MOL2NET'21, Conference on Molecular, Biomedical & Computational Sciences and Engineering, 7th ed. An Interactive framework under conditions of uncertainty for multi-objective optimization

To solve multiobjective problems, an evolutionary multi-objective algorithm is needed, which employs techniques to generate random solutions


Introduction
There are strategies to understand and solve real-life problems and thus achieve the best advantage; practically, the decision maker faces the uncertainty present in the problems since this can be found present in the information that comes from the uncertain future states of nature that cause variability; therefore, if the information is not processed or modeled appropriately, can lead to a poor decision (Bastiani S. et al., 2017). That is why it is necessary to make crucial decisions; for example, Ackoff, in his 1978 book The Art of Problem Solving (Ackoff R.L., 1978), describes that a problem is made up of five elements: the decision-makers facing the problem, the controllable variables of the problem that the decision-maker can control, the variables not controllable by the decision maker that will affect the outcome of the selection, the constraints of controllable and uncontrollable variables, and finally the possible outcomes of the choice made by the decision maker.
For Ackoff, a problem is best solved when the decision maker selects the values of the controllable variables that optimize the value of the result; In addition, you need to be very clear about the objective you want to achieve. However, real-world problems frequently include more than one objective, which has different degrees of importance or weight for the decision-makers. The selection process becomes somewhat complicated when you have a fairly large set of feasible solutions.
In this work, an interactive framework is proposed that allows a decision maker to analyze the solutions in stages and guide the search until the best solution that meets the objectives is found, that is, to find the compromise solution. To achieve this, a methodology was developed that integrates a set of software tools that will guide the search, and the methodology comprises various modules. First, the data entry (TELEGRAM API), some of the data includes uncertainty, that is, its value is a range of values and not a single value, for example, the costs and benefits of the projects; immediately the information is sent to the optimizer (MS-DOSS OPTIMIZATION FRAMEWORK) that looks for the best set of proposals for the decision maker, at this stage the uncertainty is included in the variables of the decision model in addition to those received from the input instances of the problem. It communicates with the module that orders the solutions based on the weights assigned by the decision maker (ITPOSIS), which also handles https://mol2net-07.sciforum.net/ variables with uncertainty that come from the problem; from the ordered solutions, the best ones are taken. Finally, the module that is fed is fed. will recalculate the parameters of the decision model (PREFERENCE DISAGGREGATION ANALYSIS, PDA) in this module variable with uncertainty are also included since the parameters of the decision maker's preference model are handled, which will be included again in the MS-DOSS until the decision maker finds the best solution according to their objectives. The final results are presented by VisTHAA, which is a visual tool to analyze and graph the results obtained from the optimization algorithms.

Materials and Methods
This section will include the materials needed for the project development and thus meet the objectives of testing the proposed methodology.
Decision-making or selection of alternative problems is complex process involving multiple criteria, for which it is necessary to use tools that allow discerning between them to obtain a solution that best satisfies the combination of possible alternatives (Gómez O. and Cabrera O., 2008). Furthermore, the problems generally include multiple objectives, which conflict with each other, making this process more complex and thus generating the need for a tool or method that allows these multiple criteria to be compared against the range of possible alternatives (Balderas F. et al., 2022).
The alternatives to be evaluated can be included in tools that process a natural language input from a user and generate intelligent responses in context, which are sent back to the user; these tools are known as chatbots (Khan, R., and Das, A., 2018). The term chatterbot was first used in 1994 and was initially coined by Michael Mauldin, the creator of the verbal robot Julia.
Chatbots today are powered by rule-driven or artificial intelligence (AI) engines that interact with users, typically through text-based interfaces. They are independent computer programs that can be integrated into any platform messaging, allowing developers to use them through an API, such as Facebook Messenger, Slack, Skype, and Microsoft Teams, among others (Centribal, 2021).
The mobile application market, which is growing rapidly in information technology, uses APIs. These were developed primarily for exchanging information between two or more programs, enabling code reuse and improving software development productivity. Many tools are developed for mobile applications, but one of the most used is the Telegram API.
The Telegram Bot API is a set of procedures, protocols, and definitions used by third-party developers to integrate Telegram Bots with the central platform. In other words, it is possible to carry out the development of a Bot safely since many processes are used as black boxes without knowing all the processes they develop (Ofoeda J. et al., 2019).
Telegram bots are special accounts that do not require an additional phone number to create. Instead, these accounts serve as an interface to execute code on the developer's server. You do not need to know how the MTProto encryption protocol used by Telegram works, as your intermediary server will take care of all the encryption and communication with the Telegram API.
MOL2NET, 2022, 7, ISSN: 2624-5078 4 https://mol2net-07.sciforum.net/ After receiving the data with Telegram, it will be sent to the Optimization Framework. A framework is a set of files and directories that facilitate the creation of applications since they incorporate functionalities already developed, tested, and implemented in a specific programming language. These are intended to make things easier when developing an application, allowing you to only focus on the real problem.
The optimization framework used is known as MS-DOSS (Ponce N., 2021), and its objective is to find the best solution from the set of options introduced through the telegram bot or some instance input file. MS-DOSS comprises various modules that interact to solve the problem at hand and deliver the best set of solutions for the decision-maker.
Among the modules necessary to find the best solution are: the instance module, which is designed to contain the instance of any problem in such a way that when generalizing its information, it can be addressed by the problem module, regardless of the format used by the authors of each instance. The problem module allows you to generalize different optimization problems, emphasizing their common characteristics and connecting with the preferences and algorithms modules.
Preference modeling plays a crucial role in decision-making, so interest in addressing multi-objective algorithms incorporating preference information has recently increased. The DM can provide preferential information in an a priori, a posteriori, and an interactive manner (Hwang & Masud, 1979).
Interactive approaches rely on the progressive definition of the DM's preferences and exploration of the target space. Preference articulation takes place during the optimization process so that progress towards a particular region of the Pareto optimal front is made. The DM must be willing to participate in the solution process and direct it according to his preferences. As the interactive process of identifying the best solutions progresses, the DM specifies his preferences, learns about the problem, and can adjust his aspiration levels.
The preferences module deals with a relational system of preferences composed of several binary relationships such as Indifference, Strict preference, Weak preference, Incomparability, K-preference, and No preference, and it works together with the algorithm module, which allows manipulating the information generated by the problem module, according to the behavior of each algorithm. This allows generalizing different algorithms, emphasizing their common characteristics, and facilitating the creation and extension of their classes. Finally, the solution module allows generalizing the solutions created by the algorithm module to be presented to the decision maker.
When MS-DOSS generates the best final solutions, these make up an extensive set of solutions, so to help make the best decision, MS-DOSS sends the results to the module where the found solutions will be ordered. It should be noted, as mentioned before, that the data includes uncertainty; Therefore, the TOPSIS algorithm (Balderas F., 2022) was modified to handle the uncertainty, generating the ITOPSIS algorithm.
MOL2NET, 2022, 7, ISSN: 2624-5078 5 https://mol2net-07.sciforum.net/ ITOPSIS (Interval Technique of Order Preference Similarity to the Ideal Solution) is a method for multicriteria decision analysis developed by Yoon in 1981. The method is based on the idea that the desired solution should have the shortest geometric distance to the ideal solution and the longest to the anti-ideal solution. The ideal alternative is the one that has a geometric distance closest to the best solution. In contrast, the anti-ideal alternative has a distance that is very far from the best solution (Balderas F., 2017). After evaluating the set of solutions and being ordered by ITOPSIS, the best results will be taken and sent to the Preference Disaggregation Analysis (PDA) module, which consists of the analysis of the global preferences of the decision maker (DM) to deduce the relative importance of the evaluation criteria and thus develop the preference model corresponding to global preferences (Zopounidis & Doumpos, 1999). To solve the PDA you need a set of reference solutions (RS) previously evaluated by the DM as bad solutions (C1) or good solutions (C2). Subsequently, MOEA/D (Rosas-Solorzano L., 2020) must solve the PDA(RS) problem to estimate a new set of preferential parameters (weights, vetoes, credibility, majority, dominance) of the outranking model; said set of values will be loaded again in the MS-DOSS Optimization Framework module, until the decision maker considers having found the best compromise solution, that is, the one that meets his objectives.
The final results can be presented in text or graphic format. To help shape the results, the VisTHAA tool (Ponce J., 2020) is used as a visual tool to analyze and graph the results obtained. Optimization https://mol2net-07.sciforum.net/ algorithms. Figure 1 shows the process followed by the interactive framework under uncertainty conditions for multi-objective optimization.

Results and Discussion
Decision problems are periodically faced by all people or companies, in many moments of our lives, every day we make "good" or "bad" decisions that impact our well-being or that of our companies; that is to say: the good use of personal or organizational resources, as well as establishing a course of action in the short or long term.
As part of the interactive process, the first action of the bot is to provide the decision maker with ten random solutions from which the DM can only choose one, in order to obtain the compromise solution.
To verify that the random solutions obtained from the MS-DOSS framework correspond to those presented by the bot, a text file has been generated from the MS-DOSS framework, which contains each of the random solutions, to be able to compare them with the results. Telegram bot messages. Figure 2 shows that the data obtained by the framework corresponds to the solutions shown to the decision-maker by the Telegram bot. Therefore, one of the tasks that the decision-maker must perform is to evaluate the solutions generated by the MOEA/D algorithm, which has been implemented in the MS-DOSS framework.
The DM evaluates solutions to say whether he likes the solution or not. To verify that the classification has been carried out correctly, it has been decided to display the DM's choices on the console to compare them with the reference sets R1 and R2 provided to the PDA. Figure 3 shows the classification made by the DM through the bot; this corresponds to the reference sets provided to the PDA. Note that on the left side of figure 3, the zeros represent the solutions that the DM did not like, and the ones represent the solutions that he did like. In addition, the right part of figure 3 shows the reference set R1 corresponding to the "bad" solutions, so the ones represent the solutions that the DM did not like. In the reference set R2 the ones corresponding to the "good" solutions. Finally, the separation between the compromise solution and the last solution obtained in the interactive process has been calculated to validate the results obtained in the interactive process. The metric used in Figure 4 is the Euclidean distance (Fernandez E., 2022). As can be seen, there are differences between the obtained solutions and the compromise solution; this means that the DM has navigated in the space of solutions selecting those that he considers to be the best solutions, and this has helped the MS-DOSS optimization framework, which by being fed with new decision values has allowed him to find new solutions and reach the best compromise solution.

Conclusions
In this research, an interactive framework has been designed and validated under uncertainty conditions for multi-objective optimization. To validate it, a software tool was built that is composed of a set of modules that communicate and interact with each other to solve the problem of finding the best solution that represents the objectives of a decision-maker.
Until now, we have experimented with instances of standard problems from the DTLZ (Fernandez E., 2022) library, and it has been proven that the interactive framework improves the quality of the solutions MOL2NET, 2022, 7, ISSN: 2624-5078 8 https://mol2net-07.sciforum.net/ by exploring the search space, until finding the best compromise solution for the policyholder. of decisions. Future research work is to validate usability and check the contribution of interactivity.