A general approach to solving hardware and software partitioning problem based on evolutionary algorithms

Highlights

• A general algorithm framework for hardware software partitioning problem is proposed based on evolutionary algorithms.

• An effective method to deal with the infeasible solution of hardware software partitioning problem is proposed

• The performances of genetic algorithm (GA), binary particle swarm optimization (BPSO), binary differential evolution algorithm with hybrid encoding (HBDE), and group theory based optimization algorithm (GTOA) for solving hardware software partiti on ing problem are compared.

• According to the comparison results, it is pointed out that GTOA and BPSO are more suitable for solving hardware software partitioning problem than GA and HBDE

Abstract

Hardware/software partitioning (HW/SW) is a significant problem in hardware-software co-design, and it is also an NP-hard problem. In order to solve the HW/SW quickly and effectively by evolutionary algorithms, the HW/SW is firstly regarded as a variant of knapsack problem. Based on a new greedy strategy, a greedy repair and optimization algorithm GROM is proposed to eliminate the infeasible solutions. Subsequently, a general algorithm framework based on discrete evolutionary algorithm for HW/SW problem is proposed. On the basis of the above algorithm framework, genetic algorithm (GA), binary particle swarm optimization (BPSO), binary differential evolution algorithm with hybrid encoding (HBDE) and group theory-based optimization algorithm (GTOA) are used to solve large-scale HW/SW instances. The feasibility and effectiveness of the algorithm framework proposed in the paper are verified by comparing the good and bad of the calculation results of above algorithms, and pointed out that the performance of GTOA and BPSO is better than that of HBDE and GA, they are more suitable for solving large-scale HW/SW problem.

Introduction

With the extensive application of embedded systems, hardware and software co-design has become a significant research problem. The hardware is fast to execute, but the cost is high, and it takes more resources. Although the software is slow to execute, the cost is low, and the operation is relatively flexible. According to the requirements, the components in the embedded system are reasonably partitioned software and hardware for execution, which will greatly improve the performance of the entire system. Therefore, hardware/software partitioning (HW/SW)[1] has become a vital problem in hardware-software collaborative design.

Due to the fact that the HW/SW problem is an NP-hard problem [2], when its scale is large, the running speed of determinate algorithms [3], [4], [5], [6]is often very slow. Hence, the determinate algorithms are difficult to satisfy the requirements of the fast solution in practical applications. In recent years, solving large-scale the HW/SW problems based on heuristic algorithms has gradually become a research hotspot, such as Arato et al. [7] proposed a two-dimensional search heuristic algorithm for solving the HW/SW problems. This heuristic makes use of problem-specific knowledge to find high-quality solutions rapidly. Wu et al. [8] regarded the HW/SW problem as an extended 0-1 knapsack problem with communication costs, and proposed a 1D Search Algorithms to solve the problem. Comparing with the method in [7], their approach not only improves the performance of the algorithm, but also reduces the time complexity. Due to the method of Wu in [8] lacks a theory basis, Quan et al. [9] perfected their method. Wang et al. [10] proposed the HEUR algorithm and used it to give a new method for solving the HW/SW problem, in which the communication cost is firstly ignored, the HW/SW problem is transformed a standard 0-1 knapsack problem, whose solution is obtained as a potential solution to the original problem. Then, according to the communication cost, the potential solution is adjusted by tabu search, so as to obtain a feasible solution that satisfies the constraint conditions of HW/SW. Although the HEUR algorithm has greatly improved the quality of the solution than the 1D Search Algorithms [8], tabu search is also very time-consuming in further optimizing the solution when solving large-scale the HW/SW instances. Chen et al. [11] proposed the NodeRank algorithm on the basis of the idea of the Page Rank algorithm. In some cases, the quality of the solutions obtained by NodeRank is better than HEUR. Although many achievements have been made in solving HW/SW problem based on heuristic algorithm, there is still a lack of a fast and effective method to solve it because of its difficulty. At the same time, there is no research report on the general algorithm framework using evolutionary algorithm to solve it quickly. To this end, this paper studies how to use evolutionary algorithms (EAs) [12], [13], [14] to solve the HW/SW problem. Based on an efficient algorithm for handling infeasible solutions of HW/SW, a general algorithm framework for solving HW/SW by using EAs is proposed. On the basis of the framework, GA, BPSO, HBDE, and GTOA were used to solve HW/SW, and the performance of the four algorithms was compared.

Evolutionary algorithm is a kind of heuristic swarm intelligence algorithms, which do not need to calculate derivatives and gradients, do not require the continuity of the objective function, and have inherent implicit parallelism and strong global optimization capabilities [15]. It has been successfully used to solve scheduling problems [16], multi-dimensional knapsack problem [17], set covering problem [18], feature selection problem[19], traveling salesman problem [20], [21] and other combinatorial optimization problems. EAs are generally divided into two categories: one is the discrete evolutionary algorithm that can be directly used to solve combinatorial optimization problems, such as genetic algorithm (GA) [22], ant colony algorithm (ACO) [23], [24], group theory-based optimization algorithms (GTOA) [25], etc.; the other is the continuous evolutionary algorithm, which is suitable for solving numerical optimization problems and cannot be directly used to solve combinatorial optimization problems, such as particle swarm optimization (PSO) [26], differential evolution (DE) [12], [27], grey wolf optimizer (GWO) [28], bat algorithm (BA)[29], [30], multi-heuristic based search method (MHSM)[31] and so on. In order to use continuous evolutionary algorithms to solve binary optimization problems, scholars have proposed many discrete versions of continuous evolutionary algorithms, such as a discrete binary version of the particle swarm optimization (BPSO) [32], binary differential evolution algorithm with hybrid encoding (HBDE) [33], binary artificial algae algorithm (BAAA) [34], binary dragonfly algorithm (BDA) [35], binary-weighted superposition attraction algorithm (BWSA) [36], binary grey wolf optimizer (BGWO) [37], and novel binary artificial bee colony algorithm (BABC) [38], etc. Obviously, the continuous evolutionary algorithm has been successfully used to solve various combinatorial optimization problems, so it is feasible to use it to solve HW / SW. Therefore, in order to give an effective method for solving HW/SW based on EAs, this paper draws lessons from the idea of literature [8] to transform HW/SW into an extended 0/1 knapsack problem with communication cost, and then proposes a new method to solve HW/SW based on EAs.

The remainder of the paper is organized as follows. Section 2 introduces the definition and model of HW/SW. In Section 3, a repair and optimization algorithm by a new greedy strategy is firstly proposed to deal with the infeasible solutions. Then, a general algorithm framework of solving HW/SW based on EAs is proposed. Subsequently, the principles and pseudo-code of GA, BPSO, HBDE, and GTOA are simply described in Section 4. In Section 5, the generation rules and parameter values of different scales of HW/SW instances are introduced firstly. Secondly, the reasonable parameters of each algorithm are given. Finally, comparing and analysing the calculation results that GA, BPSO, HBDE and GTOA for solving the 6 cases of 16 HW/SW instances. Section 6 summarizes the full text and looks forward to future research work.