<p>This study presents a novel approach to solving complex transportation models characterized by multi-choice parameters and stochastic constraints using soft computing techniques. The transportation problem under investigation involves random availability and demand parameters following continuous distributions such as exponential and logistic. The primary objective is to derive optimal solutions by transforming probabilistic constraints into deterministic ones and utilizing Evolutionary Algorithms (EAs) for optimization. Leveraging Lagrange’s Interpolation Method, the study identifies the most favourable choices from the multi-choice parameters, facilitating the subsequent conversion of probabilistic constraints into deterministic equivalents. The research introduces a range of soft computing algorithms, including a real-parameter Genetic Algorithm, a variant of Differential Evolution, an Evolution Strategy, and a Particle Swarm Optimization. Two numerical illustrations are employed to evaluate the proposed techniques, allowing for a thorough comparison of algorithmic efficiency and solution quality. A comprehensive performance metric tracks the evolution of optimum solutions, the non-dominated solution sets generated in each iteration, and the convergence rate of the algorithms. The study’s contributions lie in addressing intricate transportation problems marked by uncertainty in parameter values. Combining EAs with soft computing strategies offers a robust framework for optimizing multi-choice transportation models. The research sheds light on various soft computing algorithms’ effectiveness and suitability for solving similar challenges in diverse domains.</p>