QA688 : Novel Neural Networks for Approximating the Pareto Front in Multi-Objective Optimization Problems
Thesis > Central Library of Shahrood University > Mathematical Sciences > PhD > 2025
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Abstarct: Multi-objective optimization problems involve more than one objective function that must be
optimized simultaneously. Instead of yielding a single solution, such problems provide a set of
efficient solutions forming the Pareto front.
This study presents neural network models and novel algorithms for effectively solving
linear, convex, and non-convex multi-objective problems.
First, for linear problems, neural network models are designed baxsed on Karush-Kuhn-
Tucker (KKT) optimality conditions, which directly extract efficient solutions without transforming
the multi-objective problem into a single-objective one. The stability, and their global
convergence of the models is proved using Lyapunov’s method is mathematically established.
Next, for non-convex problems, two algorithmic frxameworks are developed: 1) reducing the
feasible region and applying a branch and bound approach combined with equivalent convex
reformulations solved via neural networks, 2) rewriting the non-convex problem into a convex
one using the expolar transformation and solving it with the proposed neural network.
In addition, specialized algorithms are proposed in each section to generate uniformly
distributed points on the Pareto front, improving its uniformity, coverage, and accuracy. The
performance of the models and algorithms is evaluated using a set of standard test problems
and compared with existing approaches through metrics such as purity, uniformity, coverage,
and distance.
The obtained results demonstrate that the proposed approach outperforms conventional methods in terms of accuracy and efficiency.
Keywords:
#Neural networks #Multi-objective optimization #KKT conditions #Lyapunov stability #Convergence #Pareto generation algorithms. Keeping place: Central Library of Shahrood University
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