Comparative Approaches for Solving the Nonlinear Transportation Problem with Quadratic Costs

The nonlinear transportation problem (NTP) extends the classical transportation model by incorporating nonlinear cost structures, leading to increased computational complex-ity. A quadratic NTP is solved using three approaches: Wolfe's reduced-gradient method, a Genetic Algorithm (GA), and convex quadratic programming (CQP) implemented in Python using CVXPY and OSQP. A benchmark 7 x 7 quadratic transportation problem is employed for performance evaluation. Wolfe's method yields feasible but suboptimal solutions due to sensitivity to initialization. The GA achieves near-optimal results with strong global search capability but exhibits slower convergence and limited reproducibil-ity. In contrast, the CQP approach consistently reproduces the benchmark solution with high numerical accuracy, efficiency, and stability. This study provides a systematic com-parison of classical, heuristic, and convex optimization techniques for quadratic nonlinear transportation problems, highlighting their complementary strengths and limitations.