A hybrid evolutionary algorithm for multiobjective variation tolerant logic mapping on nanoscale crossbar architectures

Multi-objective redundancy hardening with optimal task mapping for independent tasks on multi-cores

“…A naive way to find an MMW-PM (i.e., the optimal mapping) is to find all perfect matchings in the given bipartite graph first and then select the one whose maximal edge weight is minimal. Instead of using such an enumeration method, we use an efferent heuristic algorithm [proposed in our previous work (Zhong et al 2016) for MMW-PM problem with low time complexity.…”

“…Our heuristic is to select an edge e in G and remove all the edges whose weights are larger than that of e in G, while a perfect matching method (i.e., Hungarian algorithm (Kuhn 1955)) is used to check whether a perfect matching exists. The framework of the heuristic method is iterative based on binary search, as shown in Algorithm 2 (Zhong et al 2016). The algorithm starts with an initial perfect matching M obtained by the Hungarian algorithm (line 1), and then we have E 0 by sorting E in ascending order according to their weights (line 2).…”

“…Obviously, Algorithm 2 (Zhong et al 2016) would return a perfect matching of the input graph, as the resulting matching M has the same cardinality as the initialized M obtained from the input graph (line 1). Besides, the edges in G are removed according to the ascending order of their weights, so the resulting matching M satisfies that the maximal weight of the edges in M has a minimal value among all perfect matchings of the input graph.…”

“…This paper builds upon the analysis that, for independent tasks (Bleuse et al 2017;Hong and Prasanna 2007) (i.e., there is no data dependence between tasks), if the solution of task hardening is given, the solution of task mapping can be optimally obtained by employing min-max-weight perfect matching (MMW-PM). Specifically, both DMR-and TMR-based hardening techniques are considered, and we show how to link the problem of task mapping with the goal of minimizing the worst-case makespan (i.e., the maximum completion time of all tasks) to the MMW-PM model, and then, based on binary search and Hungarian algorithm (Kuhn 1955), we use an efficient heuristic algorithm [proposed in our previous work (Zhong et al 2016) to obtain an MMW-PM from a bipartite graph with polynomial time complexity. Besides, as there is a trade-off between cost and time performance (Erbas et al 2006), we propose a multi-objective memetic algorithm (MOMA) -based task hardening method to obtain a set of solutions with different numbers of cores (i.e., costs), so the designer can choose a solution from the Pareto front according to user preferences, such as cost budget or performance requirement.…”

A Fast Hill Climbing Algorithm for Defect and Variation Tolerant Logic Mapping of Nano-Crossbar Arrays

“…Another evolutionary algorithm is proposed by Zhong et al [22]; it is a bi-level multi-objective optimization algorithm that uses different approaches on row and column mappings defined as lower and upper level problems. Every individual of an upper level problem is required to be first solved as a lower level problem that puts too much burden on the lower level (row order) algorithm.…”