scholarly journals A constrained tropical optimization problem: Complete solution and application example

Author(s):  
Nikolai Krivulin
Author(s):  
John Eddy ◽  
Kemper Lewis

Abstract Many designers concede that there is typically more than one measure of performance for an artifact. Often, a large system is decomposed into smaller subsystems each having its own set of objectives, constraints, and parameters. The performance of the final design is a function of the performances of the individual subsystems. It then becomes necessary to consider the tradeoffs that occur in a multi-objective design problem. The complete solution to a multi-objective optimization problem is the entire set of non-dominated configurations commonly referred to as the Pareto set. Common methods of generating points along a Pareto frontier involve repeated conversion of multi-objective problems into single objective problems using weights. These methods have been shown to perform poorly when attempting to populate a Pareto frontier. This work presents an efficient means of generating a thorough spread of points along a Pareto frontier using genetic programming.


2019 ◽  
Vol 10 (1) ◽  
pp. 171 ◽  
Author(s):  
Lizhuang Tan ◽  
Wei Su ◽  
Peng Cheng ◽  
Liangyu Jiao ◽  
Zhiyong Gai

Long flow detection and load balancing are crucial techniques for data center running and management. However, both of them have been independently studied in previous studies. In this paper, we propose a complete solution called Sonum, which can complete long flow detection and scheduling at the same time. Sonum consists of a software-defined synergetic sampling approach and an optimal network utilization mechanism. Sonum detects long flows through consolidating and processing sampling information from multiple switches. Compared with the existing prime solution, the missed detection rate of Sonum is reduced by 2.3%–5.1%. After obtaining the long flow information, Sonum minimizes the potential packet loss rate as the optimization target and then translates load balancing into an optimization problem of arranging a minimum packet loss path for long flows. This paper also introduces a heuristic algorithm for solving this optimization problem. The experimental results show that Sonum outperforms ECMP and Hedera in terms of network throughput and flow completion time.


Filomat ◽  
2019 ◽  
Vol 33 (5) ◽  
pp. 1369-1379
Author(s):  
Elmira Abdyldaeva ◽  
Akylbek Kerimbekov

The optimal control problem is investigated for oscillation processes, described by integrodifferential equations with the Fredholm operator when functions of external and boundary sources nonlinearly depend on components of optimal vector controls. Optimality conditions having specific properties in the case of vector controls were found. A sufficient condition is established for unique solvability of the nonlinear optimization problem and its complete solution is constructed in the form of optimal control, an optimal process, and a minimum value of the functional.


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