Multiobjective Optimization at Evolutionary Search with Binary Choice Relations

Abstract

A multiobjective optimization problem is considered, in which binary choice relations are used instead of optimized functions. To solve this problem, it is proposed to use an evolutionary random search algorithm, in which the function of choice in the form of a lock is used instead of the choice function in the form of a preference,. The convergence of the proposed evolutionary algorithms is analyzed, and sufficient conditions for convergence are formulated. The results of the proposed evolutionary search are compared with the results of well-known evolutionary algorithms for one test problem.

Development of evolutionary search algorithms with binary choice relations when making decisions for pellet tubular heaters

“…When looking for a solution to the optimization problem for a heat exchanger as finding the most preferable solution, one can instead look for a blocking solution taking into account three criteria. In this case, following the approach [24], the binary choice relation can be written as: An evolutionary search for a solution to such an optimization problem in the presence of three criteria is shown in Fig. 5.…”

Mathematical and Computer Modeling of Heat Supply System From Solar Film Collectors With Heat Pump

“…Таким чином, ці важливі критерії роботи системи «сонячний колектор плівкового типу та тепловий насос» знаходяться в протиріччі: бажання отримати більше корисної теплової енергії в результаті роботи такої системи стикається з більшими витратами механічної (електричної) енергії для теплового насосу компресійного типу. Приймати керуюче рішення щодо режиму роботи системи можливо в результаті рішення задачі багатокритеріальної оптимізації, використовуючи, наприклад, алгоритм багатокритеріальної оптимізації за наявності бінарних відношень вибору [11].…”

Evolutionary Search for Stochastic Optimization with Binary Choice Relations Under Fuzzy Modeling

“…The use of binary choice relations for decision-making has a history in works from Devraj and Chen [19], Aizerman [20], Aizerman and Litvakov [21], and Sholomov and Yudin [22]. Decision-making in complex systems by selforganization methods developed in the works of Irodov et al [23] and his followers [10]. In the works of Yudin and Sholomov [24] and other authors [25], computational methods of decision theory were considered, in which the problems of finding solutions are formulated in terms of binary relations; thus, the problems of nonlinear mathematical programming are transformed into problems of generalized mathematical programming.…”

“…Methods of evolutionary search for solutions in problems with binary choice relations were developed [26]; a study of the convergence of evolutionary search algorithms for binary choice relations when applying the preference function in an iterative process is presented [27]. An evolutionary algorithm for multi-criteria optimization in evolutionary search with a binary choice relation was presented [23], where the blocking function is used instead of the preference function. Liu et al [28] proposed an algorithm for building a selection mechanism for decision-making in multi-criteria systems where there is a sample of fuzzy experimental results.…”