Integration of Simulation and Optimization for Solving Complex Decision Making Problems S.IASSINOVSKI, A.ARTIBA, V.BACHELET, F.RIANE CREGI – Centre de Recherches et d’Études en Gestion Industrielle Facultés Universitaires Catholiques de Mons Chaussée de Binche, 151 B7000 Mons BELGIUM
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[email protected] Abstract: - This paper concerns the development of an unified formal modeling framework designed to provide for model sharing, reusability and integration of simulation and optimization methods in order to allow the decision-maker to master the dynamics of complex discrete systems. We should point out that the different steps of problem identification, modeling and application generation use the same integrated formalism and environment. We give the general approach of our methodology and then describe the way we integrate simulation and optimization for solving decision making problems. Key-Words: - simulation, optimization, decision making, modeling, discrete systems.
1
Introduction
Many domains (scientific research, modern industry, …) increasingly require appropriate decision making methods and/or tools for complex discrete systems (CDS) management. Many decision making (DM) problems are concerned with both simulation and optimization. Nowadays, a great deal of various decision making methods and tools are available. These DM methods are concerned with either only modeling methodology or solving tools with only few conceptual aspects(language for representation, methodology, …). The lack of the appropriate integrated tools have lead many researchers (Zeigler et el., 1996; Drissi and Abdulrab, 1994; Atabakhsh and Chan, 1994; Nadoli and Biegel, 1993; Araar and Co 1997; Sharma et al. 1994) to attempt to develop so-called hybrid systems, combining in one integrated application the different tools, originating from operations research, artificial intelligence, object-oriented approach and simulation. LOP (Drissi and Abdulrab, 1994), a system of programming by logical objects, is an example of integration of logical programming, object-oriented approach, constraint programming and simulation. The Extool system (Atabakhsh and Chan, 1994), which allows one to associate a production rules base with any object of a simulation model, is another illustration. The IMSAT tool (Nadoli and Biegel, 1993) uses the concept of intelligent agents to simulate the process of fabrication. Araar and Co (1997) describe the behavior of an event by a production rule which is to be executed when the event occurs. Robinson et al. (1998) present a tool combining
simulation model and an expert system, which serves for decision making within the model. The problem in this way is that each tool uses its own representation of the system considered, that embarrasses the data exchange. This results in rather “heavy” applications and demands the development of dedicated interfaces.
Problem domain
Application generator
Solving Engine Modeling Methodology
Language
Modeling aspect
Solution domain
Solving aspect
Fig. 1. Unified approach for solving decision making problems Obviously, a hybrid tool based on a unique system representation for simulation, optimisation and decision making would be preferable. We have been working on this issue for a decade and have proposed some first developments tackling different aspects of this approach. A multi-model approach combining simulation, artificial intelligence (AI) and operations
research (OR) tools is proposed in (Artiba 1995;Artiba and Aghezzaf, 1997). An integration of simulation and state graph search optimisation technique is discussed is (Iassinovski, 1997). The intelligent simulator RAO has been designed for integration of AI techniques (Artiba et al., 1998). Moreover, the co-operatiion of different metaheuristic methods has been studied in the COSEARCH approach by (Bachelet et al., 2000) This paper relates the design and the development of an open framework that includes concepts, methodology, language, and solving engines. It integrates several decision problem solving approaches in a unified manner (Fig. 1). The unification aspect of the framework relies on the application of the same set of concepts at different levels of the modeling and solving process, from the modeling methodology to the solving engines. The modeling methodology in this framework inherits from several usually used representation methods: object-based and intelligent agents approaches to describe the system elements; production rules and process oriented approach to represent the system’s Solving Knowledge
Simulation Optimization Expert System …
This framework provides well known decision methods with methodology and language for problem representation. That way, we discuss, in this paper, a step towards standardization of decision problems modeling and solving.
2
The proposed framework
In this section, we present the idiosyncrasies of the proposed framework. The figure Fig. 2 shows two chains of components of the framework: the derivation chain and the transformation chain. The derivation chain illustrates the unified approach from solving knowledge to solving engines. The transformation chain shows the transition from problem domain to solution domain. Analyzing the knowledge in the domain of decision problem solving, we have selected several general concepts which represent the basement of our unified approach. We propose a systemic and hierarchical representation of a CDS, aside a three-contexts-based description: static, dynamic and decisional. These
Concepts of the project
Legend :
Systemic Hierarchical 3 contexts: - static - dynamic - decisional
Methodology
Derivation Transformation Using
Language (visual) Hierarchical Object Oriented … Application generator
Engine / OS
Problem Domain system structure system parameters strategy
Problem Conceptual Model
Model
Data Conceptual Model
Data
Executable Models
Run-time Models
Solution Domain
Fig. 2 The framework for unification and integration
dynamic. The proposed framework provides with a same platform for using well known decision making methods, allowing interaction in solving the given problem. This integration aspect of the framework allows the combinations of methods such as simulation methods, metaheuristics, expert systems, exact methods, or others. This framework is designed as an open platform, allowing new solving methods to be integrated.
concepts are detailed in section 3. The concepts are applied along the derivation chain to design tools for building the transformation chain: a modeling methodology, a representation language, an application generator and solving engines. In the transformation chain, once the problem domain is defined, problem and data conceptual models are developed following the modeling methodology. Then (visual) language is used to
translate the problem conceptual model to a generic operational model using as well as possible existing (sub)models stored in a structured library (the framework is endowed with mechanisms that enable reuse and exchange of components and methods to build up new models). The language is also used to specify the data necessary for problem solving using the information system of the problem domain. The operational model is translated by the application generator into as many executable models as the number of available engines and their operating system environments. Afterward, executable model is run by its corresponding solving engine, using data, to yield a solution.
3
Modeling methodology
According to a systemic approach, a CDS is an organized set of components which interact in order to fulfill a given objective. The conceptual model we propose follows a hierarchical approach that means the components of a CDS are (sub-) CDS (Fig. 3). Moreover, a three contexts approach is used for a system to be modeled. The static context describes the system’s state variables and the components that may be other CDSs. The dynamic context is concerned with the functioning of the components. Activities (state changes), process and communications are described. The third context deals with the strategy for solving a given problem, possibly combining different methods.
relations are a result of control operations that affect the system's state (Booch, 1991; Hill David, 1996). In our object-oriented representation of a CDS (Fig. 4), object’s attributes correspond to the static context, and the relations stand for the description of the dynamic and control context. The CDS representation is completed with an observation part: performance measures, tracing and animation. In the static context, the CDS state is modelled according to the hierarchical structure of the state variables and their corresponding definition domains. In the dynamic context, activities and communications are described. We define an activity as an elementary change of a CDS state. From the simulation point of view, any change of the system state is an event. So we can say the activities represent events logic in a particular case of simulation. For the simulation purposes, activities may have duration. In this case they represent the actions. Activities are described by means of modified production rules, introduced in the RAO method (Artiba et al., 1998). We also propose the description of processes inside the CDS as a graph of activities. The description of the communication between the CDSs relies on the multiagent paradigm (Weiss G., 2000). The decisional context is concerned with the strategy for solving the CDS’s intrinsic decision problem. The strategy states which decision making tool is used. It may involve combinations of several tools (e.g. simulation and optimization). Conceptual CDS
objects
interactions
(sub) CDS :
Definition
- static context state variables
Objects, sub-systems
Describe the static context (CDS state)
- dynamic activities, process
Activities, processes, communication
Describe the dynamic context: interaction between the (sub) CDS components
- decisional solving strategy
Decision
Describes the strategy for solving
Observation
Fig. 3 The problem conceptual model
4
Conceptual aspects of the language
A building block of the conceptual model we propose is the representation of a CDS using an object-oriented paradigm. According to this paradigm, a system is defined as an interaction between two kinds of entities: the objects and the relations. The objects are the system's elements described by a set of attributes. The
Performance measures
Allow us to analyse an object operation
Animation pictures
Describe different possibilities to display the object state
Tracing / replay
Allow us to tune tracing information to be further processed
RK 0.042 1 3 RK 0.057 1 3 ...
Fig. 4 Conceptual representation of a CDS Performance measures allow the calculation of statistics about the evolution of the CDS’s state, animation pictures display the CDS’s state, and
tracing samples describing the content and format of the data written in a trace medium for the further analysis. Our conceptual model of a CDS describes an objet having its own state, behaviour (local processes), being able to communicate, to observe and to display its state. Although we believe that a textual language is required to describe all the nuances of real problems, we assume that graphical interfaces should be developed to make the description of the system’s elements and their behavior easier and quicker.
5
Solving architecture
The solving architecture consists in the applications generator and corresponding engines. This architecture is based on interactions between different solving tools (simulation, metaheuristics, exact methods, expert systems, …) . The interaction process is based on the blackboard paradigm (Fig. 5). The blackboard represents a CDS state. Each tool evolve the system from one state to another. The blackboard controller realizes the CDS’s solving strategy, calling the corresponding solving tools in the necessary order. The blackboard paradigm provides the architecture with openness for addition of any solving tool which manages system states. Meta – heuristic
Simulator
Blackboard controller
System state
Other
human
Fig. 5 The solving architecture
6
Conclusion
In this paper, we have presented our advancement in developing a unified framework integrating simulation and optimization. This work is the issue of our research activities in the multi-model approach (combination of simulation AI and OR). Some features of this framework have been validated using the RAO simulator as well as several prototypes. In order to validate our methodology, we continue the assembly of all described concepts in a one integrated prototype while tackling real industrial
problems.
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