RESUMO
Highly constrained multiobjective optimization problems (HCMOPs) refer to constrained multiobjective optimization problems (CMOPs) with complex constraints and small feasible regions, which are commonly encountered in many real-world applications. Current constraint-handling techniques will face two difficulties when dealing with HCMOPs: 1) feasible solution is hard to be found and too much search effort is spent in locating the feasible region and 2) since the total feasible region of an HCMOP can consist of several disconnected subregions, the search process might be stuck in the comparatively larger feasible subregion, which does not contain the whole Pareto front (PF). To address these two issues, an evolutionary algorithm with constraint relaxation strategy based on differential evolution algorithm, that is, CRS-DE, is proposed in this article. In each generation, the CRS-DE relaxes the constraints by dividing the infeasible solutions into two subpopulations based on total constraint violation, that is, the "semifeasible" subpopulation (SF) and "infeasible" subpopulation (IF), respectively. The SF provides information on the promising regions of finding the feasible solution and is the driving force for convergence toward the PF, while the IF focuses on global exploration for new promising regions. Corresponding reproduction and selection strategies are devised for the SF, IF, and feasible subpopulations, which create a clear division of labor with cooperation to facilitate the search for feasible solutions. To leverage the influence of CRS and prevent the population from premature convergence, a mobility restriction mechanism is developed to restrict the individuals in the SF and IF from entering the feasible subpopulation and enhance the diversity of the whole population. Comprehensive experiments on a series of benchmark test problems and a real-world CMOP demonstrate the competitiveness of our method compared with other representative algorithms in terms of effectiveness and reliability in finding a set of well-distributed optimal solutions for HCMOPs.
RESUMO
In our earlier study, an energy-efficient passive UAV radar imaging system was formulated, which comprehensively analyzed the system performance. In this article, based on the evaluator set, a mission planning framework for the underlying energy-efficient passive UAV radar imaging system is proposed to achieve optimized mission performance for a given remote sensing task. First, the mission planning problem is defined in the context of the proposed synthetic aperture radar (SAR) system and a general framework is outlined, including mission specification, illuminator selection, and path planning. It is found that the performance of the system is highly dependent upon the flight path adopted by the UAV platform in a 3-D terrain environment, which offers the potential of optimizing the mission performance by adjusting the UAV path. Then, the path planning problem is modeled as a single-objective optimization problem with multiple constraints. Path planning can be divided into two substages based on different mission orientations and low mutual correlation. Based on this property, a path planning method, called substage division collaborative search (Sub-DiCoS), is proposed. The problem is divided into two subproblems with the corresponding decision space and subpopulation, which significantly relax the constraints for each subproblem and facilitates the search for feasible solutions. Then, differential evolution and the whole-stage best guidance technique are devised to cooperatively lead the subpopulations to search for the best solution. Finally, simulations are presented to demonstrate the effectiveness of the proposed Sub-DiCoS method. The result of the mission planning method can be used to guide the UAV platform to safely travel through a 3-D rough terrain in an energy-efficient manner and achieve optimized SAR imaging and communication performance during the flight.