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5. NEURAL NETWORK BASED ADAPTIVE OPTIMAL CONTROL: UNIK-LP/NN

5.1. NEURAL NETWORK MODEL FOR THE CONTROL OF OPTIMIZATION MODEL

When the future information for an LP model is not complete, the model tends to incorporate uncertainties as some assumptions for the coefficients. As time passes and more precise information is accumulated, the initial LP model may no longer correctly represent the problem. For instance, the daily demand cannot be reliably estimated at the crude purchase point, which is usually 3 months ahead. So the daily demands, which should appear as coefficients, are estimated by the average of monthly demands. As time passes, we become able to identify which day tankers will arrive to pick up the final products. Then we have to adjust the coefficients concerning daily demands, while maintaining the initial optimal solution as much as possible.

So we have developed a tool -- UNIK-LP/NN -- that can support the construction and recall of the neural network model on top of the semantic optimization model UNIK-LP, and the semantic neural network building aid UNIK-NEURO. Basically, the semantic neural network means that the architecture and details about the model is represented by objects, so that the neural network model can communicate with the semantic optimization model. In this manner, UNIK-LP/NN can effectively automate most of the neural network construction and recall procedure for optimal control (Lee and Kim, 1996).


FIGURE 6 AND/OR graphical relationships among embedded structures, constraints, and BOT distinctivenesses.


FIGURE 7 Concept of the adaptive optimal control.

The process of adaptive optimal control on an LP model is diagrammatically shown in Figure 7. The process of performing the adaptive optimal control using the neural network can be summarized as follows.

  1. Generate instances of paired values of controllable coefficients and optimized values of designated decision variables from the optimization model.
  2. Using the instances, train a neural network model that has the designated decision variables as input nodes and the controllable coefficients as output nodes.
  3. Input the desired values of designated decision variables into the neural network to obtain the suggested values of controllable coefficients.
  4. To evaluate the performance of neural network based control, the optimization model is modified with the suggested coefficients from the neural network, and the optimal solution is obtained accordingly. By comparing the desired decision values and the realized ones from the optimization model with the modified coefficients, the error of the neural network model can be computed. This process is graphically depicted in Figure 7. The validity of the neural network approach is proven with real-world problems found in the refinery plant.

5.2. ARCHITECTURE OF UNIK-LP/NN

The architecture of UNIK-LP/NN is depicted in Figure 8. UNIK-LP/NN has two major parts: adaptive optimal control model constructor and adaptive optimal controller. The constructor supports users in choosing a target optimization model and in defining a specific neural network model for adaptive optimal control. From the adaptive optimal control model definition, the constructor automatically develops a neural network model via the interaction with UNIK-LP and UNIK-NEURO. The adaptive optimal controller computes the values of adjusted controllable coefficients along with the corresponding feasible decision variables.


FIGURE 8 Architecture of UNIK-LP/NN environment.

6. INTEGRATION OF RULES WITH CONSTRAINT SATISFACTION PROBLEM: UNIK-CRSP

Constraint and Rule Satisfaction Problem (CRSP) is a hybrid representation and reasoning method encompassing both Constraint Satisfaction Problems (CSP) and rule-based systems. CSP is a kind of problem in Artificial Intelligence that requires the assignment of values to variables that are subject to a set of compatibility constraints (Kumay, 1992; Macworth, 1986). Much research has improved the applicability of CSP methodology to practical field problems (Bowen and Bahler, 1991; Davis and Rosenfield, 1981; Detcher and Pearl, 1988; Montanari and Rossi, 1991). To enhance the representational power of CSP, the integration of constraints and rules in a unified framework is attempted (Lee and Kwon, 1995).

6.1. CONSTRAINT AND RULE SATISFACTION PROBLEMS

To understand CRSP, consider the differences between CSP and the rule-based model. Typical constraints in CSP represent compatibility between variables, thus they have no directionality, and all relationships between constraints are conjunctive. The disjunctive relationship can be implicitly represented within a constraint by arranging disjunctive values to a variable. The rule, on the other hand, can effectively represent causality and subsumption relationships, so rules have directionality. A rule may have multiple conjunctive conditional variables, while the relationship between rules that directs the same consequent variables is regarded as disjunctive. Considering the contrast between CSP and rule-based systems, CRSP can be formally defined as follows.

"For the given variables associated with a set of constraints and rules, solving CRSP is the assignment of values to variables so as to satisfy the concerned goals without violating the set of constraints and rules."

6.2. UNIFIED REASONING FOR CRSP

Unified reasoning is a process of assigning consistent values to each variable so as to satisfy the concerned goals without violating constraints and rules. Unified reasoning involves the following three features:

  1. The decision maker should be able to interactively input his/her intention about the problematic situation and control the negotiation process among multiple conflicting objectives.
  2. CRSP should be able to be decomposed into multiple subproblems so that concurrent reasoning would be possible, starting from the multiple most critical variables. The possible conflicts at the boundary of subproblems becomes the point of negotiation between conflicting associated objectives.
  3. The forward and backward reasoning methods usually used in rule-based systems are integrated with constraint propagation methods developed for CSP.


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