An analysis between exact and approximate algorithms for the k-center problem in graphs

<span lang="EN-US">This research focuses on the k-center problem and its applications. Different methods for solving this problem are analyzed. The implementations of an exact algorithm and of an approximate algorithm are presented. The source code and the computation complexity of these algorithms are presented and analyzed. The multitasking mode of the operating system is taken into account considering the execution time of the algorithms. The results show that the approximate algorithm finds solutions that are not worse than two times optimal. In some case these solutions are very close to the optimal solutions, but this is true only for graphs with a smaller number of nodes. As the number of nodes in the graph increases (respectively the number of edges increases), the approximate solutions deviate from the optimal ones, but remain acceptable. These results give reason to conclude that for graphs with a small number of nodes the approximate algorithm finds comparable solutions with those founds by the exact algorithm.</span>

A study of uncertain multi-objective nonlinear programming problems for rough intervals

In real conditions, the parameters of multi-objective nonlinear programming (MONLP) problem models can’t be determined exactly. Hence in this paper, we concerned with studying the uncertainty of MONLP problems. We propose algorithms to solve rough and fully-rough-interval multi-objective nonlinear programming (RIMONLP and FRIMONLP) problems, to determine optimal rough solutions value and rough decision variables, where all coefficients and decision variables in the objective functions and constraints are rough intervals (RIs). For the RIMONLP and FRIMONLP problems solving methodology are presented using the weighting method and slice-sum method with Kuhn-Tucker conditions, We will structure two nonlinear programming (NLP) problems. In the first one of this NLP problem, all of its variables and coefficients are the lower approximation (LAI) it’s RIs. The second NLP problems are upper approximation intervals (UAI) of RIs. Subsequently, both NLP problems are sliced into two crisp nonlinear problems. NLP is utilized because numerous real systems are inherently nonlinear. Also, rough intervals are so important for dealing with uncertainty and inaccurate data in decision-making (DM) problems. The suggested algorithms enable us to the optimal solutions in the largest range of possible solution. Finally, Illustrative examples of the results are given.

A Real Time Algorithm for Versatile Mode Parking System and Its Implementation on FPGA Board

This paper presents the design and development of a technique for an Autonomous and Versatile mode Parking System (AVPS) that combines a various number of parking modes. The proposed approach is different from that of many developed parking systems. Previous research has focused on choosing only a parking lot starting from two parking modes (which are parallel and perpendicular). This research aims at developing a parking system that automatically chooses a parking lot starting from four parking modes. The automatic AVPS was proposed for the car-parking control problem, and could be potentially exploited for future vehicle generation. A specific mode can be easily computed using the proposed strategy. A variety of candidate modes could be generated using one developed real time VHDL (VHSIC Hardware Description Language) algorithm providing optimal solutions with performance measures. Based on simulation and experimental results, the AVPS is able to find and recognize in advance which parking mode to select. This combination describes full implementation on a mobile robot, such as a car, based on a specific FPGA (Field-Programmable Gate Array) card. To prove the effectiveness of the proposed innovation, an evaluation process comparing the proposed technique with existing techniques was conducted and outlined.

Composing Vessel Fleets for Maintenance at Offshore Wind Farms by Solving a Dual-Level Stochastic Programming Problem Using GRASP

Background: Dual-level stochastic programming is a technique that allows modelling uncertainty at two different levels, even when the time granularity differs vastly between the levels. In this paper we study the problem of determining the optimal fleet size and mix of vessels performing maintenance operations at offshore wind farms. In this problem the strategic planning spans decades, while operational planning is performed on a day-to-day basis. Since the operational planning level must somehow be taken into account when making strategic plans, and since uncertainty is present at both levels, dual-level stochastic programming is suitable. Methods: We present a heuristic solution method for the problem based on the greedy randomized adaptive search procedure (GRASP). To evaluate the operational costs of a given fleet, a novel fleet deployment heuristic (FDH) is embedded into the GRASP. Results: Computational experiments show that the FDH produces near optimal solutions to the operational day-to-day fleet deployment problem. Comparing the GRASP to exact methods, it produces near optimal solutions for small instances, while significantly improving the primal solutions for larger instances, where the exact methods do not converge. Conclusions: The proposed heuristic is suitable for solving realistic instances, and produces near optimal solution in less than 2 h.

Humans depart from optimal computational models of interactive decision-making during competition under partial information

Decision making under uncertainty in multiagent settings is of increasing interest in decision science. The degree to which human agents depart from computationally optimal solutions in socially interactive settings is generally unknown. Such understanding provides insight into how social contexts affect human interaction and the underlying contributions of Theory of Mind. In this paper, we adapt the well-known ‘Tiger Problem’ from artificial-agent research to human participants in solo and interactive settings. Compared to computationally optimal solutions, participants gathered less information before outcome-related decisions when competing than cooperating with others. These departures from optimality were not haphazard but showed evidence of improved performance through learning. Costly errors emerged under conditions of competition, yielding both lower rates of rewarding actions and accuracy in predicting others. Taken together, this work provides a novel approach and insights into studying human social interaction when shared information is partial.

Continuous dependence and optimal control of a dynamic elastic-viscoplastic contact problem with non-monotone boundary conditions

<p style='text-indent:20px;'>In this paper, we consider continuous dependence and optimal control of a dynamic elastic-viscoplastic contact model with Clarke subdifferential boundary conditions. Since the constitutive law of elastic-viscoplastic materials has an implicit expression of the stress field, the weak form of the model is an evolutionary hemivariational inequality coupled with an integral equation. By providing some equivalent weak formulations, we prove the continuous dependence of the solution on external forces and initial conditions in the weak topologies. Finally, the existence of optimal solutions to a boundary optimal control problem is established.</p>

Global optimality conditions and duality theorems for robust optimal solutions of optimization problems with data uncertainty, using underestimators

<p style='text-indent:20px;'>In this paper, a robust optimization problem, which features a maximum function of continuously differentiable functions as its objective function, is investigated. Some new conditions for a robust KKT point, which is a robust feasible solution that satisfies the robust KKT condition, to be a global robust optimal solution of the uncertain optimization problem, which may have many local robust optimal solutions that are not global, are established. The obtained conditions make use of underestimators, which were first introduced by Jayakumar and Srisatkunarajah [<xref ref-type="bibr" rid="b1">1</xref>,<xref ref-type="bibr" rid="b2">2</xref>] of the Lagrangian associated with the problem at the robust KKT point. Furthermore, we also investigate the Wolfe type robust duality between the smooth uncertain optimization problem and its uncertain dual problem by proving the sufficient conditions for a weak duality and a strong duality between the deterministic robust counterpart of the primal model and the optimistic counterpart of its dual problem. The results on robust duality theorems are established in terms of underestimators. Additionally, to illustrate or support this study, some examples are presented.</p>

An analysis of the possibility of realization steganography in C#

The computing power of modern computers is sufficient to break many cryptographic keys, therefore it is necessary to create an additional security layer which hides the very fact of transmitting a secret message. For this purpose, steganographic methods can be used. The article is devoted to the analysis of the possibility of implementing digital images steganography with the use of the C # programming language. Firstly, existing libraries and mathematical transformations which can help with performing steganography were found. Also, own code solutions were implemented. In order to objectively evaluate the methods of data hiding, the parameters describing the degree of distortion of transforms and hidden images were calculated. Subsequently, optimal solutions for specific problems were identified and demonstrational data hiding was performed. Based on the obtained results, it can be concluded that it is possible to successfully implement steganography in the C # language. There are many ready-made libraries and tools, the effectiveness of which has been verified in the conducted analysis. Due to the contradictory of stenographic requirements, it is not possible to meet all of them optimally, i.e. undetectability, resistance to destruction and information capacity. For this reason, it is not possible to clearly indicate the best solutions. In order to achieve satisfactory results, one should look for compromises between the set requirements.

Understanding Population Dynamics in Multi- and Many-Objective Evolutionary Algorithms for High-Resolution Approximations

Achieving a high-resolution approximation and hitting the Pareto optimal set with some if not all members of the population is the goal for multi- and many-objective optimization problems, and more so in real-world applications where there is also the desire to extract knowledge about the problem from this set. The task requires not only to reach the Pareto optimal set but also to be able to continue discovering new solutions, even if the population is filled with them. Particularly in many-objective problems where the population may not be able to accommodate the full Pareto optimal set. In this work, our goal is to investigate some tools to understand the behavior of algorithms once they converge and how their population size and particularities of their selection mechanism aid or hinder their ability to keep finding optimal solutions. Through the use of features that look into the population composition during the search process, we will look into the algorithm’s behavior and dynamics and extract some insights. Features are defined in terms of dominance status, membership to the Pareto optimal set, recentness of discovery, and replacement of optimal solutions. Complementing the study with features, we also look at the approximation through the accumulated number of Pareto optimal solutions found and its relationship to a common metric, the hypervolume. To generate the data for analysis, the chosen problem is MNK-landscapes with settings that make it easy to converge, enumerable for instances with 3 to 6 objectives. Studied algorithms were selected from representative multi- and many-objective optimization approaches such as Pareto dominance, relaxation of Pareto dominance, indicator-based, and decomposition.