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A Modular Design Space Exploration Framework for Embedded Systems

Simon K¨ nzli, Lothar Thiele and Eckart Zitzler ? u

Abstract This paper introduces design space exploration as one of the major tasks in embedded system design. After reviewing existing exploration methods at various layers of abstraction, a generic approach is described based on multi-objective criteria, black-box optimisation and randomised search strategies. The interface between problem-speci?c and generic parts of the exploration framework is made explicit by de?ning an interface called PISA. This speci?cation and implementation interface and the availability of a wide range of randomised multi-objective search methods makes the proposed framework accessible to a wide range of exploration problems. It resolves the problem that existing optimisation methods can not be coupled easily to the problem-speci?c part of a design exploration tool.

1 Introduction

Embedded systems are usually evaluated according to a large variety of con?icting criteria such as performance, cost, ?exibility, power and energy consumption, size and weight. As a consequence, embedded systems are usually domain-speci?c and try to use the characteristics of the particular application domain in order to arrive at competitive implementations. In addition, they are often complex in that they consist of heterogeneous subcomponents (dedicated processing units, application-speci?c instruction set processors, general purpose computing units, memory structures and communication means like buses or networks). Finally, embedded systems are resource constrained because of tight cost bounds. Therefore, there is resource sharing on almost all levels of abstraction and resource types that makes it dif?cult for a designer to assess the quality of a design and the ?nal effect of design choices. This combination of a huge design space on the one hand and the complexity in interactions on the other hand makes automatic or semi-automatic (interactive) methods for exploring different designs important. Following the usual hierarchical approach to embedded system design, there are several layers of abstraction on which design choices must be taken. A simpli?ed view on the integration into an abstraction layer is shown in Fig. 1. For example, if the layer of abstraction is the ’programmable architecture’, then the generation of a new design point may involve the choice of a cache architecture. The estimation of non-functional properties may be concerned with performance of task execution on the underlying processor architecture, the size of the cache or the total energy consumption. The estimation may either be done using analytic methods or by a suitable simulator by use of suitable input stimuli, e.g. memory access traces. In any case, properties

Information Technology and Electrical Engineering, Computer Engineering and Networks Lab, ETH Z¨ rich, Switzerland, {kuenzli,thiele,zitzler}@tik.ee.ethz.ch u

? Department

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of the sub-components (from logic design) are necessary, e.g. the relations between area, power consumption, structure and size of the cache. The generation of new design points has to satisfy various constraints, e.g. in terms of feasible cache sizes or structures. The choice of a cache will then lead to re?ned constraints for the design of its sub-components (digital design layer).

input stimuli and requirements for component design properties of component

higher level of abstraction

Design Decision Generation of new design points Estimation of non-functional properties

current level of abstraction

lower level of abstraction

input stimuli and constraints for sub-components properties of sub-components

Figure 1: Embedding of exploration in a hierarchical design trajectory for embedded systems. Figure 1 makes also apparent the interplay between exploration on the one hand and estimation on the other. The methods and tools applied to the estimation of non-functional properties very much depend on the particular abstraction layer and the design objectives. In the present paper, we will concentrate on the generation of new design points and the decision process that ?nally leads to a design decision, estimation will not be covered. The purpose of the paper is to review existing approaches to design space exploration of embedded systems and to describe a generic framework that is based on multi-objective decision making, black-box optimisation and randomised search strategies. The framework is based on the PISA (Platform and Programming Language Independent Interface for Search Algorithms) protocol that speci?es a problem-independent interface between the search/selection strategies on the one hand and the domain-speci?c estimation and variation operators on the other. It resolves the current problem that state-of-the-art exploration and search strategies are not (easily) accessible to solve the domain-speci?c exploration problems in embedded systems design. The main questions we would like to answer in the paper can be phrased as follows: How can we apply ef?cient design space exploration to a new design problem in embedded system design? How can we integrate a new estimation methodology into a complete design space exploration in a simple and ef?cient way?

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2 Approaches to Design Space Exploration

There is a vast number of approaches available that make use of an automated or semi-automated design space exploration in embedded systems design. Therefore, only a representative subset will be discussed with an emphasis on the exploration strategies, whereas the different estimation methods for non-functional properties will not be discussed further. As described in Section 1, exploration of implementation alternatives happens at various levels of abstraction in the design. These various layers are described next and existing design space exploration approaches are classi?ed accordingly: ? Logic Design and High Level Synthesis: Here we are concerned with the synthesis of digital logic starting from either a register-transfer speci?cation or a more general imperative program. Here, we also include the manual design of dedicated computing units. Typical design choices concern speed vs. implementation area vs. energy consumption, see e.g. [1, 2]. ? Programmable Architecture: The programmable architecture layer contains all aspects below the instruction set. There are numerous examples of exploration on this level of abstraction; they concern different aspects such as caches and memories [3, 4, 5], or the whole processor architecture especially the functional unit selection [6, 7, 8]. ? Software Compilation: This layer concerns all ingredients of the software development process for a single task such as code synthesis from a model-based design or a high level program speci?cation. Within the corresponding compiler, possible exploration tasks are code size vs. execution speed vs. energy consumption. There are attempts to perform a cross-layer exploration with the underlying processor architecture, see e.g. [9, 10]. ? Task Level: If the whole application is partitioned into tasks and threads. Therefore, the task level refers to operating system issues like scheduling, memory management and arbitration of shared resources. Therefore, typical trade-offs in choosing the scheduling and arbitration methods are energy consumption vs. average case vs. worst case timing behaviour, e.g. [11]. ? Distributed Operation: Finally, we are faced with applications that run on distributed resources. This abstraction layer is sometimes called system-level and the design choices concern the whole system composition out of components as well as the mapping of application to the architecture and the necessary (distributed) scheduling and arbitration methods, see e.g. results on the communication infrastructure [12, 13], on distributed systems [14] or multiprocessor systems and systems-on-chip, e.g. [15, 16, 17, 18, 19]. Following the focus of the paper, we will classify existing approaches in a way that is orthogonal to the abstraction layers, namely the methods that are applied to perform the exploration itself. This way it becomes apparent that the exploration process is largely independent of the abstraction level. This property will be used later on in de?ning the new generic framework. If only a single objective needs to be taken into account in optimisation, the design points are totally ordered by their objective value. Therefore, there is a single optimal design (if all have different objective values). The situation is different if multiple objectives are involved. In this case, design points are only partially ordered, i.e. there is a set of incomparable optimal solutions. 3

They re?ect the trade-offs in the design. Optimality in this case is usually de?ned using the concept of Pareto-dominance: A design point dominates another one if it is equal or better in all criteria and strictly better in at least one. In a set of design points, those are called Pareto-optimal which are not dominated by any other. Using this notion, available approaches to the exploration of design spaces can be characterised as follows: 1. Exploration by hand: The selection of design points is done by the designer himself. The major focus is on ef?cient estimation of the selected designs, e.g. [16]. 2. Exhaustive Search: All design points in a speci?ed region of the design parameters are evaluated. Very often, this approach is combined with local optimisation in one or several design parameters in order to reduce the size of the design space, see e.g. [4, 20]. 3. Reduction to a Single Objective: For design space exploration with multiple con?icting criteria, there are several approaches available that reduce the problem to a set of single criterion problems. To this end, manual or exhaustive sampling is done in one (or several) directions of the search space and a constraint optimisation, e.g. iterative improvement or analytic methods is done in the other, see e.g. [2, 3, 12, 8]. 4. Black-box Randomised Search: The design space is sampled and searched via a black-box optimisation approach, i.e. new design points are generated based on the information gathered so far and by de?ning an appropriate neighbourhood function (variation operator). The properties of these new design points are estimated which increases the available information about the design space. Examples of sampling and search strategies used are Pareto Simulated Annealing [21] and Pareto Tabu Search, e.g. [10, 7], evolutionary multi-objective optimisation [14, 18, 13, 22], or Monte Carlo methods improved by statistical estimation of bounds. e.g. [1]. These black box optimisation are often combined with local search methods that optimise certain design parameters or structures, e.g. [11]. 5. Problem-dependent Approaches: In addition to the above classi?cation, we ?nd also a close integration of the exploration with a problem-dependent characterisation of the design space. Several possibilities have been investigated so far: (1) Use the parameter independence in order to prune the design space, e.g. [17, 23]. (2) Restrict the search to promising regions of design space, e.g. [6]. (3) Investigate the structure of the Pareto-optimal set of design points, for example using hierarchical composition of sub-component exploration and ?ltering [15, 5]. (4) Explicitly model the design space, use an appropriate abstraction, derive a formal characterisation by symbolic techniques and use pruning techniques, e.g. [24]. Finally, usually an exhaustive search or a black-box randomised search is carried out for those parts of the optimisation that are inaccessible for tailored techniques. From the above classi?cation, one can state that most of the above approaches use randomised search techniques one way or the other, at least for the solution of subproblems. This observation does not hold for the exploration by hand or the exhaustive search, but these methods are only feasible for small design spaces with a few choices of the design parameters.

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While constructing tools that perform design space exploration of embedded systems at a certain level of abstraction, we are faced with the question, how to apply exploration to a new design problem: How do we connect the problem-speci?c parts of the exploration with a randomised black-box search engine? What is an appropriate interface between the generic and problemdependent aspects? Which search strategy should we use? How can we achieve a simple implementation structure that leads to a reliable exploration tool? The next section 4 of the paper is devoted to this problem.

archive

Design Decision

Add new design points to set of promising design points (archive)

new design points including objective values

Estimation of nonfunctional properties (objective values)

feedback in case of local search new design points

Select a subset of design points for variation based on objective values

selected design points for variation

Generate new design points by variation of design parameters

generic black-box randomized search PISA protocol

problem-specific part of exploration framework

Figure 2: Overview of the proposed framework for design space exploration based on the PISA protocol. The basis of the proposed solution is the protocol PISA (Platform and Programming Language Independent Interface for Search Algorithms), see [25]. It is tailored towards black-box randomised search algorithms and is characterised by the following properties: (1) The problemspeci?c and the generic parts of the exploration method are largely independent from each other, i.e. the generic search and selection should be treated as a black-box (separation of concerns). (2) The framework itself should not depend on the machine types, operating systems or programming languages used (portability). (3) The protocol and framework should be tailored towards a reliable exploration. The main components of the proposed framework in Fig. 2 are a re?nement of Fig. 1. It shows the separation into the problem-speci?c variation and estimation part on the one hand and generic black-box search on the other.

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3 A Simple Example: Design Space Exploration of Cache Architectures

Before we describe the PISA-framework in detail, let us consider a simple example application that will be used throughout the remainder of this paper for illustration purposes. Note, that it is not the purpose of the example to present any new results in cache optimisation. Suppose we want to optimise the architecture of a cache for a prede?ned benchmark application. Restricting ourselves to L1 data caches only, the design choices include the cache size, the associativity level, the block size, and the replacement strategy. The goal is to identify a cache architecture that (i) maximises the overall computing performance with respect to the benchmark under consideration and (ii) minimises the chip area needed to implement the cache in silicon. Nr. 1 2 3 4 Parameter # of cache lines Block size Associativity Replacement strategy Range with k = 6 . . . 14 2k Bytes, with k = 3 . . . 7 2k , with k = 0 . . . 5 LRU or FIFO 2k ,

Table 1: Parameters determining a cache architecture

In Table 1, all parameters and possible values for the cache architecture are given. A design point is therefore determined by three integer values and a Boolean value. The integers denote the number of cache lines, the cache block size and the cache associativity; the Boolean value encodes the replacement strategy: f alse denotes FIFO (?rst-in-?rst-out), true denotes LRU (least recently used). Fig. 3 graphically depicts the design parameters. The values for the number of cache lines, block size and associativity have to be powers of 2, due to restrictions in the tools used for evaluation of the caches. The ?rst objective according to which the cache parameters are to be optimised is the CPI (cycles per instruction) achieved for a sample benchmark application, and the second objective is the chip area needed to implement the cache on silicon. To estimate the corresponding objective values, we used two tools, namely sim-outorder of SimpleScalar [26] and CACTI [27] provided by Compaq. The ?rst tool served to estimate the CPI for the benchmark compress95 running on the plain text version of the GNU public license as application workload. The smaller the CPI for compress95 for a particular solution, the better is this solution for this objective. The second tool calculated an estimate for the silicon area needed to implement the cache. The smaller the area, the better is the cache for the area objective.

4 A General Framework for Design Space Exploration

As discussed in Section 2, we propose a general framework for design space exploration that separates application-speci?c aspects from the optimisation strategy. The resulting two parts are implemented as independent processes communicating via text ?les, as will be detailed in Section 4.3. This concept (cf. Fig. 2) re?ects the working principle of black-box randomised search algorithms. Black-box methods are characterised by the fact that they do not make any assumptions about 6

2

cache block size

3

cache associativity

1

....

....

4

....

number of cache lines

replacement strategy

Figure 3: Illustration of the considered design choices for an L1 data cache architecture. the objective functions, and in this sense they treat the design criteria as black boxes which can contain arbitrarily complex functionalities. Initially, they create one or several designs at random, which are then evaluated with respect to the objective functions under consideration. Afterwards, the information about the already considered design(s) is used in order to generate one or several different designs that are then evaluated as well. This process is repeated until a certain number of iterations has been carried out or another stopping condition is ful?lled. The goal here is to exploit structural properties of the design space such that only a fraction of the design space needs to be sampled to identify optimal resp. nearly optimal solutions. This implies that different search space characteristics require different search strategy, and accordingly various black-box optimisers such as randomised local search, simulated annealing, evolutionary algorithms, etc. and variants thereof are available, see e.g. [28]. Two principles form the basis for all randomised search algorithms: selection and variation. On the one hand, selection aims at focusing the search on promising regions of the search space as will be discussed in Section 4.1. This part is usually problem independent. On the other hand, variation means generating new designs by slightly modifying or combining previously generated ones. Although standard variation schemes exists—details can be found in Section 4.2—the generation of new designs based on existing ones is strongly application dependent, similarly to the internal representation and the evaluation of designs.

4.1 Selection

The selection module implements two distinct phases: selection for variation and selection for survival. The former type of selection chooses the most promising designs from the set of previously generated designs that will be varied in order to create new designs. Because for practical reasons not all of the generated designs can be kept in memory another selection phase is necessary in order to decide which of the currently stored designs and the newly created ones will remain in the working memory. We will refer to this phase as selection for survival or environmental selection, 7

in analogy to the biological terminology used in the context of evolutionary algorithms. 4.1.1 Selection for Variation

Selection for variation is usually implemented in a randomised fashion. One possibility is to randomly pick two solutions from the working memory based on a uniform probability distribution and hold a tournament between them. For each tournament, the better design is copied to a temporary set which is denoted as mating pool. By repeating this procedure, several designs can be selected for variation, where high-quality designs are more likely to have one or multiple copies in the mating pool. This selection method is known as binary tournament selection; many alternative schemes exist as well (see [29]). Most of these selection algorithms assume that the usefulness or quality of a solution is represented by a scalar value, the so-called ?tness value. While ?tness assignment is straight forward in case of a single objective function, the situation is more complex in a multiobjective scenario. Here, one can distinguish between three conceptually different approaches: ? Aggregation: Traditionally, several optimisation criteria are aggregated into a single objective by, e.g., using a weighted sum of the distinct objective function values. To obtain several optimal trade-off designs, multiple weight combinations need to be explored either in parallel or subsequently. Nevertheless, not necessarily all Pareto-optimal designs can be found as illustrated in Fig. 4. Similar problems occur with many other aggregation methods, see [30]. ? Objective Switching: The ?rst papers using evolutionary algorithms to approximate the Pareto set suggested to switch between the different objectives during the selection step, for instance, Schaffer [31]. ? Dominance-based Ranking: Nowadays, most popular schemes use ?tness assignments that directly make use of the dominance relation or extensions of it. E.g., the dominance rank gives the number of solutions by which a speci?c solution is dominated, the dominance count represents the number of designs that a particular design dominates, and the dominance depth denotes the level of dominance when the set of designs is divided into nonoverlapping nondominated fronts (see [28] for details). These ?tness assignment schemes can also be extended to handle design constraints. For dominance-based approaches, the dominance relation can be modi?ed such that feasible solutions by de?nition dominate infeasible ones, while among infeasible designs the one with the lower constraint violation is superior—for feasible solutions, the de?nition of dominance remains unchanged (cf. [28]). An alternative is the penalty approach which can be used with all of the above schemes. Here, the overall constraint violation is calculated and summarised by a real value. This value is then added to the original ?tness value (assuming that ?tness is to be minimised); thereby, infeasible are penalised. Finally, another issue that is especially important in the presence of multiple objectives is maintaining diversity among the designs stored. Again, there is variety of different methods that cannot be discussed here in detail.

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f2

f2

not detectable

w1f1+w2f2

f1

f1

Figure 4: Illustration of the weighted-sum approach for two objectives. The left hand side shows how a particular weight combination (w1 , w2 ) uniquely identi?es one Pareto-optimal design. The right hand side demonstrates that not for all Pareto-optimal designs a weight combination exists that detects this solution. 4.1.2 Selection for Survival

When approximating the Pareto set, it is desirable not to loose promising designs due to random effects, for theoretical investigations see e.g. [32, 33, 32]. Similar issues as with selection for variation come into play here. If there are too many nondominated solutions, then additional diversity information is used to further discriminate between these designs. Furthermore, as many randomised search algorithms only keep a single solution in the working memory, often a secondary memory, a so-called archive (see also Fig. 2), is maintained that stores the current approximation of the Pareto set. For instance, PAES [34], a randomised local search method for multiobjective optimisation, checks for every generated design whether it should be added to the archive. 4.1.3 Multiobjective Optimisers

The above discussion could only touch the aspects involved in the design of the selection process for a multi-objective randomised search algorithm. In fact, a variety of methods exist, cf. [28], which over the time have become more complex, see e.g. [35]. In the evolutionary computation ?eld, even a rapidly growing subdiscipline emerged focusing on the design of evolutionary algorithms for multiple criteria optimisation [36]. However, an application engineer who would like to carry out a design space exploration is not necessarily an expert in the optimisation ?eld. He is rather interested in using state-of-art multi-objective optimisers. For this reason, the proposed design space exploration framework separates the general search strategy from the applicationspeci?c aspects such as variation. Thereby, it is possible to use pre-compiled search engines without any implementation effort.

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4.2 Variation

In this subsection, we describe the application-speci?c part of the proposed design space exploration framework. In particular, the variation module encapsulates the representation of a design point and the variation operators, see also the overview in Fig. 2. It is the purpose of this component in the design space exploration framework to generate suitable new design points from a given set of selected ones. Therefore, the variation is problem-speci?c to a large extent and provides a major opportunity to include domain-knowledge. 4.2.1 Representation

A formal description of a design needs to be appropriately encoded in the optimisation algorithm. The main objectives for suitable design representations are as follows: ? The encoding should be designed in a way that enables an ef?cient generation of design points in an appropriate neighbourhood, see also the next subsection on variation operators. ? The representation should be able to encode all relevant design points of the design space. In particular, if the design space has been pruned using problem-dependent approaches, the chosen representation should re?ect these constraints in a way that enables ef?cient variation for the determination of a neighbourhood. ? The design parameters should be independent of each other as much as possible in order to enable a suitable de?nition of variation operators. A representation of a solution can, e.g., consist of real or integer values, or vectors thereof to encode clock speeds, memory size, cache size, etc. Bit vectors can be used to describe the allocation of different resources. Another class of representations could be the permutation of a vector with ?x elements to represent, e.g., a certain task scheduling. Furthermore, variable length data structures such as trees or lists can be used for the representation of, e.g., graphs (see [29] for an overview). All parameters for the representation have to lie inside the problem speci?cation that spans the design space of possible solutions. A solution parameter could therefore be, e.g., a real value in the range given in the speci?cation, an integer value in a list of possible integers, or a selected edge in a problem speci?cation graph. In the cache example, we use integer values to represent the number of cache lines in the solution cache, the block size and the associativity. The integer values are the actual cache parameters, such that these lie in the range speci?ed in Table 1. The cache line replacement strategy is represented by a boolean value. 4.2.2 Variation Operators

The purpose of the variation operators is to determine new design points given a set of selected previously evaluated design points. There are several objectives for selecting appropriate variation operators: ? The variation operators operate on the design representation and generate a local neighbourhood of the selected design points. These new design points will be evaluated by the 10

parent solution

parent solution #1

parent solution #2

parameter mutated

child solution

child solution #1

child solution #2

Figure 5: Variation operators used in the cache example: mutation (left), recombination (right). estimation, see Fig. 1. Therefore, the construction of the variation operators is problemdependent and a major possibility to include domain-knowledge. ? The constructed neighbourhood should not contain infeasible design points, if possible. ? In case of design points that are infeasible because non-functional properties are outside of given constraints, one may use a feedback loop shown in Fig. 1 in order to correct. ? The variation operator may also involve problem-dependent local search (e.g. by optimising certain parameters or hidden optimisation criteria) in order to relieve the randomised search from optimisation tasks that can better be handled with domain-knowledge. In principle, we can distinguish different variation operators according to the number of solutions they operate on. Most randomised search algorithms generate a single new design point by applying a randomised operator to a known design point. For simulated annealing and randomised local search algorithms this operator is called neighbourhood function, whereas for evolutionary algorithms this operator is denoted as mutation operator. We will use the term mutation in the remainder of this section. In the context of evolutionary algorithms there also exists a second type of variation, in addition to mutation. Since evolutionary algorithms maintain a population of solutions, it is possible to generate one or more new solutions based on two or more existing solutions. The existing designs selected for variation are often referred to as parents, whereas the newly generated designs are called children. The operator that generates ≥ 1 children based on ≥ 2 parents is denoted as recombination. Mutation: The assumption behind mutation is that it is likely to ?nd better solutions in the neighbourhood of good solutions. Therefore, mutation operators are usually designed in such a way that the probability of generating a speci?c solution decreases with increasing distance from the parent. There exist several approaches to implement mutation. It is, e.g., possible to always change exactly one parameter in the representation of a solution and keep all other parameters unchanged. A different mutation operator changes each of n parameters with probability 1/n, which leads to the fact that one parameter is changed in expectation. This approach is also used in the cache example.

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Changing a parameter means changing its value, i.e., ?ipping a bit in a binary representation, or choosing new parameter values according to some probability distribution for an integer- or realvalued representation. For representations based on permutations of vector elements the mutation operator changes the permutation by exchanging two elements. If the speci?cation is based on lists of possible values, the mutation operator selects a new element according to some probability distribution. In general, a mutation operator should on the one hand produce a new solution that is “close” to the parent solution with a high probability, but on the other hand be able to produce any solution in the design space, although with very small probability. This is to prevent the algorithm from being stuck in a local optimum. For the cache example, we used the following mutation operator: Each of the design parameters is mutated with probability 0.25 (as we have 4 different parameters). The change that is applied to each of the parameters is normally distributed, i.e., the value of a parameter is increased by a value that is normally distributed around 0 inside the ranges given in Table 1; e.g. the block size parameter change is normally distributed between -4 and +4. Note, that in the example we also allow changes of size 0, i.e. the parameter remains unchanged. Recombination: Recombination takes two or more solutions as input, and then generates new solutions that represents combinations of the parents. The idea behind recombination is to take advantage of the good properties of each of the parent to produce even better children. In analogy to the mutation operator, a good recombination vector should produce solutions that lie “between” the parents either with respect to the parameter space or to the objective space. For vectors in general, recombination of two parents can be accomplished by cutting both solutions at randomly chosen positions and rearranging the resulting pieces. For instance, onepoint crossover creates a child by copying the ?rst half from the ?rst parent and the second half from the second parent. If the cut is made at every position, i.e., at each position randomly either the value from the ?rst or the second parent is copied, the operator is called uniform recombination. A further approach for real-valued parameters is to use the average of the two parents’ parameter values, or some value between the parents’ parameter values. A detailed overview of various recombination operators for different representation data structures can be found in [37]. For the cache example we used uniform recombination, i.e., for each of the parameters like cache block size we randomly decided from which parent solution we should use the parameter for the ?rst child solution, where all unused parameters of the parent solution are then used for the second child solution. See Fig. 5 on the right hand side for a graphical representation of uniform recombination. Infeasible Solutions: It can happen that after mutation or recombination a generated solution is not feasible, i.e., the solution represented by the parameters doesn’t describe a valid system. To solve this problem there are different possibilities. First, we could ensure that the variation operators do not create infeasible solutions by controlling the construction of new solutions, we can call this approach “valid by construction”. Second, we could implement a repair method, that turns constructed solutions that are infeasible into feasible ones by ?xing the infeasible parameters. The third possibility is to introduce an additional constraint and to penalise infeasible designs in the way as described in Section 4.1. Finally, one can use the concept of penalty functions in order to guide the search away from areas with infeasible design points.

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4.3 Implementation Issues

In this section we brie?y describe the protocol used in PISA, see [38]. It is the purpose of PISA to make state-of-the-art randomised search algorithms for multi-objective optimisation problems readily available. Therefore, for a new design space exploration task in embedded system design, one can concentrate on the problem-dependent aspects, where the domainknowledge comes in. The protocol has to be implemented by any design space exploration tool that would like to bene?t from pre-compiled and ready-to-use search algorithms available at http://www.tik.ee.ethz.ch/pisa. Besides, the web-site also contains a set of application problems and benchmark applications for the development of new randomised search algorithms. The detailed protocol including ?le formats and data type de?nitions is given in [38]. In the protocol description, we call the application-speci?c part ’variator’ and the search algorithm is called ’selector’, according to Figure 6. The variator also contains the estimation of non-functional properties.

variator parameters

Variator

cfg

alpha 3 mu 3 lambda 1 dim 2

ini

4 0 5.6 1 4.7 2 7.1 3 3.4 END 6.3 8.2 3.4 9.0

arc

3 0 2 3 END

sel

2 3 0 END

var

1 4 5.3 2.3 END 2

sta

selector parameters

Selector

Figure 6: Communication between modules through text ?les as de?ned by the PISA protocol. The ?les contain sample data. The details of the protocol have been designed with several objectives in mind: ? Small amount of data that need to be communicated between the two different processes (selector and variator). ? The communicated data should be independent of the problem domain in order to enable a 13

generic implementation of the selector process. ? Separation into problem-independent (selector) and problem-dependent (variator) processes. ? The implementation of the protocol should be as much as possible independent of the programming languages, hardware platforms and operating systems. The protocol de?nes the sequence of actions performed by the selector and variator processes (cf. Table 2). The communication between the two processes is done by exchange of text ?les over a common ?le system. The handshake protocol is based on states and ensures that during the optimisation process only one module is active at any time. During the inactive period a process polls the state ?le for changes. Whenever a module reads a state that requires some action on its part, the operations are performed and the next state is set. The core of the optimisation process consists of state 2 and state 3: In each iteration the selector chooses a set of parent individuals and passes them to the variator. The variator generates new child solutions on the basis of the parents, computes the objective function values of the new individuals, and passes them back to the selector. In addition to the core states two more states are necessary for normal operation. State 0 and state 1 trigger the initialisation of the variator and the selector, respectively. In state 0 the variator reads the necessary parameters. Then, the variator creates an initial population, determines the objective values of the individuals and passes the initial population to the selector. In state 1, the selector also reads the required parameters, then selects a sample of parent individuals and passes them to the variator. The four states 0–3 provide the basic functionality of the PISA-protocol. To add some ?exibility the PISA-protocol de?nes a few more states which are mainly used to terminate or reset both the variator process and the selector process. Table 2 gives an overview over all de?ned states. The additional states 4–11 are not mandatory for a basic implementation of the protocol. State State 0 State 1 State 2 State 3 State 4 State 6 State 8 State 10 Action Variator reads parameters and creates initial solutions Selector reads parameters and selects parent solutions Variator generates and evaluates new solutions Selector selects solutions for variation Variator terminates. Selector terminates. Variator resets. (Getting ready to start in state 0) Selector resets. (Getting ready to start in state 0) Next State State 1 State 2 State 3 State 2 State 5 State 7 State 9 State 11

Table 2: States for the PISA-protocol. The main states of the protocol are printed in bold face. The data transfer between the two modules introduces some overhead compared to a traditional monolithic implementation. Thus, the amount of data exchange for each individual should be minimised. Since all representation-speci?c operators are located in the variator, the selector does not have to know the representation of the individuals. Therefore, it is suf?cient to convey only the following data to the selector for each individual: an identi?er and its objective vector. In return,

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the selector only needs to communicate the identi?ers of the parent individuals to the variator. The proposed scheme allows to restrict the amount of data exchange between the two modules to a minimum. For PISA-compliant search algorithms to work correctly, a designer has to ensure, that all objectives are to be minimised. In addition the variator and selector have to agree on a few common parameters: (i) the population size α , (ii) the number of parent solutions ? , (iii) the number of child solutions λ and (iv) the number of objectives dim. These parameters are speci?ed in the parameter ?le with suf?x cfg, an example ?le is shown in Figure 6. The selector and the variator are normally implemented as two separate processes. These two processes can be located on different machines with possibly different operating systems. This complicates the implementation of a synchronisation method. Most common methods for interprocess communication are therefore not applicable. In PISA, the synchronisation problem is solved using a common state variable which both modules can read and write. The two processes regularly read this state variable and perform the corresponding actions. If no action is required in a certain state, the respective process sleeps for a speci?ed amount of time and then rereads the state variable. The state variable is an integer number stored to a text ?le with suf?x sta. We use text ?les instead of, e.g., sockets, because ?le access is completely portable between different platforms and familiar to all programmers. All other data transfers between the two processes besides the state are also performed using text ?les. The initial population is written by the variator to the ?le with suf?x ini, the population is written by the selector to a ?le with suf?x arc. In a text ?le with suf?x sel the selector stores the parent solutions that are selected for variation. The newly generated solutions are passed from the variator to the selector through a ?le with suf?x var. All text ?les for data transfer have to begin with the number of elements that follow and to end with the keyword END. Once the receiving process has completely read a text ?le, it has to overwrite the ?le with 0, to indicate that it successfully read the data.

4.4 Application of PISA for Design Space Exploration

For the cache example presented in Section 3, we coded the variator part in Java. The mutation and recombination operator were implemented as described in 4.2, and the combination with a selector is PISA-compliant as described in Section 4.3. The selector was downloaded from the PISA website. We performed the design space exploration for L1 data caches using SPEA2, an evolutionary multiobjective optimiser described in [35]. The solutions selected by SPEA2 for variation were pairwise recombined with probability 0.8, and the resulting solutions were then mutated with probability 0.8. Afterwards the generated solutions were added to the population and passed to the search algorithm for selection. The design space with all solutions is shown in Fig. 7. These design points have been generated using exhaustive search in order to compare the heuristic search with the Pareto front of optimal solutions. The front of non-dominated solutions found for the cache example with SPEA2 after a typical optimisation run with 40 generation for a population size of 6 solutions is marked with circles. Although the cache design space exploration problem is simple in nature, we can make some observations which also hold for more involved exploration problems. The two objectives, namely the minimisation of the silicon area and the minimisation of the CPI, are con?icting, resulting in an area vs. performance trade-off. This results in the fact that we do not have a single opti15

mal solution, but a front of Pareto-optimal solutions. All points on this front represent different promising designs, leaving the ?nal choice for the design of the cache up to the designer’s preference. Further, we can observe in Fig. 7 that the evolutionary algorithm found solutions close to the Pareto-optimal front.

0.59 0.58

CPI for compress95

0.57 0.56 0.55 0.54 0.53 0.52 0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

silicon area [cm^2]

Figure 7: All 540 possible design points determined using exhaustive search and the best design trade-offs found by the multi-objective search algorithm SPEA2 after 40 generations. The reduction of the problem to a single-objective optimisation problem, e.g. using a weighted-sum approach is dif?cult already for this simple example, because it represents a true multi-objective problem. It is not at all clear how to relate area to performance, which would be needed for the weighted-sum approach. For the simple cache example we could have explored the design space using exhaustive search instead of employing evolutionary algorithms, which we actually did to determine all solutions shown in Fig. 7. For larger design spaces, as the one explored with EXPO, a tool for design space exploration of complex stream processor architectures, exhaustive search is prohibitive, and only randomised search algorithms can be used. It has been shown in many studies (e.g. in [28]) that evolutionary algorithms perform better on multi-objective optimisation problems than other simpler randomised search algorithms. On the PISA website, many different ready-to-use evolutionary search algorithms can be downloaded. Additionally, a tool for design space exploration can be found. The only steps needed for a ?rst design space exploration using the PISA framework are as follows: (1) download the exploration tool EXPO and one of the search algorithms, (2) unpack the components, and (3) run them. PISA enables the use of different evolutionary algorithms without having to change the implementation of the exploration tools. A recent study [39] has shown that for EXPO the quality of the approximation of the Pareto-optimal front may differ between different evolutionary algorithms. With a modular framework based on the PISA protocol it is possible to test the design space exploration performance of different randomised search algorithms to ?nd the search algorithm most 16

suitable to the exploration problem.

5 Conclusion

The paper introduced a framework for design space exploration of embedded systems. It is characterised by (1) multiple optimisation criteria, (2) randomised search algorithms and (3) a software interface that clearly separates problem-dependent and problem-independent parts of an implementation. In particular, the interface PISA formally characterises this separation. It is implemented in a way that is independent of programming language used and the underlying operating system. As a result, it is easily possible to extend any existing method to estimate non-functional properties with an effective multi-objective search. It should be pointed out, that effective automatic or semi-automatic (interactive) exploration needs deep knowledge about the speci?c optimisation target, i.e. the level of abstraction, the optimisation goals, ef?cient and accurate estimation methods. Nevertheless, the PISA framework separates the problem-dependent variation and estimation from the generic search and selection. Therefore, the user is relieved from dealing with the complex and critical selection mechanisms in multi-objective optimisation. On the other hand, his speci?c domain knowledge will be important when designing the variation operators that determine a promising local neighbourhood of a given search point. Finally, it is common knowledge that the class of randomised search algorithms described in the paper do not guarantee to ?nd the optimal solutions. In addition, if there is domain knowledge available that allows problem-speci?c exploration methods to be applied, then there is little reason to use a generic approach. But usually, those analytic methods do not exist for complex optimisation scenarios as found in embedded system design.

Acknowledgement

The work described in this paper was supported by the Swiss Government within the KTI program. The project was part of the MEDEA+ project SpeAC.

References

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