Hybrid Nested Particle Swarm Optimization for a Waste Load Allocation Problem in River System

Abstract

The aim of this article is to develop a hybrid nested particle swarm optimization to solve a Pigovian tax-based waste load allocation problem for river systems. The river system at the Tuojiang River basin is the prototype which is then extended to a generalized waste load allocation problem. The responsible environmental protection agency (EPA), as the leader, sets the pollution tax standards at a given checkpoint to resolve the conflict between the dischargers, and each discharger, as the follower, makes biological oxygen demand (BOD) removal decisions to minimize their own pollution costs under the specified pollution and pollution tax standards. A cooperative bilevel multifollower decision-making model is established that takes into account the objectives and constraints. The particular nature of this model requires the development of a nested particle swarm optimization algorithm. Instead of using a traditional particle performance measurement method, an exact algorithm for solving the lower-level model, called a multi-agent-based dynamic extremal value algorithm (ma-DEV), is proposed and nested to deal with the bilevel model’s specific decision rule. Results for the Deyang section of the Tuojiang River are presented to demonstrate the performance of the proposed optimization method, which proved to be very effective and efficient compared to other heuristic algorithms.