A mathematical formulation and an NSGA-II algorithm for minimizing the makespan and energy cost under time-of-use electricity price in an unrelated parallel machine scheduling.

In many countries, there is an energy pricing policy that varies according to the time-of-use. In this context, it is financially advantageous for the industries to plan their production considering this policy. This article introduces a new bi-objective unrelated parallel machine scheduling problem with sequence-dependent setup times, in which the objectives are to minimize the makespan and the total energy cost. We propose a mixed-integer linear programming formulation based on the weighted sum method to obtain the Pareto front. We also developed an NSGA-II method to address large instances of the problem since the formulation cannot solve it in an acceptable computational time for decision-making. The results showed that the proposed NSGA-II is able to find a good approximation for the Pareto front when compared with the weighted sum method in small instances. Besides, in large instances, NSGA-II outperforms, with 95% confidence level, the MOGA and NSGA-I multi-objective techniques concerning the hypervolume and hierarchical cluster counting metrics. Thus, the proposed algorithm finds non-dominated solutions with good convergence, diversity, uniformity, and amplitude.

Swarm Robotics: A Perspective on the Latest Reviewed Concepts and Applications.

Known as an artificial intelligence subarea, Swarm Robotics is a developing study field investigating bio-inspired collaborative control approaches and integrates a huge collection of agents, reasonably plain robots, in a distributed and decentralized manner. It offers an inspiring essential platform for new researchers to be engaged and share new knowledge to examine their concepts in analytical and heuristic strategies. This paper introduces an overview of current activities in Swarm Robotics and examines the present literature in this area to establish to approach between a realistic swarm robotic system and real-world enforcements. First, we review several Swarm Intelligence concepts to define Swarm Robotics systems, reporting their essential qualities and features and contrast them to generic multi-robotic systems. Second, we report a review of the principal projects that allow realistic study of Swarm Robotics. We demonstrate knowledge regarding current hardware platforms and multi-robot simulators. Finally, the forthcoming promissory applications and the troubles to surpass with a view to achieving them have been described and analyzed.