## 4 Discussion
To make the comparison of the proposed method with the heuristic methods, a description of the latter follows first, then the comparison is made. There are several classes into which the heuristic methods can be divided. The first class contains procedures that move within the space or product features. Article [14], a representative of the class, proposed a method that selects product(s) randomly, then through a random selection of a feature and a random change of its value tests if it leads to a more profitable product portfolio. This procedure continues until it cannot find a more profitable portfolio. The method is not guaranteed to find a global optimum. Ref. [15] is an example of employing genetic algorithms, and is also an important member of the class. The method starts with a population of random solutions, instead of one solution. The fittest individuals/products then mate by changing its features, with a flavor of mutation, to create a new and better \"population\". This continues until a stopping condition is achieved. The method is not guaranteed to find a global optimum, actually not even a local optimum, but it often attains a local optimum. The second class contains methods that change entire products, not just some of their features. The class includes the strategy of greedy heuristics. This strategy was introduced in [16] and extended in [17]. The algorithm starts with a single product that maximizes profits and in the subsequent steps, it always adds one other product to the already selected product line which maximally increases the portfolio-based profit. The procedure is not guaranteed to find even a local optimum. A similar algorithm is represented by the \"interchange heuristic\": it randomly selects a product portfolio and then tests, in each step, whether any of the current portfolio products can be swapped with a non-portfolio product so that the portfolio-implied profit is increased. The method looks for an interchange that maximally increases the profit. When it cannot find a beneficial swap, it stops. The procedure is not guaranteed to find a global optimum, just a local optimum. The third class involves methods that work only with a subset of all product features and evaluate product variants only on these subsets first. This allows them to eliminate in advance some adverse feature combinations before considering other features. Methods of this type include the dynamic programming method presented by [18] and their extension to an entire product portfolio, as presented in [19]. The methods are not guaranteed to find local optima. None of the major algorithms that have been presented find global optima, some of them not even local optima. They may find them, but the methods will not recognize it. Some of the methods work with a single optimal product, others with a whole product portfolio. Recent development has moved from the heuristics to procedures that would finally be able to find global optima. Such a method has indeed originated, but it is too complex for companies to apply them (to outline the complexity, the calculations last more than one day). The procedure combines the so-called Lagrangian relaxation strategy [20] and a branch-and-bound method [21]. Compared to the above, the proposed method has some advantages and disadvantages, although direct comparison is also complicated by the fact that while the proposed method is more focused on detection of market preferences, disregarding the possibility that the problem can be very complex with respect to the accompanying calculations, the heuristic methods deal, on the contrary, primarily with the calculation problems, not with the identification of market feelings about the product features. One of the advantages of the method is, as has just been outlined, that, through approximate identification of weights of the entire market, it tries to communicate with the perceptions of the entire market.