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Scalarization is a frequently used approach for finding efficient solutions that satisfy the preferences of the Decision Maker (DM) in multicriteria optimization. The applicability of a scalarization problem to solve integer multicriteria problems depends on the possibilities it provides for the decrease of the computing complexity in finding optimal solutions of this class of problems. This paper presents a reference-neighbourhood scalarizing problem, possessing properties that make it particularly suitable for solving integer problems. One of the aims set in this development has also been the faster obtaining of desired criteria values, defined by the DM, requiring no additional information by him/her. An illustrative example demonstrates the features of this scalarizing problem.
In this work we consider a specific problem of optimal planning of maritime transportation of multiproduct cargo by ships of one (corporate strategy) or several (partially corporate strategy) companies: the core of the problem consists of the existence of the network of intermediate seaports (i.e. transitional seaports), where for every ship arrived the cargo handling is done, and which are situated between the starting and the finishing seaports. In this work, there are mathematical models built from scratch in the form of multicriteria optimization problem; then the goal attainment method of Gembicki is used for reducing the built models to a one-criterion problem of linear programming.
The paper presents Pareto-optimum method and POLOPT computer program enabling, with the use of principle of conversation with computer, assessment of solutions (variants) in the view of two or more criteria (up to 10). The Pareto-optimal set is univariate in a few cases only, and therefore, in remaining cases to selection of the best solution from this set one proposed the distance function. The chosen procedure of the multicriteria optimization was tested on the example of selection of the best variant of the manufacturing process of rotors to the open end spinning machine.
.L., Morin, T.L. and Moskowitz, H. (1990). Generalized dynamic programming for multicriteriaoptimization, European Journal of Operational Research 44 (1): 95–104. Chalkia, E., Grau, J.M.S., Bekiaris, E., Ayfandopoulou, G., Ferarini, C. and Mitsakis, E. (2014). Routing algorithms for the safe transportation of pupils to school using school buses, Transport Research Arena (TRA) 5th Conference: Transport Solutions from Research to Deployment, Paris, France , pp. 1–10. Chen, P. and Nie, Y.M. (2013). Bicriterion shortest path problem with a general nonadditive cost
This paper is a presentation of a web based decision support system “WebOptim” for solving single and multiple criteria optimization problems. It targets a wide range of user typeseducators, researchers, managers and business people. It also provides two types of communication interfaces user friendly graphical interface for human interaction and programming interface for machine communication with other third party software systems. The interfaces facilitate the problem solving process of different types of optimization problems, mainly single and multi-objective programming optimization problems with continuous or integer variables.
The paper presents multi-thread calculations using parallel evolutionary algorithms (EA) for single and multicriteria design optimization. This approach was implemented to avoid a negative influence of incorrectly chosen initial and EA’s control parameters for the accuracy of generated solutions and thereby to improve the effectiveness of the EA’s use. Parallel computation for single optimization problems relies just on running n threads with different randomly chosen parameters in order to find the best final solution. For multicriteria optimization problems, each thread generates a set of Pareto optimal solutions and at the end these sets are combined together, giving a real set of Pareto optimal solutions. During the run of the algorithm, random interactions between threads were applied. The experiments were carried out using ten-thread processes for different examples of single and multicriteria design optimization problems, two of which are presented in the paper.
The issues of cutting environment and a suitable choice of cutting conditions by drilling are the main subjects of the article. Attention is paid to the application of the drilling process into the carbon steel. Analysed were the phenomena that adversely affect the tool life. The article demonstrated solutions how to remove these adverse effects. The multicriteria optimisation of input factors (cutting fluid concentration, cutting speed) for a defined target function (tool life) was applied. The measured values were subjected to mathematical–statistical analysis (ANOVA). Based on the implemented experiment and study of this issue, we determined the combinations of input factors, which achieved minimal values of target functions. Based on the implemented experiment and study of this issue, we also determined the combinations of input factors, which achieved minimal values of target functions. Based on this allegation, the most appropriate combination of the following input factors was proved: concentration 6.3 % and cutting speed 100 m/min.
Configuration of distribution system can be changed manually or automatically, by changing the status of the respective switching elements, with the aim of reducing power losses, increase system reliability, or improving the power quality. When changing the status of switching equipment it is necessary to satisfy the requirement for the radial and connected structure of the distribution network. Using the single criteria optimization it is possible to improve one of the characteristics of the distribution network, on the other hand by using multicriteria optimization it is possible to find a network configuration that enhances multiple distribution system characteristics at the same time. In this paper, a modification of the multi-criteria Gray Wolf optimization algorithm is proposed in order to create an efficient algorithm that can be implemented in the management functions of smart grid concept of modern distribution systems. The proposed reconfiguration algorithm was tested on standard symmetrical IEEE 33 test distribution network.