Aspiration level

From past experience and an examination of the results provided by each of the P agents, a first tentative group of aspiration levels, y, that one should aim to reach, is defined by the user (yf = excellent, y = good-or-excellent2, etc.) ... 

Before beginning the search for feasible zones of the decision space where the preceding tentative aspiration levels can be achieved, a preliminary check for the possibility of existence of such a zone is conducted. If the perceived ideal, y, does not pass this preliminary check, i.e., there is no commensurable solution to the multiobjective problem, the decisionmaker is asked to relax y, in order to transform the problem into one with commensurable solutions. For instance, if the initial tentative perceived... 

The aspiration levels inherited from the previous step, y, are used to guide the search process. Each agent i employs the corresponding aspiration level, y, and through the application of the learning methodology presented in Section IV tries to identift feasible hyperrectangles, Xf, that lead to performance consistent with y. ... 

However, conflicts between the fulfillment of different objectives and aspiration levels may prevent any feasible zone of the decision space from leading to satisfactory joint performances. If the search procedure fails to uncover at least one feasible final solution, X, consistent with y, a number of options are available to the decisionmaker to try to overcome this impasse. Namely, the decisionmaker can revise the initial problem definition, by either... 

After successive interactive relaxations, all of them leading to an insufficient number of (x,y) pairs that jointly satisfy the aspiration levels, we finally came down to the following revision of the perceived ideal ... 

The tabu status of a move can be overridden if the objective value after the move is better than a specified threshold, called an aspiration level. 

The purpose of a tabu restriction is to prevent a move from being reversed during the length of the short-term memory, which is a number of future moves specified by the variable tabu size. If, at a given iteration, jobs p(i) and p(j) are swapped, then any move that places job p(i) earlier in the sequence than position i is tabu, until tabu size iterations have occurred or the aspiration level is exceeded. To keep track of which moves are tabu and to free those moves from their tabu status, Laguna et al. define the following data structures... 

The aspiration level allows a tabu move of a job p(j) to an earlier position if... 

Current objective value + move value < aspiration level for job p(j)... 

The aspiration level for a job is initialized to a large value and updated as follows. Let P be the current sequence and assume that the move of jobs p(i) and p(j) has the best move value. 

If aspiration level (p(j)) > objective(P) + move value, then aspiration level (p(j)) = objective (F) + move value. 

If the economist s question is asked, it is often assumed that it is unlikely that organic farming as a fixed system coincides in respect to environmental performance with the aspiration level of society for each indicator (Alvensleben 1998). This point of view follows the Tinbergen rule of economic theory that tells us that the number of policy instruments chosen should at least equal to the number of targets set (Ahrens and Lippert 1994, Henrichsmeyer and Witzke 1994). This is theoretically sound if the following prerequisites are given ... 

The superiority beta (fi) function was further manipulated to examine the effects it had on associated risk. It was formd that manufacturing a wine of lower consumer utility (higher beta) can, in some cases, reduce the risk at similar aspiration levels. A decrease in risk is always accompanied by a lower opportunity value. This delicate balance between associated risk and opportunity value is an important factor for decision making in economics. 

The DM can specify preference information in many ways and the task is to find a format that the DM finds most natural and intuitive. One possibility is that the DM specifies aspiration levels Zi i = 1,..., k) that are desirable or acceptable objective function values. The vector z G R consisting of aspiration levels is called a reference point. 

In reference point based methods, the DM first specifies a reference point z S consisting of desirable aspiration levels for each objective and then this reference point is projected onto the Pareto optimal set. That is, a Pareto optimal solution closest to the reference point is found. The distance can be measured in different ways. Specifying a reference points is an intuitive way for the DM to direct the search of the most preferred solution. It is straightforward to compare the point specified and the solution obtained without artificial concepts. Examples of methods of this t rpe are the reference point method and the light beam search . 

Because of the intuitive character of reference points, it is advisable to use the achievement scalarizing function even when it is not possible to use an interactive approach. This means that the DM expresses his/her hopes in the form of a reference point and the solution of (6.4) is then shown to him/her. In this way, a reference point based approach can be used as an a priori method. It is also possible to use reservation levels representing objective values that should be achieved (besides aspiration levels). For further details, see Wierzbicki et al. (2000). 

For functions whose values the DM wants to improve, (s)he also has to specify desirable aspiration levels. If some function has an acceptable value, it is set as the corresponding aspiration level. Under some assumptions, it is possible to calculate how much impairment should be allowed in the other objective functions in order to attain the desired improvements. This is... 

Nakayama, H. (1995). Aspiration level approach to interactive multi-objective programming and its applications, in P. Pardalos, Y. Siskos and C. Zo-pounidis (eds.), Advances in Multicriteria Analysis (Kluwer Academic Publishers), pp. 147-174. 

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