IEEE TRANSACTIONS ON FUZZY SYSTEMS, VOL. 7, NO. 2, APRIL 1999 295 Learning Fuzzy Rules with Tabu Search— An Application to Control Maurizio Denna, Giancarlo Mauri, and Anna Maria Zanaboni Abstract— In this paper, we present a new approach for the automatic definition of the fuzzy rules for a fuzzy controller based on the use of the tabu search (TS) scheme. We show also how the application of the TS process to the learning of a fuzzy rule base can be improved using heuristic symbolic meta rules. The paper is divided in two parts. The first part (Sections I–III) presents an introduction to TS and different learning schemes which can be used to apply it for the determination of the fuzzy control rules. The second part (Sections IV–VI) illustrates the application of the proposed techniques to a specific control problem—the parking of a truck and trailer. In particular, Section V illustrates the definition of a rule base for a static fuzzy controller, while Section VI presents the construction of an adaptive parking controller. Index Terms— Control, fuzzy systems, rule extraction, tabu search, truck parking, unsupervised learning. I. INTRODUCTION I N the last few years, there has been an increasing interest in the application of the fuzzy set theory [17] to indus- trial control problems [18]. Fuzzy control has been applied in combination with neural networks [16], expert systems, and traditional control systems [23] giving promising results, especially in cases where the processes are too complex to be analyzed by conventional techniques [12] or where the available information is qualitative, inexact, or uncertain. An essential part in the design of a fuzzy controller [21], [22] is the definition of the fuzzy control rules. This is generally done using one of the following three methods. 1) Derivation of the control rules from the experience of a process operator or control engineer. This approach requires a verbalization of the experience-based control strategy. 2) Derivation of the control rules from the observation of the (state, control) pairs recorded from successful control tasks by the human controller. 3) Derivation of the control rules from the observation of the control actions generated by an existing controller. The first two methods can be combined in order to minimize the loss of information that occurs when the control strategy is converted into a set of control rules [24]. The third method is adopted in [2] where fuzzy rules are found by a clustering algorithm, and in many other works present in the neuro-fuzzy Manuscript received July 25, 1995; revised March 22, 1998. The authors are with the Computer Science Department, University of Milano, Milano, 20135 Italy. Publisher Item Identifier S 1063-6706(99)02802-7. literature. Backpropagation-based solutions are proposed in [39]–[41], [43], and [44]; adaptive resonance theory (ART)- based solutions are proposed in [45]–[48]; a solution based on Kohonen networks is proposed in [49]. Despite these methods having been successfully applied in a large number of cases [6], they have some significant drawbacks: first of all the derived rule base may not be consistent from one operator to another or even from one process cycle to another. Furthermore, it is assumed that the control strategy used by the operator is the optimum one for the plant; in practice, this assumption is generally false, because the operator tends to avoid high work loads by minimizing his interaction with the plant, or just because s/he doesn’t know a better way to control the plant. To avoid this kind of problem, it is necessary to develop a strategy for the automatic identification of the control rules, based on the minimization of a predefined objective function, which defines the desired closed-loop behavior. In this paper, we present a method for the automatic derivation of the control rules based on the use of the tabu search (TS) algorithm [13]–[15]. This method has been applied to the definition of a fuzzy rule base for the backup of a simulated truck-and-trailer to a loading dock in a planar parking area. A. Structure of a Fuzzy Controller We will give a brief description of the internal structure of a fuzzy controller. For a more detailed discussion of this topic, please refer to [4] and [5]. A fuzzy controller allows us to use a control strategy expressed in the form of linguistic rules for the definition of an automatic control strategy. A typical fuzzy controller can be decomposed in four basic components (see Fig. 1). • Fuzzification unit—Convert a crisp process state into a fuzzy one so that it is compatible with the fuzzy set representation of the process state required by the inference unit. • Knowledge base—The knowledge base consists of two components: a rule base that describes the control actions and a data base that contains the definition of the fuzzy sets representing the linguistic terms used in the rules. The knowledge base is generally represented by a fuzzy associative memory (FAM, see [2]) • Inference unit—This unit is the core of the fuzzy con- troller: it generates fuzzy control actions applying the rules in the knowledge base to the current process state. 1063–6706/99$10.00  1999 IEEE