Funplex: A Modified Simplex Algorithm to Efficiently Explore Near-Optimal Spaces

TL;DR

This paper introduces Funplex, a solver-tailored, multi-objective Simplex-based algorithm for Modeling to Generate Alternatives (MGA) in energy systems. By generating MGA objectives from random unit-direction vectors, tracking intermediary vertices, and using a similarity-driven sequence of objectives, Funplex achieves higher-quality near-optimal spaces with substantially fewer pivots than state-of-the-art MGA methods, demonstrated on a 4-variable energy-hub case. The results show Funplex is roughly five times faster and yields larger, more representative near-optimal spaces; its performance scales favorably with the number of MGA objectives and investment variables, though memory and numerical stability pose practical limits. The study highlights the potential of solver-level innovations to improve MGA accessibility and suggests paths forward, including integrating advanced solver techniques to enable larger-scale applications.

Abstract

Modeling to generate alternatives (MGA) is an increasingly popular method in energy system optimization. MGA explores the near-optimal space, namely, system alternatives whose costs are within a certain fraction of the globally optimal cost. Real-world stakeholders may prefer these alternatives due to intangible factors. Nonetheless, widespread MGA adoption is hampered by its additional computational burden. Current MGA methods identify boundary points of the near-optimal space through repeated, independent optimization problems. Hundreds of model runs are usually required, and such individual runs are often inefficient because they repeat calculations or retrace previous trajectories. In this study, we transcend such limitations by introducing a novel algorithm called Funplex, which uses methods from multi-objective Simplex to optimize many MGA objectives with minimal computational redundancy. For a simple linear-programming energy hub case study, we show that Funplex is five times faster than existing methods and yields higher-quality near-optimal spaces. Furthermore, sensitivity analyses suggest that Funplex scales well with the number of investment variables, making it promising for capacity planning models. The current proof-of-concept implementation based on a full multi-objective tableau may face memory and stability limitations for large models. Nonetheless, future developments based on more advanced versions of Simplex may overcome such barriers, thereby making MGA more accessible and standard among modeling teams.

Figures (8)

• Figure 1: Overview of Funplex's five steps illustrated using the two-dimensional illustration of the near-optimal space in terms of solar and wind capacity.
• Figure 2: Overview of the modelled energy system. The energy hub model optimizes the investment and operation of the seven available technologies over the time horizon of one year, which is approximated using a user-defined number of representative days.
• Figure 3: Cost-optimal solution of the Energy Hub model
• Figure 4: Four-dimensional near-optimal space in terms of wind capacity, PV capacity, gas boiler capacity, and heat pump capacity projected in two dimensions. The lines indicate the outline of the near-optimal space identified by the respective MGA algorithm.
• Figure 5: Near-optimal space of the energy-hub model in terms of wind capacity, PV capacity, gas boiler capacity, and heat pump capacity. The plot shows the region identified by Funplex in (1) its standard form, (2) a version which only saves optimal and not intermediary vertices and (3) a version in which variables are not adjusted for scale.