Multi-criteria methods

This paper is constructed as follows section 2 describes state of the art relevant to multi-criteria methods. Object oriented design of software for multicriteria analysis is given in section 3. Results of practical calculations are contained by section 4. 

Many companies operating in the market environment use their machines in quite different environment conditions (Jodejko-Pietruczuk et al. 2008). Therefore they are interested in multi-criteria methods which would allow them to combine reliabihty and economic characteristics of their specific operation process in order to get the most rational solutions (Klyatis Klyatis 2006). 

SalminenP, HokkanenJ, and Lahdelma (1998) Comparing multi-criteria methods in the context of environmental problems. European Journal of Operational Research 104 485-496. 

Pre-qualification reduces a large set of initial suppliers to a smaller set of acceptable suppliers for further assessment. De Boer et al. (2001) have cited many different techniques for pre-qualification. Some of these techniques are categorical methods, data envelopment analysis (DEA), cluster analysis, case-based reasoning (CBR) systems, and multi-criteria decision making method (MCDM). Several authors have worked on pre-qualification of suppliers. Weber and Ellram (1992) and Weber et al. (2000) have developed DEA methods for pre-qualification. Hinkel et al. (1969) and Holt (1998) used cluster analysis for pre-qualification and finally Ng and Skitmore (1995) developed CBR systems for pre-qualification. Mendoza et al. (2008) developed a three phase multi-criteria method to solve a general supplier selection problem. The paper combines analytic hierarchy process (AHP) with goal programming for both pre-qualification and final order allocation. 

Mendoza, A., A. Ravindran, and E. Santiago, E. 2008. A three phase multi-criteria method to the supplier selection problem. International Journal of Industrial Engineering. 15(2) 195-210. 

In all procedures it must be respected that assets and causes of risks have different natures that cause incommensurabihty of criterions and reasons, which only allows apphcation of multi-criteria methods, tools and techniques that are suitable, i.e. correct and valid for a given problem target. 

In practice often more than one quality criterion is relevant. In the case of the need to build in robustness, at least two criteria are already needed the quality criterion itself and its associated robustness criterion. Hence, optimization has to be done on more than one criterion simultaneously. If a simultaneous optimization technique is used then there are procedures to deal with multiple optimization criteria. Several methods for multi-criteria optimization have been proposed and recently a tutorial/review has appeared [22]. 

In contrast to single-objective problems where optimization methods explore the feasible search space to find the single best solution, in multi-objective settings, no best solution can be found that outperforms all others in every criterion (3). Instead, multiple best solutions exist representing the range of possible compromises of the objectives (11). These solutions, known as non-dominated, have no other solutions that are better than them in all of the objectives considered. The set of non-dominated solutions is also known as the Pareto-front or the trade-off surface. Figure 3.1 illustrates the concept of non-dominated solutions and the Pareto-front in a bi-objective minimization problem. 

Limits of detectability for the desired elemental analyses vary depending upon the matrix, elements, methods of sample preparation, and quality of instrumentation applied. Generally, these are on the order of 1 to 100 parts per million. The limit of detectability, however, is only one criterion in evaluating methods of analysis. The liiue of analysis is important, particularly in production and process control laboratories, in multi element spectrometers, it is possible to perform as many as 30 simultaneous elemental determinations in from 20 to 120 seconds, depending upon the material being analyzed. 

Sequential optimisation methods are used for multi-parameter optimisation. The simplex method starts with some initial experiments, evaluates from them the values of a sum optimisation criterion (COF), on the basis of these results determines the next combination of operation parameters to be used for running a new chromatographic experiment and compares the value of the COF obtained from the new experiment with the old one. On the basis of this prediction, a new combination of the operation parameters is calculated which is expected to yield an improved value of the COF, the separation is run at these new conditions and the procedure is repeated until maximum COF with no further improvement is eventually obtained, for which — hopefully — the optimum combination of operation parameters has been obtained (Fig. 1.22). Any combination of operation parameters can be optimised in this way and no knowledge about the nature of the chromatographic process is necessary ( black-box philosophy). Some HPLC control systems allow the simplex optimisation to run unattended. 

When tackling a multi-objective problem by GAs, various approaches to fitness definition may be adopted Fonseca (1995). In what follows we will resort to the so called Pareto-based methods Goldberg (1989) once a population of chromosomes has been created, these are ranked according to the Pareto dominance criterion by looking at the /-dimensional space of the fitnessesfi U), i = Firstly,... 

One criterion to distinguish the miscibility of blends is the glass transition temperature (Tg) that can be measured with different calorimetric methods [95]. Tg is the characteristic transition of the amorphous phase in polymers. Below Tg, polymer chains are fixed by intermolecular interactions, no diffusion is possible, and the polymer is rigid. At temperatures higher than Tg, kinetic forces are stronger than molecular interactions and polymer chain diffusion is likely. In binary or multi-component miscible one-phase systems, macromolecules are statistically distributed on a molecular level. Therefore, only one glass transition occurs, which normally lies between the glass transition temperatures of the pure components. 

One example of a component-based testing method is the Vehicle Related Pedestrian Safety Index (VERPS) [73, 74]. This index utilizes a linear scale for both active and passive safety measures. The pedestrian head impact in frontal passenger vehicle collisions is assessed using the Head Injury Criterion (HIC) as metric. The method delivers specific results for a given vehicle and pedestrian combination. The evaluation process includes accident data analysis for relevant scenarios, kinematic analysis (via multi-body simulation), hardware component testing, and a procedure to obtain the VERPS index [73, 74]. The VERPS index takes only the probability for AIS3+ head injuries due to impact on the vehicle into account, since this probability can be derived from the HIC measurement. 

It could be argued that the apparent lack of trade-off between the two objectives could be a consequence of the ISE not being a good criterion. However, this impression might be also a question of scaling (i.e. check figure 9d). Moreover, replacing the ISE metric by others, like the ITSE, led to similar results for the Pareto front. In any case, we would like to stress that these are a posteriori conclusions which can only be taken if the multi-objective problems are properly solved with robust methods, the main objective of our chapter (otherwise, the results can be artifacts due to the nonconvexity of the NLPs, as we discussed). 

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