Heuristics and Optimization-Based Methods for the Detection of Generalized Nash Games Solution Sets

Title: Heuristics and Optimization-Based Methods for the Detection of Generalized Nash Games Solution Sets | Academic Seminar
Speaker: Monica G. Cojocaru | Associate Dean Research and Graduate Studies | Director, AI4Casting Hub |College of Computational, Mathematical and Physical Sciences University of Guelp
Date: Wednesday, April 22, 2026
Time: 4:00 PM
Room: LH3058 (Math Boardroom) & Hybrid

Zoom Meeting Link: https://wilfrid-laurier.zoom.us/j/97395852823?pwd=pMvZvxl2KaGlaibjZbo9lGlmUo0m50.1 
Meeting ID: 973 9585 2823
Zoom Meeting Passcode: 609166

SUMMARY

In this paper, we use both numerical optimization methods (NOMs) and heuristic algorithms to compute and describe the set of Generalized Nash Equilibria (GNEs) forming the solution set of a Generalized Nash Game (GNG). We introduce novel performance metrics to assess the quality of the solution sets produced by these algorithms. The two heuristic algorithms, namely the Evolutionary-Inspired Algorithm (EIA) and Stochastic Gradient Descent (SGD), iteratively evolve populations of points within the players’ feasible sets. In contrast, NOMs are executed in parallel from multiple initial points to obtain as many solutions as possible. We implement three NOMs alongside the two heuristic methods on a collection of eleven Generalized Nash Equilibrium Problems (GNEPs), including nine examples with known solution sets and two without. Computational experiments show that EIA generally outperforms all other algorithms in terms of diversity and coverage, including examples without known true solution sets, while the Gauss-Seidel Method (one of the NOMs) achieves slightly better overall performance under the Hausdorff distance (HD) criterion, though EIA attains lower HD values in most individual examples. Overall, the results show that EIA effectively approximates the known solution sets, producing solutions that are diverse, accurate, and well-distributed. Given these findings and the growing popularity of heuristic algorithms, we anticipate that heuristics will be a practical and effective choice for practitioners in applied fields who need to compute multiple equilibria of a GNEP.

BIOGRAPHY

Professor Monica Cojocaru, is a mathematician whose work sits at the intersection of dynamical systems, game theory, and modeling of health and population processes. She is a Professor of Mathematics at the University of Guelph, with more than twenty years of contributions to applied mathematics and biomathematics. Her research spans projected dynamical systems, generalized Nash games, and agent‑based models, with applications to infectious disease transmission, behavioural responses to public‑health interventions, and population‑level decision making. In addition to her research, she held/holds major academic leadership roles, including Associate Dean of Research and Graduate Studies (current) and Interim Dean, (co-)Assist. Vice-president Research Services at UoG. She helped launch interdisciplinary research hubs such as AI4Food, the Canada Cyber Foundry, the AI4Casting Hub, and the Intelligent Environmental Solutions Initiatives, supported the recruitment of 4 CRC chairs and currently oversees the CERC/CIRC chair process in AI4Quntum strategic areas. Professor Cojocaru’s career is also marked by sustained mentorship and international engagement. She has secured more than $3.5 million in PI research funding (Canada, US and EU sources), supervised over 40 HQP, held multiple international visiting positions including a Fulbright Visiting Chair and a Senior Visiting Fellowship, and authored 80+ publications across journals, proceedings, and book chapters.