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# The ParadisEO-PEO Framework

## Introduction

ParadisEO-PEO is a white-box object-oriented framework dedicated to the reusable design of parallel and distributed metaheuristics (PDM). ParadisEO-PEO provides a broad range of features including evolutionary algorithms (EA), local searches (LS), the most common parallel and distributed models and hybridization mechanisms, etc. This high content and utility encourages its use at European level. ParadisEO-PEO is based on a clear conceptual separation of the solution methods from the problems they are intended to solve. This separation confers to the user a maximum code and design reuse. Furthermore, the fine-grained nature of the classes provided by the framework allow a higher flexibility compared to other frameworks. ParadisEO-PEO is one of the rare frameworks that provide the most common parallel and distributed models. Their implementation is portable on distributed-memory machines as well as on shared-memory multiprocessors, as it uses standard libraries such as MPI, PVM and PThreads. The models can be exploited in a transparent way, one has just to instantiate their associated provided classes. Their experimentation on the radio network design real-world application demonstrate their efficiency.

In practice, combinatorial optimization problems are often NP-hard, CPU time-consuming, and evolve over time. Unlike exact methods, metaheuristics allow to tackle large-size problems instances by delivering satisfactory solutions in a reasonable time. Metaheuristics are general-purpose heuristics that split in two categories: evolutionary algorithms (EA) and local search methods (LS). These two families have complementary characteristics: EA allow a better exploration of the search space, while LS have the power to intensify the search in promising regions. Their hybridization allows to deliver robust and better solutions

Although serial metaheuristics have a polynomial temporal complexity, they remain unsatisfactory for industrial problems. Parallel and distributed computing is a powerful way to deal with the performance issue of these problems. Numerous parallel and distributed metaheuristics (PDM) and their implementations have been proposed, and are available on theWeb. They can be reused and adapted to his/her own problems. However, the user has to deeply examine the code and rewrite its problem-specific sections. The task is tedious, errorprone, takes along time and makes harder the produced code maintenance. A better way to reuse the code of existing PDM is the reuse through libraries. These are often more reliable as they are more tested and documented. They allow a better maintainability and efficiency. However, libraries do not allow the reuse of design.

## Parallel and distributed metaheuristics

### Parallel distributed evolutionary algorithms

Evolutionary Algorithms (EA) are based on the iterative improvement of a population of solutions. At each step, individuals are selected, paired and recombined in order to generate new solutions that replace other ones, and so on. As the algorithm converges, the population is mainly composed of individuals well adapted to the "environment", for instance the problem. The main features that characterize EA are the way the population is initialized, the selection strategy (deterministic/stochastic) by fostering "good" solutions, the replacement strategy that discards individuals, and the continuation/stopping criterion to decide whether the evolution should go on or not.

Basically, three major parallel and distributed models for EA can been distinguished: the island (a)synchronous cooperative model, the parallel evaluation of the population, and the distributed evaluation of a single solution.

- Island (a)synchronous cooperative model. Different EA are simultaneously deployed to cooperate for computing better and robust solutions. They exchange in an asynchronous way genetic stuff to diversify the search. The objective is to allow to delay the global convergence, especially when theEAare heterogeneous regarding the variation operators. The migration of individuals follows a policy defined by few parameters: the migration decision criterion, the exchange topology, the number of emigrants, the emigrants selection policy, and the replacement/integration policy.

- Parallel evaluation of the population. It is required as it is in general the most timeconsuming. The parallel evaluation follows the centralized model. The farmer applies the following operations: selection, transformation and replacement as they require a global management of the population. At each generation, it distributes the set of new solutions between differentworkers. These evaluate and return back the solutions and their quality values. An efficient execution is often obtained particularly when the evaluation of each solution is costly. The two main advantages of an asynchronous model over the synchronous model are: (1) the fault tolerance of the asynchronous model; (2) the robustness in case the fitness computation can take very different computation times (e.g. for nonlinear numerical optimization). Whereas some time-out detection can be used to address the former issue, the latter one can be partially overcome if the grain is set to very small values, as individuals will be sent out for evaluations upon request of the workers.

- Distributed evaluation of a single solution. The quality of each solution is evaluated in a parallel centralized way. That model is particularly interesting when the evaluation function can be itself parallelized as it is CPU time-consuming and/or IO intensive. In that case, the function can be viewed as an aggregation of a certain number of partial functions. The partial functions could also be identical if for example the problem to deal with is a data mining one. The evaluation is thus data parallel and the accesses to data base are performed in parallel. Furthermore, a reduction operation is performed on the results returned by the partial functions. As a summary, for this model the user has to indicate a set of partial functions and an aggregation operator of these.

### Parallel distributed local searches

#### Local searches

All metaheuristics dedicated to the improvement of a single solution are based on the concept of neighborhood. They start from a solution randomly generated or obtained from another optimization algorithm, and update it, step by step, by replacing the current solution by one of its neighboring candidates. Some criterion have been identified to differentiate such searches: the heuristic internal memory, the choice of the initial solution, the candidate solutions generator, and the selection strategy of candidate moves. Three main algorithms of local search stand out: Hill Climbing (HC), Simulated Annealing (SA) and Tabu Search (TS).

#### Parallel local searches

Two parallel distributed models are commonly used in the literature: the parallel distributed exploration of neighboring candidate solutions model, and the multi-start model.

- Parallel exploration of neighboring candidates. It is a low-level Farmer-Worker model that does not alter the behavior of the heuristic. A sequential search computes the same results slower.At the beginning of each iteration, the farmer duplicates the current solution between distributed nodes. Each one manages some candidates and the results are returned to the farmer. The model is efficient if the evaluation of a each solution is time-consuming and/or there are a great deal of candidate neighbors to evaluate. This is obviously not applicable to SA since only one candidate is evaluated at each iteration. Likewise, the efficiency of the model for HC is not always guaranteed as the number of neighboring solutions to process before finding one that improves the current objective function may be highly variable.

- Multi-start model. It consists in simultaneously launching several local searches. They may be heterogeneous, but no information is exchanged between them. The resultswould be identical as if the algorithms were sequentially run.Very often deterministic algorithms differ by the supplied initial solution and/or some other parameters. This trivial model is convenient for low-speed networks of workstations.

## Hybridization

Recently, hybrid metaheuristics have gained a considerable interest. For many practical or academic optimization problems, the best found solutions are obtained by hybrid algorithms. Combinations of different metaheuristics have provided very powerful search methods. Two levels and two modes of hybridization have been distinguished: Low and High levels, and Relay and Cooperative modes. The low-level hybridization addresses the functional composition of a single optimization method. A function of a given metaheuristic is replaced by another metaheuristic. On the contrary, for high-level hybrid algorithms the different metaheuristics are self-containing, meaning no direct relationship to their internal working is considered. On the other hand, relay hybridization means a set of metaheuristics is applied in a pipeline way. The output of a metaheuristic (except the last) is the input of the following one (except the first). Conversely, co-evolutionist hybridization is a cooperative optimization model. Each metaheuristic performs a search in a solution space, and exchange solutions with others.

## Paradiseo goals and architecture

The "EO" part of ParadisEO-PEO means Evolving Objects. EO is a C++ LGPL open source framework and includes a paradigm-free Evolutionary Computation library (EOlib) dedicated to the flexible design of EA through evolving objects superseding the most common dialects (Genetic Algorithms, Evolution Strategies, Evolutionary Programming and Genetic Programming). Furthermore, EO integrates several services including visualization facilities, on-line definition of parameters, application check-pointing, etc. ParadisEO-PEO is an extended version of the EO framework. The extensions include local search methods, hybridization mechanisms, parallelism and distribution mechanisms, and other features that are not addressed in this paper such as multi-objective optimization and grid computing. In the next sections, we present the motivations and goals of ParadisEO-PEO, its architecture and some of its main implementation details and issues.

### Motivations and goals

A framework is normally intended to be exploited by as many users as possible. Therefore, its exploitation could be successful only if some important user criteria are satisfied. The following criteria are the major of them and constitute the main objectives of the ParadisEO-PEO framework:

- Maximum design and code reuse. The framework must provide for the user a whole architecture design of his/her solution method. Moreover, the programmer may redo as little code as possible. This objective requires a clear and maximal conceptual separation between the solution methods and the problems to be solved, and thus a deep domain analysis. The user might therefore develop only the minimal problem-specific code.

- Flexibility and adaptability. It must be possible for the user to easily add new features/ metaheuristics or change existing ones without implicating other components. Furthermore, as in practice existing problems evolve and new others arise these have to be tackled by specializing/adapting the framework components.

- Utility. The framework must allow the user to cover a broad range of metaheuristics, problems, parallel distributed models, hybridization mechanisms, etc.

- Transparent and easy access to performance and robustness. As the optimization applications are often time-consuming the performance issue is crucial. Parallelism and distribution are two important ways to achieve high performance execution. In order to facilitate its use it is implemented so that the user can deploy his/her parallel algorithms in a transparent manner. Moreover, the execution of the algorithms must be robust to guarantee the reliability and the quality of the results. The hybridization mechanism allows to obtain robust and better solutions.

- Portability. In order to satisfy a large number of users the framework must support different material architectures and their associated operating systems.

### ParadisEO-PEO architecture

The architecture of ParadisEO-PEO is multi-layer and modular allowing to achieve the objectives quoted above. This allows particularly a high flexibility and adaptability, an easier hybridization, and more code and design reuse. The architecture has three layers identifying three major categories of classes: Solvers, Runners and Helpers.

- Helpers. Helpers are low-level classes that perform specific actions related to the evolution or search process. They are split in two categories: Evolutionary helpers (EH) and Local search helpers (LSH). EH include mainly the transformation, selection and replacement operations, the evaluation function and the stopping criterion. LSH can be generic such as the neighborhood explorer class, or specific to the local search metaheuristic like the tabu list manager class in the Tabu Search solution method. On the other hand, there are some special helpers dedicated to the management of parallel and distributed models 2 and 3, such as the communicators that embody the communication services.

  Helpers cooperate between them and interact with the components of the upper layer i.e. the runners. The runners invoke the helpers through function parameters. Indeed, helpers have not their own data, but they work on the internal data of the runners.

- Runners. The Runners layer contains a set of classes that implement the metaheuristics themselves. They perform the run of the metaheuristics from the initial state or population to the final one. One can distinguish the Evolutionary runners (ER) such as genetic algorithms, evolution strategies, etc., and Local search runners (LSR) like tabu search, simulated annealing and hill climbing. Runners invoke the helpers to perform specific actions on their data. For instance, an ER may ask the fitness function evaluation helper to evaluate its population. An LSR asks the movement helper to perform a given movement on the current state. Furthermore, runners can be serial or parallel distributed.

- Solvers. Solvers are devoted to control the evolution process and/or the search. They generate the initial state (solution or population) and define the strategy for combining and sequencing different metaheuristics. Two types of solvers can be distinguished. Single metaheuristic solvers (SMS) and Multiple metaheuristics solvers (MMS). SMSs are dedicated to the execution of only one metaheuristic.MMS are more complex as they control and sequence several metaheuristics that can be heterogeneous. Solvers interact with the user by getting the input data and delivering the output (best solution, statistics, etc).

According to the generality of their embedded features, the classes of the architecture split in two major categories: Provided classes and Required classes. Provided classes embody the factored out part of the metaheuristics. They are generic, implemented in the framework, and ensure the control at run time. Required classes are those that must be supplied by the user. They encapsulate the problem-specific aspects of the application. These classes are fixed but not implemented in ParadisEO-PEO. The programmer has the burden to develop them using the OO specialization mechanism.