Comparative study of multi-variate metaheuristic algorithms : a case study of the hydrogen supply chain design including production and transport technologies in Belgium

In the last two decades, metaheuristic algorithms have progressively emerged as promising methods to identify near-optimal solutions of complex optimization problems. Beyond their initial development specific to the solution of NP-hard optimization problems, recent versions of these algorithms have been proposed for the solution of Mixed Integer Linear (MILP) and Nonlinear (MINLP) optimization problems. This is the case for the class of Multi-Variate (MV) metaheuristics, capable of handling both continuous and discrete decision variables for application to engineering optimization problems. The present work focuses on the identification of the best Multi-Variate metaheuristic algorithm for the solution of the complex problem of the nonlinear hydrogen supply chain design (HSCD), generally studied in its mixed-integer formulation and solved with mathematical programming. Five Multi-Variate metaheuristics are considered: Ant Colony Optimization, Particle Swarm Optimization, Genetic Algorithms, Differential Evolution and Adaptive Estimation of Distribution Algorithms. First, this master thesis explains the structure of each algorithm, then it studies the hyperparameters specific to each metaheuristic which maximize their performance. By comparing the five algorithms on the same problem instance, the best is selected and applied to the optimization of the HSCD in Belgium. All these algorithms are iterative algorithms based on the use of the same solution archive which stores tentative solutions in a matrix of dimension (k, nR + nO), where k is the number of tentative solutions temporarily stored in the memory and nR+nO is the total number of decision variables handled by the algorithm. The key difference among these algorithms consists in the construction of new tentative solutions. In the multi-variate version of Ant Colony Optimization (ACO) a new solution is computed based on the variance and the mean of the solution archive. In Particle Swarm Optimization (PSO) the vectors in the solution archive are considered as the position of a moving particles and their positions change between two iterations according their respective velocity. In Genetic Algorithm (GA) a crossover operator uses the information of two parents to create two new solutions, then the mutation operator creates a perturbation around those new solutions. Differential Evolution (DE) creates a mutant solution composed of a tentative solution and the difference between two other tentative solutions. The crossover operator exchanges part of this mutant with part of yet another tentative solution to build the new solution. Adaptive Estimation of Distribution Algorithm (AEDA) constructs a distribution, whose mean and variance are calculated based on part of the solution archive, the new solutions are then created by sampling this distribution. Adaptive Estimation of Distribution (AEDA) uses both a Gaussian and a Cauchy distribution. For all these algorithms, the discrete variables of the Multi-Variate version are handled by mapping the discrete search space to the continuous domain. As part of this work, for Genetic Algorithm, the HX-PM (Heuristic Crossover-Power Mutation) is found to be the best type of Genetic Algorithm for application with the solution archive and for dealing with discrete variables. A sensitivity analysis is performed in order to tune these metaheuristic algorithms in order for them to reach their maximal potential. It is showed that the performances of each metaheuristic are highly dependent on the choice of their hyperparameters. In addition, a combination of hyperparameter values, which have showed good performances on a benchmark function, is proposed. Finally, this work identifies the Adaptive Estimation of Distribution as the best choice (among the five metaheuristic algorithms considered) to design the hydrogen supply chain in Belgium as MINLP optimization problem. The Ant Colony Optimization is also a good choice for this specific optimization problem as it finds solutions close to the best one found by AEDA in less iterations. Regarding Differential Evolution and Particle Swarm Optimization they both have shown good results, but take more time to converge. Also, the specific HX-PM Genetic Algorithm considered in this study is not recommended to design the hydrogen supply chain in Belgium. Finally, the reduction in computational time obtained by the introduction of a discretization of real decision variables is considered not worth for the HSCD, due to the associated high reduction in the accuracy of the results.