dramatically affect fish migrations and other ecosystem services, such as navigation and transportation. In the context of river networks, different variants of dendritic connectivity are important to characterize the movements of different fish species and human populations. Our approaches are general and can be applied to optimizing for dendritic connectivity for a variety of multi-objective problems on tree-structured networks.

Tackling Climate Change with Machine Learning

“…This overlap has already been fruitful; numerous papers have considered problems relevant to climate change from the perspective of reconciling conflicting objectives and minimizing side-effects (negative externalities): for instance, in energy planning [662][663][664] and generation (e.g. [665], see also §1), computational sustainability for design or planning of infrastructure [89,666,667] (see also §3) and manufacturing [668], waste management [669], decisions about land use (e.g. [670,671]; see also §5), supply-chain management [672], air-quality measurement [673], and policy development [674].…”

Tackling Climate Change with Machine Learning

“…Practitioners have applied bio-inspired algorithms such as particle swarm, genetic, or evolutionary algorithms to search for or compute Pareto-optimal solutions that satisfy the constraints. This approach has been applied in a number of climate change-related fields, including energy and infrastructure planning [38,325,525,635,732,856], industry [122,334], land use [462,809], and more [127,317,539,761]. Previous work has also employed parallel surrogate search, assisted by ML, to efficiently solve multi-objective optimization problems [11].…”

Reducing adverse impacts of Amazon hydropower expansion

“…This optimization problem is computationally intensive because it requires accounting for 2 509 (~10 153 ) possible combinations of the 509 current and proposed dams in the Amazon basin. To overcome this challenge, we developed a fully polynomialtime approximation algorithm based on dynamic programming that, unlike previous heuristic approaches, can quickly approximate the Pareto frontier for multiple environmental criteria simultaneously and with guarantees of theoretical optimality (27)(28)(29). Given the vast number of Pareto-optimal solutions and the limitations of human cognition to visualize high-dimensional spaces such as a six-dimensional Pareto frontier, we developed an interactive graphical user interface (GUI) to navigate the high-dimensional solution space for Amazon dams (see materials and methods section 2.5 in the supplementary materials) (30).…”