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Today, many-objective optimization problems have attracted widespread attention. There are significant advantages of the grid-based algorithm in solving multi-objective problems. Grid-based algorithm could offer a transformation of objectives and further distinguish the non-dominated solutions. However, the advantages of grid have not been fully exploited. For example, the traditional homogeneous grid divisions can’t sufficiently reveal the similarity of adjacent solutions. And overemphasizing the selection pressure may cause the diversity decline of grid. To exploit the potentialities of grid, an inhomogeneous grid-based evolutionary algorithm (named IGEA) is proposed. IGEA applies a dynamic inhomogeneous grid division approach and redefining the coordinate assignment of individuals, which makes the dominance relationship more obvious. IGEA also applied the shift-based density estimation (SDE) strategy in discriminating the non-dominated solutions in grid coordinate. SDE can provide a good balance of convergence and diversity. The IGEA compares with several state-of-the-art evolutionary algorithms against the regular and irregular many-objective optimization problems. The experimental results demonstrate that IGEA is very competitive against the peer algorithms in terms of providing a good balance between convergence and diversity.

With the continuous development of E-commerce, warehouse logistics is also facing emerging challenges, including more batches of orders and shorter order processing cycles. When more orders need to be processed simultaneously, some existing task scheduling methods may not be able to give a suitable plan, which delays order processing and reduces the efficiency of the warehouse. Therefore, the intelligent warehouse system that uses autonomous robots for automated storage and intelligent order scheduling is becoming mainstream. Based on this concept, we propose a multi-robot cooperative scheduling system in the intelligent warehouse. The aim of the multi-robot cooperative scheduling system of the intelligent storage is to drive many robots in an intelligent warehouse to perform the distributed tasks in an optimal (e.g., time-saving and energy-conserved) way. In this paper, we propose a multi-robot cooperative task scheduling model in the intelligent warehouse. For this model, we design a maximin-based multi-objective algorithm, which uses a one-by-one update scheme to select individuals. In this algorithm, two indicators are devised to discriminate the equivalent individuals with the same maximin fitness value in the environmental selection process. The results on benchmark test suite show that our algorithm is indeed a useful optimizer. Then it is applied to settle the multi-robot scheduling problem in the intelligence warehouse. Simulation experiment results demonstrate the efficiency of the proposed algorithm on the real-world scheduling problem.

Surrogate-assisted evolutionary algorithms have received a surge of attentions for their promising ability of solving expensive optimization problems. Existing surrogate-assisted evolutionary algorithms usually adopt the regression models and the binary classification models to guide the evolution of the population for solving the multiobjective optimization problems. However, the regression models will make the algorithm to be increasingly computation-expensive as the number of objectives increases, while the use of the binary classification models might suffer from the poor diversity since the diversified information of solutions cannot be reflected in these classification models. For this issue, this paper proposes a surrogate-assisted many-objective evolutionary algorithm using the cooperation of the multi-classification and regression models to improve the search quality while reducing the computational cost. Our approach includes two parts: At the model training stage, a multi-classification model is constructed to divide the whole population into several classes for ensuring diversity, a distance regression model and an angle regression model are used to select solutions with better convergence and diversity in each class; At the evolution stage, a coevolutionary framework is used to guide the evolution according to a new selection criterion. Experimental results verify the effectiveness of the proposed algorithm on a set of expensive test problems with up to 10 objectives.