Particle swarm optimization (PSO), an intelligent optimization algorithm inspired by the flocking behavior of birds, has been shown to perform well and widely used to solve the continuous problem. But the traditional PSO and most of its variants are developed for optimization problems in continuous space, which are not able to solve the binary combinational optimization problem. To tackle this problem, Kennedy extended the PSO and proposed a discrete binary PSO. But its performance is not ideal and just few further works were conducted based on it. In this paper, we propose a novel probability binary particle swarm optimization (PBPSO) algorithm for discrete binary optimization problems. In PBPSO, a novel updating strategy is adopted to update the swarm and search the global solution, which further simplify the computations and improve the optimization ability. To investigate the performance of the proposed PBPSO, the multidimensional knapsack problems are used as the test benchmarks. The experimental results demonstrate that PBPSO has a better performance for solving the multidimensional knapsack problem in terms of convergent speed and global search ability.

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Urban sustainability is a crucial part of the United Nations (UN) Sustainable Development Goals (SDGs) and one of the core objectives of China’s national strategy to promote new urbanization and achieve integration in the Yangtze River Delta (YRD). This paper mainly focused on the 11th SDG, which is a universal call to make cities and human settlements inclusive, safe, resilient and sustainable. The full permutation polygon synthetic indicator (FPPSI) method was applied to synthetically evaluate the sustainable level of 26 cities in the YRD urban agglomeration from 2007 to 2016. The results showed that: (1) the synthesis indicators were increasing year by year, which implied that the sustainable development of the YRD has shown obvious progress in recent years. However, each city faced its own challenges to achieving the sustainable development goals. The sustainability level for the majority of cities was restricted by obstacles such as the per capita green area, air quality and commercial housing sales area; (2) Among the 26 cities, small and medium-sized cities were subject to the traditional strong sustainability indicators while large and mega cities were more affected by weak sustainability indicators; (3) Spatial differences were found for the overall sustainable development level of the YRD. The diffusion and assembly effect among cities had not yet been formed; however, the strong spillover effect of developed cities might influence the ability of other cities to achieve sustainable development goals in many aspects of the environment, economy and society. The results suggest the need for a stronger focus on improving regional developing patterns and strengthening coordination in the process of achieving the sustainable development goal of urban agglomeration in the YRD. Furthermore, according to the conditions of different cities, integrated policies are required to address all aspects of sustainability and to avoid unintended consequences.

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