Adaptive Methods for Multiobjective Unit Commitment

TL;DR

This paper introduces scalable optimization methods for multiobjective unit commitment, effectively balancing environmental and economic objectives while reducing computational time compared to traditional heuristics.

Contribution

It proposes a novel optimization framework using epsilon constraints, adaptive weights, and McCormick relaxations to efficiently approximate Pareto frontiers in multiobjective unit commitment.

Findings

Significant reduction in computational time with the proposed methods

Effective approximation of Pareto frontiers on real network data

Outperforms standard solvers like Gurobi in efficiency

Abstract

This work considers a multiobjective version of the unit commitment problem that deals with finding the optimal generation schedule of a firm, over a period of time and a given electrical network. With growing importance of environmental impact, some objectives of interest include CO2 emission levels and renewable energy penetration, in addition to the standard generation costs. Some typical constraints include limits on generation levels and up/down times on generation units. This further entails solving a multiobjective mixed integer optimization problem. The related literature has predominantly focused on heuristics (like Genetic Algorithms) for solving larger problem instances. Our major intent in this work is to propose scalable versions of mathematical optimization based approaches that help in speeding up the process of estimating the underlying Pareto frontier. Our contributions are computational and rest on two key embodiments. First, we use the notion of both epsilon constraints and adaptive weights to solve a sequence of single objective optimization problems. Second, to ease the computational burden, we propose a Mccormick-type relaxation for quadratic type constraints that arise due to the resulting formulation types. We test the proposed computational framework on real network data from [1,50] and compare the same with standard solvers like Gurobi. Results show a significant reduction in complexity (computational time) when deploying the proposed framework.