Document Type : Research Article
Authors
1 Department of Mathematics, College of Education for Pure Sciences, University of Babylon, Babylon, Iraq
2 College of Information Technology, University of Babylon, Babylon, Iraq
Abstract
We formulate roadside greenbelt design in arid highway corridors as a constrained multi-objective mixed-integer nonlinear program on a discretized cross-section consisting of a median and two verges. Activating a cell installs a cluster of one species, and a per-zone irrigation variable fixes the realized crown geometry. Three functionals are minimized: the daily sensible-heat release, the worst-case A-weighted level at residential receivers, and a roadside risk index that combines fixed-object hazard with aeolian shelter. The irrigation volume is bounded by an ε-constraint. We prove that the marginal risk response is non-monotone in lateral offset, with a unique interior minimizer beyond the clear zone; that the functionals select incompatible sides, so that every efficient design is transversely asymmetric; and that the scalarized problem is NP-hard. A converged evolutionary study on a 1 km corridor at 33.3◦N recovers both structural predictions: the designs place 63–100% of the activated verge cells on the receiver side, that is, the side carrying the modeled residences.
Highlights
- Cross-sectional highway greenbelt design is posed as a three-zone, cell-activation MINLP with irrigation-coupled crown growth.
- Proves that the marginal safety effect of roadside planting is non-monotone in lateral offset, with a unique interior minimiser.
- Shows acoustic and safety objectives structurally disagree on which verge to plant, forcing transverse asymmetry in every efficient design.
- Establishes NP-hardness of the scalarised design problem, including a strongly NP-hard case under crown-spacing constraints.
- NSGA-II study on a 1 km, 550-cell corridor recovers both structural predictions without any built-in side or offset preference.
Keywords
- Multi-objective optimization
- Mixed-integer nonlinear programming
- Pareto front
- Roadside safety
- Spatial discretization
Main Subjects
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