Interactive Multi-Objective Optimization

As said in the introduction, in interactive multi-objective optimization methods, a solution pattern is formed and repeated and the DM specifies preference information progressively during the solution process. In other words, the solution process is iterative and the phases of preference elicitation and solution generation alternate. In brief, the main steps of a 

The most important stopping criterion is the satisfaction of the DM in some solution. (Some interactive methods use also algorithmic stopping criteria but we do not go into such details here.) In each iteration, some information about the problem or solutions available is given to the DM and then (s)he is supposed to answer some questions or to give some other kind of information. New solutions are generated based on the information specified. In this way, the DM directs the solution process towards such Pareto optimal solutions that (s)he is interested in and only such solutions are generated. 

The advantage of interactive methods is that the DM can specify and correct his/her preferences and selections during the solution process. Because of the iterative nature, the DM does not need to have any global preference structure and (s)he can learn during the solution process. This is a very important strength of interactive methods. Actually, finding the final solution is not always the only task but it is also noteworthy that the DM gets to know the problem, its possibilities and limitations. 

We can say that interactive methods overcome weaknesses of a priori and a posteriori methods the DM does not need a global preference structure and only interesting Pareto optimal solutions need to be considered. The latter means both savings in computational cost, which in many computationally complicated real problems is a significant advantage, and avoids setting cognitive overload on the DM, which the comparison of many solutions typically implies. 

Many interactive methods exist and none of them is superior to all the others but some methods may suit different DMs and problems better than the others. Methods differ from each other by both the style of interaction and technical realization e.g., what kind of information is given to the DM, the form of preference information specified by the DM and what kind of a scalarizing function is used or, more generally, which inner process is used to generate Pareto optimal solutions (Miettinen, 1999). It is always 

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Sakawa, M., Fuzzy Sets and Interactive Multi-Objective Optimization, Plenum Press, New York, 1993. 

Hakanen, J., Miettinen, K., Makela, M. M. and Manninen, J. (2005). On interactive multi-objective optimization with NIMBUS in chemical process design, J. Multi-Crit. Beds. Anal, 13, pp. 125-134. 

Why Use Interactive Multi-Objective Optimization in Chemical Process Design ... 

To be more specific, when classifying objective functions the DM indicates which function values should improve, which ones are acceptable and which are allowed to get worse. In addition, amounts of improvement or impairments are asked from the DM. There exist several classification-based interactive multi-objective optimization methods. They use different numbers of classes and generate new solutions in different ways. 

Interactive multi-objective optimization methods have considerable advantages over the methods mentioned above. However, they have been used very rarely in chemical engineering. For example, interactive methods can not be found in the survey of Marler and Arora (2004) and they are only briefly mentioned in Andersson (2000) and Bhaskar et al. (2000). This might be due to the lack of knowledge of interactive methods or the lack of appropriate interactive multi-objective optimization software. The few examples of interactive multi-objective optimization in chemical engineering include Grauer et al. (1984) and Umeda and Kuriyama (1980). 

Interactive multi-objective optimization can successfully be applied in chemical process design problems. For example, encouraging experiences... 

We can say that interactive methods have not been used to optimize SMB processes and, usually, only one or two objective functions have been considered. The advantages of interactive multi-objective optimization in SMB processes has been demonstrated in Hakanen et al. (2008, 2007) for the separation of fructose and glucose (the values of the parameters in the SMB model used come from Hashimoto et al. (1983) Kawajiri and Biegler (2006b)). In Hakanen et al. (2008, 2007), the problem formulation consists of four objective functions maximize throughput (T, m/h ), minimize consumption of solvent in the desorbent stream (D, m/h ), maximize product... 

We have shown with three applications how interactive multi-objective optimization can be utilized in chemical process design and demonstrated the benefits an interactive approach can offer. In all the cases, it was possible to solve the problems in their true multi-objective character and an efficient tool was created to support the DM (or designer) in the decision making problem. 

Shin, W. S. and A. Ravindran. 1991. Interactive multi objective optimization Survey I-continuous case. Computers and Operations Research. 18 97-114. 

On the other hand, it is not sensible, e.g., to restrict consideration to two objectives only, for the purpose of intuitive visualization. It is better to consider the problem as a whole and use as many objectives as needed instead of artificial simplifications. Furthermore, as mentioned earlier, EMO approaches do not necessarily guarantee that they generate Pareto optimal solutions. Because of the above-mentioned aspects, EMO approaches may not always be the best methods for solving multi-objective optimization problems and that is why we introduce scalarization based and interactive methods, in particular, to be considered as alternative approaches. When using them, the DM can concentrate on interesting solutions only and computational effort is not wasted. Furthermore, the DM can decide how many solutions (s)he wants to compare at a time. 

In what follows, we describe and summarize research on multi-objective optimization in chemical engineering reported in Hakanen (2006) and Haka-nen et al. (2004, 2005, 2006, 2008, 2007). These studies have focused on offering chemical engineering an efficient and practical way of handling all the necessary aspects of the problem, that is, to be able to simultaneously consider several conflicting objective functions that affect the behaviour of the problem considered. Therefore, they have been solved using the interactive NIMBUS method. 

Two numerical examples with flexibility preference in source-stream temperatures is presented here to demonstrate that the proposed interactive two-phase fuzzy optimization method can provide a feasible and better compensatory solution for multi-objective HEN synthesis. 

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