A simple immune-based multi-objective optimizer(IBMO) is proposed, and a rigorous running time analysis of IBMO on three proposed bi-objective pseudo-Boolean functions(Bi-Trap, Bi-Plateau and Bi-Jump) is presented. Th...A simple immune-based multi-objective optimizer(IBMO) is proposed, and a rigorous running time analysis of IBMO on three proposed bi-objective pseudo-Boolean functions(Bi-Trap, Bi-Plateau and Bi-Jump) is presented. The running time of a global simple evolutionary multi-objective optimizer(GSEMO) using standard bit mutation operator with IBMO using somatic contiguous hypermutation(CHM) operator is compared with these three functions. The results show that the immune-based hypermutation can significantly beat standard bit mutation on some well-known multi-objective pseudo-Boolean functions. The proofs allow us to understand the relationship between the characteristics of the problems and the features of the algorithms more deeply. These analysis results also give us a good inspiration to analyze and design a bio-inspired search heuristics.展开更多
Sorting an array of objects such as integers, bytes, floats, etc is considered as one of the most important problems in Computer Science. Quicksort is an effective and wide studied sorting algorithm to sort an array o...Sorting an array of objects such as integers, bytes, floats, etc is considered as one of the most important problems in Computer Science. Quicksort is an effective and wide studied sorting algorithm to sort an array of n distinct elements using a single pivot. Recently, a modified version of the classical Quicksort was chosen as standard sorting algorithm for Oracles Java 7 routine library due to Vladimir Yaroslavskiy. The purpose of this paper is to present the different behavior of the classical Quicksort and the Dual-pivot Quicksort in complexity. In Particular, we discuss the convergence of the Dual-pivot Quicksort process by using the contraction method. Moreover we show the distribution of the number of comparison done by the duality process converges to a unique fixed point.展开更多
基金the National Natural Science Foundation of China(Nos.61703183,61773410,61375053)the Public Welfare Technology Research Plan of Zhejiang Province(No.LGG19F030010)
文摘A simple immune-based multi-objective optimizer(IBMO) is proposed, and a rigorous running time analysis of IBMO on three proposed bi-objective pseudo-Boolean functions(Bi-Trap, Bi-Plateau and Bi-Jump) is presented. The running time of a global simple evolutionary multi-objective optimizer(GSEMO) using standard bit mutation operator with IBMO using somatic contiguous hypermutation(CHM) operator is compared with these three functions. The results show that the immune-based hypermutation can significantly beat standard bit mutation on some well-known multi-objective pseudo-Boolean functions. The proofs allow us to understand the relationship between the characteristics of the problems and the features of the algorithms more deeply. These analysis results also give us a good inspiration to analyze and design a bio-inspired search heuristics.
文摘Sorting an array of objects such as integers, bytes, floats, etc is considered as one of the most important problems in Computer Science. Quicksort is an effective and wide studied sorting algorithm to sort an array of n distinct elements using a single pivot. Recently, a modified version of the classical Quicksort was chosen as standard sorting algorithm for Oracles Java 7 routine library due to Vladimir Yaroslavskiy. The purpose of this paper is to present the different behavior of the classical Quicksort and the Dual-pivot Quicksort in complexity. In Particular, we discuss the convergence of the Dual-pivot Quicksort process by using the contraction method. Moreover we show the distribution of the number of comparison done by the duality process converges to a unique fixed point.
