Optimization makes processes, systems, or products more efficient, reliable, and with better outcomes. A popular topic on optimization today is multiobjective bilevel optimization (MOBO). In MOBO, an upper level problem is constrained by the solution of a lower level one. The problem at each level can include multiple conflicting objective functions and its own constraints. This survey aims to study the solution approaches proposed to solve MOBO problems, including exact methods and approximate techniques such as metaheuristics (MHs). This work explores classical literature to investigate why most classical methods, theories, and algorithms focus on linear and some convex MOBO problems to solve the optimistic MOBO. Moreover, we study and propose a taxonomy of MH-based frameworks for solving some MOBO instances, highlighting the pros and cons of five main approaches. Finally, a growing interest in MOBO has been detected in the optimization community. A significant number of possible applications and solution approaches establish an early research line to find solutions to these types of problems.

This work presents a novel path-planning approach for Unmanned Aerial Vehicles (UAVs) in continuous 3D environments. This proposal aims to minimize the path length while avoiding collisions through the suitable adjusting of control points (the points that take the UAV from a start position to a target location). The above is stated as a constrained global optimization problem. This problem considers the overall length of the path as the single objective function. Regarding the problem constraints, they are related to the collision of the obstacles with the 3D shape of a path. The assignment of the path shape is also proposed in this work to streamline the planning process. Due to the optimization problem features (high nonlinearity, multimodality, non-differentiability, and the lack of an initial guess solution), a constraints-handling mechanism is used in meta-heuristics to find suitable optimized paths. Also, an enhanced path-search mechanism is included in these algorithms to deal with complex planning scenarios. The enhanced mechanism incorporates a path computed by a variant of the A-Star method (the Pruned A-Star) in the first set of candidate solutions of the meta-heuristics. The proposed approach is tested through six complex scenarios. Moreover, the performance of three well-known meta-heuristics, Differential Evolution (DE), Particle Swarm Optimization (PSO), and the Genetic Algorithm (GA), is studied to find a potential candidate to solve the path-planning problem. In this way, the paths found by DE show outstanding performance. The paths obtained by the Pruned A-Star technique are adopted as a point of comparison to determine the advantages and drawbacks of the proposal.

The dc motor is one of the most fundamental electromechanical devices of mechatronic systems, which plays an important role in maintaining the accuracy in the execution of tasks. One of the main issues in the accuracy and robustness of dc motor control system is how to optimally tune its parameters. In this paper, a multi-objective online tuning optimization approach is proposed to adaptively tune up the velocity control parameters of the permanent magnet dc motor. This approach simultaneously considers the modeled error and the corresponding sensitivity to choose the best compromise solution in the Pareto dominance-based selection process of solutions to deal the changing optimum solutions in the dynamic environment of the tuning approach based on online optimization method and moreover, the modified differential evolution with induced initial population based on non-dominated solution through a memory is proposed to guide the search into the feasible region, and to promote the exploitation of solutions found in the previous time interval. Simulation results verify that proposed modifications provide higher robustness and better quality in the velocity regulation control of the dc motor under parametric uncertainties, and also under discontinuous dynamic load, than multi-objective differential evolution, particle swarm optimization, and non-dominated sorting genetic algorithm-II.

The efficient speed regulation of four-bar mechanisms is required for many industrial processes. These mechanisms are hard to control due to the highly nonlinear behavior and the presence of uncertainties or disturbances. In this paper, different Pareto-front approximation search approaches in the adaptive controller tuning based on online multiobjective metaheuristic optimization are studied through their application in the four-bar mechanism speed regulation problem. Dominance-based, decomposition-based, metric-driven, and hybrid search approaches included in the algorithms, such as nondominated sorting genetic algorithm II, multiobjective evolutionary algorithm based on decomposition and differential evolution, S-metric selection evolutionary multiobjective algorithm, and nondominated sorting genetic algorithm III, respectively, are considered in this paper. Also, a proposed metric-driven algorithm based on the differential evolution and the hypervolume indicator (HV-MODE) is incorporated into the analysis. The comparative descriptive and nonparametric statistical evidence presented in this paper shows the effectiveness of the adaptive controller tuning based on online multiobjective metaheuristic optimization and reveals the advantages of the metric-driven search approach.