Multi-objective optimization (MOO) is widely used for solving various engineering real-life problems. Meta-heuristic optimization has been regarded as an effective solution for such problems because it enables the successful examination of a broad range of candidate solutions and the selection of optimal ones. However, there is a high probability of the algorithms becoming ensnared in local minima due to the complex optimization surface and the unlimited number of viable solutions. Therefore, to provide the decision maker with the optimal non-dominated set of solutions, significant improvements must be made to the search process, where the efficient exploration of the population has a vital role in maintaining a good non-dominated solution in evolutionary algorithms. NSGA-II is regarded as the state of the art for the meta-heuristic MOO. NSGA-II and its variants have adopted the concept of crowding distance as a measure that can leverage the characteristics of the distribution of solutions in the search space and provide a highlevel of exploration. However, this method is not sufficient to effectively explore the search space because it ignores the direction of the exploration. In this paper, the angle quantization of solutions is combined with the crowding distance to create the MOGA-AQCD algorithm, which preserves equal exploration in all directions and aims at finding equal distribution of solutions within the search space. This approach is applied to a set of standard benchmark MOO functions. The results show that MOGA-AQCD is superior to NSGA-II and NSGA-III on the most evaluation measures for MOO.

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Wireless sensor networks (WSN) nowadays have gained more interest, pushed by the growing necessity for data collection and transmission from both civilian and military domains. WSN is constructed from interconnected sensors and limited resource (battery), which requests great importance on the deployment strategy to increase the performance metrics for WSN (lifetime, coverage, QoS connectivity). Also, the deployment is considered as a fundamental issue in (WSNs) design, and it was taken from the perspective of the multi-objective optimization problem. Many of the existing deployment strategies are based on metaheuristics algorithms such as Genetic Algorithms (GAs) to resolve the deployment problem. In this article, we use and adopt one of the most attractive approaches for wireless sensor networks deployment (WSND) optimization based on metaheuristic searching which is named Non-dominated Sorting Genetic Algorithm-III (NSGA-III) In order to reach maximum coverage and minimize the consumption of energy to maximize the network lifetime under the connectivity constraint. The comparison results have proved the NSGA-III algorithm outperformed the Constrained Pareto-based Multi-objective Evolutionary Approach (CPMEA) that taken as a benchmark for this study. Those results encourage the application of NSGA-III to real-world deployment problems, and the importance of this approach is that it can be handled many objectives.

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