Solving system-level synthesis problem by a multi-objective estimation of distribution algorithm

Highlights

• Model system-level synthesis as a multi-objective mode-identity RCPSP.

• Solve the problem by hybrid Pareto-archived estimation of distribution algorithm.

• Test with a video codec based on H.261 image compression standard.

Abstract

In this paper, the system-level synthesis problem (SLSP) is modeled as a multi-objective mode-identity resource-constrained project scheduling problem with makespan and resource investment criteria (MOMIRCPSP-MS-RI). Then, a hybrid Pareto-archived estimation of distribution algorithm (HPAEDA) is presented to solve the MOMIRCPSP-MS-RI. To be specific, the individual of the population is encoded as the activity-mode-priority-resource list (AMPRL), and a hybrid probability model is used to predict the most promising search area, and a Pareto archive is used to preserve the non-dominated solutions that have been explored, and another archive is used to preserve the solutions for updating the probability model. Moreover, specific sampling mechanism and updating mechanism for the probability model are both provided to track the most promising search area via the EDA-based evolutionary search. Finally, the modeling methodology and the HPAEDA are tested by an example of a video codec based on the H.261 image compression standard. Simulation results and comparisons demonstrate the effectiveness of the modeling methodology and the proposed algorithm.

Introduction

With the development of VLSI (Very-large-scale integration) technology, semiconductor companies like Intel can build large-scale, complex electronic systems which contain millions of transistors on a single chip. Meanwhile, due to the increasing system complexities, the system-level synthesis problem (SLSP) has emerged (Gerstlauer et al., 2009). There is a need for moving to the system level of abstraction in order to increase productivity in electronic system design. Different from high-level synthesis which is devoted to mapping behavioral description to resistor transistor logic (RTL) (Rosado-Munoz, Bataller-Mompeán, Soria-Olivas, Scarante, & Guerrero-Martínez, 2011), system-level synthesis considers the system hardware and software design simultaneously. Recently, some tools have emerged to realize and support the system-level synthesis process, such as Daedalus (Nikolov et al., 2008, Nikolov et al., 2008), SoC Environment (SCE) (Dömer et al., 2008), and SystemCoDesigner (Keinert et al., 2009).

To solve the SLSP, the mixed integer linear programming (MILP) is widely used (Schwiegershausen et al., 1996, Niemann and Marwedel, 1997, Nagaraj Shenoy et al., 2000). However, it has some disadvantages in solving the SLSP with the MILP. First, the MILP can only solve the small-scaled problems (no more than 20 tasks) in a reasonable computation time since the SLSP is NP-hard in a general case (Mann & Orbán, 2003). Second, it is difficult for the MILP to solve the SLSP with multiple objectives. As a result, it usually adopts the MILP to solve one chosen objective, and then uses the high-level synthesis tools to solve other objectives. But the MILP-based procedure still cannot guarantee the Pareto optimal solutions.

Since many real world problems are difficult to solve by traditional methods, soft computing has gained much attention during recent years in many fields, such as controller design (Wang & Li, 2011), engineering design (Zhao and Wang, 2011, Zhao et al., 2012), steelmaking scheduling (Pan, Wang, Mao, Zhao, & Zhang, 2013), and economic load dispatch (Wang & Li, 2013). During the past few years, evolutionary algorithm (EA) has also been used to solve the SLSP. Blickle (1996) first developed a single-objective EA, and later Blickle, Teich, and Thiele (1998) introduced a Pareto-ranking technique into the single-objective EA. Fan, Wang, Achiche, Goodman, and Rosenberg (2008) introduced the flow of a structured Micro-Electro-Mechanical Systems (MEMS) design process to emphasize the system-level lumped-parameter model synthesis. To trade off the predefined behavioral specifications for designers, at the system level an approach combining bond graphs and genetic programming can yield satisfactory design candidates. Zitzler and Thiele (1999) developed a multi-objective algorithm named SPEA to solve the SLSP by combining several features of previous multi-objective EAs in a unique manner. Compared to the MILP-based procedures, the EA-based procedures can deal with the large-scaled and multi-objective problems. However, the specific search operators should be designed for the EAs to solve the SLSP due to the complicated constraints. So, it is important to develop novel methodologies to model the problem reasonably as well as powerful solution algorithms to solve the problem effectively.

As a novel evolutionary algorithm, estimation of distribution algorithm (EDA) can be regarded as a general framework of statistical learning based optimization algorithm (Larrañaga & Lozano, 2002). Unlike genetic algorithm (GA) which explicitly generates new individuals by crossover and mutation, the EDA tries to predict of the movement of population in the search space and estimates the underlying probability distribution of the encoded variables of the elite individuals so as to generate new individuals. So far, the EDA has been applied to solve a variety of optimization problems in academic and industrial fields, such as feature selection (Armañanza et al., 2011), shop scheduling (Wang, Wang, Xu, Zhou, & Liu, 2012), nurse rostering (Aickelin, Burke, & Li, 2007), hybrid electric vehicle charging (Su & Chow, 2012), multi-speed planetary transmission (Simionescu, Beale, & Dozier, 2006), knapsack problem (Wang, Wang, & Xu, 2012), and software testing (Sagarna & Lozano, 2005). However, to the best of our knowledge, there is no work about EDA to solve the SLSP.

In this paper, the SLSP is solved by adopting the project scheduling concept-based model and using the EDA-based search method. First, the SLSP is modeled as a multi-objective mode-identity resource-constrained project scheduling problem with makespan and resource investment criteria (MOMIRCPSP-MS-RI). Then, a hybrid Pareto-archived estimation of distribution algorithm (HPAEDA) is proposed to solve the problem. The activity-mode-priority-resource list (AMPRL) is used to encode individuals, and a hybrid probability model is designed to predict the promising search area. During the search procedure, a Pareto archive is employed to preserve the non-dominated solutions that have been explored, and another archive is used to preserve the solutions for updating the probability model. Specific sampling and updating mechanisms are designed to make the evolution process track the most promising search areas. The modeling methodology and the proposed HPAEDA are tested with the example of a video codec based on the H.261 image compression standard. Simulation results and comparisons demonstrate the effectiveness of the modeling methodology and the proposed HPAEDA.

The remainder of the paper is organized as follows: In Section 2, the system-level synthesis problem is introduced. In Section 3, the project scheduling model for the system-level synthesis problem is described. Following the original EDA introduced in Section 4, the HPAEDA is presented in details in Section 5. An example of a video codec design based on the H.261 image compression standard is provided in Section 6. Finally, the paper is ended with some conclusions and future work in Section 7.