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1

Multi-sensor data fusion and nonlinear programming-based path prediction for escaping from engagement in combat

Gökal Enver Nurullah, Sakarya Ufuk

Archives of Control Sciences

|

2024

|

Vol. 34, No. 2

247--269

EN

One of the most important factors that bring success in modern warfare is to show air superiority. Unmanned aerial vehicles (UAVs) have now become an essential component of military air operations. UAVs can be operated in two ways: by pilots from remote control stations or by flying autonomously. Under the condition of disconnection from the control station, UAVs have trouble maintaining navigation and maneuverability. By applying multisensor data fusion, an escape path prediction algorithm was developed and presented as an engagement escape method in this study. To develop the algorithm for prediction of the optimal escape route, data from various sensors are collected and processed under the influence of noise. The data from the distance and angle sensors are interpreted in the Extended Kalman Filter and estimations are made. The instant optimal escape route is created by applying the constrained optimization method on the estimations made. The main motivation of this study is developing a deterministic-based method to get the certification of it in aviation. Therefore, instead of stochastic-based learning approaches, a deterministic approach is preferred. Nonlinear programming is used as the constraint optimization method because the constraints and objective function are nonlinear. In the selected scenarios, it can be seen in the simulation results that the proposed method shows a promising result in terms of escape from engagement.

2

Optimisation of the operating parameters of the natural gas compressor station

Osiadacz Andrzej J., Chaczykowski Maciej

Gaz, Woda i Technika Sanitarna

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2023

|

Nr 5

5--12

EN

The paper presents an algorithm of automatic search for the optimal values of the operating parameters of the natural gas compressor station. It has been assumed that natural gas can be supplied with two types of compressors: centrifugal compressors and motor-compressors. The nonlinear programming problem with continuous and discrete variables was solved to evaluate the number of simultaneously operating compressors and their operating parameters. The total fuel consumption in each time interval is minimized subject to the constraints imposed.

PL

W artykule przedstawiono algorytm automatycznego poszukiwania optymalnych wartości parametrów pracy tłoczni gazu ziemnego. Założono, ze gaz ziemny może być dostarczany za pomocą dwóch rodzajów sprężarek: odśrodkowych oraz tłokowych. Rozwiązano problem programowania nieliniowego ze zmiennymi ciągłymi i dyskretnymi w celu optymalizacji liczby jednocześnie pracujących sprężarek i ich parametrów. Minimalizowano całkowite zużycie paliwa w każdym przedziale czasowym z uwzględnieniem nałożonych ograniczeń.

3

Comparative Study of AMPL, Pyomo and JuMP Optimization Modeling Languages on a Flood Control Problem Example

Karbowski Andrzej, Wyskiel Krzysztof

Pomiary Automatyka Robotyka

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2021

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R. 25, nr 4

19--24

EN

The purpose of this work is a comparative study of three languages (environments) of optimization modeling: AMPL, Pyomo and JuMP. The comparison will be based on three implementations of an optimal discrete-time flood control problem formulated as a nonlinear programming problem. The codes for individual models and differences between them will be presented and discussed. Various aspects will be taken into account, e.g. simplicity and intuitiveness of implementation.

PL

Celem pracy jest badanie porównawcze trzech języków (środowisk) modelowania optymalizacyjnego: AMPL, Pyomo i JuMP. Porównanie jest oparte na trzech implementacjach zadania optymalnego sterowania falą powodziową z czasem dyskretnym, sformułowanego jako zadanie programowania nieliniowego. Przedstawione i omówione zostaną kody poszczególnych modeli oraz różnice między nimi. Uwzględnione zostaną różne aspekty, m.in. prostota i intuicyjność implementacji.

4

Decision maker's preferences modeling for multiple objective stochastic linear programming problems

Bellahcene Fatima

Operations Research and Decisions

|

2019

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Vol. 29, No. 3

5--16

EN

A method has been suggested which solves a multiobjective stochastic linear programming problem with normal multivariate distributions in accordance with the minimum-risk criterion. The approach to the problem uses the concept of satisfaction functions for the explicit integration of the preferences of the decision-maker for different achievement level of each objective. Thereafter, a nonlinear deterministic equivalent problem is formulated and solved by the bisection method. Numerical examples with two and three objectives are given for illustration. The solutions obtained by this method are compared with the solutions given by other approaches.

5

An integer optimization model and algorithms to support the cost-revenue study and provisory designing warehouses or other storage objects

Miatselski M., Staruch B., Staruch B.

Technical Sciences / University of Warmia and Mazury in Olsztyn

|

2018

|

nr 21(4)

257--269

EN

An optimization model for the cost–revenue study at the stage of system analysis and preliminary designs of storage objects such as warehouses, containers, packs and similar objects are developed. Our assumptions motivated by warehouses design lead us to a nonlinear integer optimization problem with the only basic constraint. We present algorithmic methods for obtaining the exact solution to the general problem with emphasizing the special case when both the objective and the constraint functions are increasing. The results of the paper may be used in developing software tools intended for supporting designers.

6

Modelling of ship’s trajectory planning in collision situations by hybrid genetic algorithm

Ni S., Liu Z., Cai Y., Wang X.

Polish Maritime Research

|

2018

|

nr 3

14--25

EN

Ship collision-avoidance trajectory planning aims at searching for a theoretical safe-critical trajectory in accordance with COLREGs and good seamanship. In this paper, a novel optimal trajectory planning based on hybrid genetic algorithm is presented for ship collision avoidance in the open sea. The proposed formulation is established based on the theory of the Multiple Genetic Algorithm (MPGA) and Nonlinear Programming, which not only overcomes the inherent deficiency of the Genetic Algorithm (GA) for premature convergence, but also guarantees the practicality and consistency of the optimal trajectory. Meanwhile, the encounter type as well as the obligation of collision avoidance is determined according to COLREGs, which is then considered as the restricted condition for the operation of population initialization. Finally, this trajectory planning model is evaluated with a set of test cases simulating various traffic scenarios to demonstrate the feasibility and superiority of the optimal trajectory.

7

Fixed-point iteration based algorithm for a class of nonlinear programming problems

Belegundu A. D.

Journal of Applied Mathematics and Computational Mechanics

|

2017

|

Vol. 16, nr 2

29--41

EN

A fixed-point algorithm is presented for a class of singly constrained nonlinear programming (NLP) problems with bounds. Setting the gradient of the Lagrangian equal to zero yields a set of optimality conditions. However, a direct solution on general problems may yield non-KKT points. Under the assumption that the gradient of the objective function is negative while the gradient of the constraint function is positive, and that the variables are positive, it is shown that the fixed-point iterations can converge to a KKT point. An active set strategy is used to handle lower and upper bounds. While fixed-point iteration algorithms can be found in the structural optimization literature, these are presented without clearly stating assumptions under which convergence may be achieved. They are also problem specific as opposed to working with general functions f, g. Here, the algorithm targets general functions which satisfy the stated assumptions. Further, within this general context, the fixed-point variable update formula is given physical significance. Unlike NLP descent methods, no line search is involved to determine step size which involves many function calls or simulations. Thus, the resulting algorithm is vastly superior for the subclass of problems considered. Moreover, the number of function evaluations remains independent of the number of variables allowing the efficient solution of problems with a large number of variables. Applications and numerical examples are presented.

8

The problem of covering the fields by the circles in the task of optimization of observation points for ground video monitoring systems of forest fires

Komyak V., Pankratov A., Patsuk V., Prikhodko A.

ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes

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2016

|

Vol. 5, No 2

133--138

EN

The problem of covering the area by circles, mathematical model of the coating offers a new coverage criteria based on which analytically describes the range of permissible solutions of the problem. Based on the analysis of the properties of the model, it is shown that the solution of the problem can be reduced to the solution of problems of nonlinear programming sequence. At the moment, there are systems of video monitoring forest land. An important class of geometric design problems is problems of irregular covering the field by geometric objects, as well as regular. In the problems of covering it is set up a claim that all points of the field were covered by geometric objects, while the conditions of non-intersection of objects between themselves and their placement in the field may be violated. One problem with the design of terrestrial video monitoring systems is to optimize the placement of observation points. optimal placement of towers problem can be formulated as a coating task. An approach to the placement of towers terrestrial video monitoring of forest fires, the main stage of which is set forth search method local extremum in the problem coverage area circles of varying radius. There is build a mathematical model to optimize the placement of variable radius circle and on its basis – the development of methods of solution and proposed an approach to obtaining a local extremum of covering problem.

9

Performance evaluation of iterative minimization methods for nonlinear programming problems with constraints

Szukalski M., Horla D.

Studia z Automatyki i Informatyki

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2015

|

T. 40

7--36

EN

The paper considers performance issues of a class of iterative minimization methods for nonlinear problems with constraints, leading to presentation of information of the algorithm that has superior properties for a given size of the problem.

PL

W artykule poruszono zagadnienie szybkości działania metod minimalizacji funkcji nieliniowej przy ograniczeniach za pomocą metod iteracyjnych. Wskazano algorytmy, które działają szybciej dla zadań o określonej strukturze.

10

Analytical Model for Optimum Warehouse Dimensions

Karakis I., Baskak M., Tanyaş M.

Research in Logistics & Production

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2015

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Vol. 5, No. 3

255--269

EN

Warehouses are essential components of any supply chain in terms of customer service and cost levels. Warehouses are one of the important players in the success or failure of businesses from not only the customer service levels perspective but also the cost perspective. Warehouses, as one of the important components of supply networks, should be continually improved from design and operation perspectives to increase the performance. All efforts and solutions regarding the performance improvement are important and complex. In other words, warehouses should operate effectively in terms of the costs and technical performance that are determined during the design phase of warehouses. There are a few studies in the literature regarding the calculations of the optimum dimensions of a warehouse along the x, y, and z directions. In this paper, an analytical model is proposed to achieve the optimum warehouse dimensions in terms of the number of stocking zones along each of three dimensional axes directions: the x-, y-, and z-axes as non-linear mathematical modelling is developed to ensure the optimality. The warehouse dimensions (length, width, and height under the rafter of the building) are then calculated according to the results obtained from the model to minimise the average travel time.

11

Optymalna partia produkcji - analiza procesowa

Śląski P.

Logistyka

|

2015

|

nr 6

474--476, CD

PL

W artykule przedstawiono możliwość wykorzystania analizy procesowej oraz programowania nieliniowego do wyznaczenia optymalnej partii produkcji. Zwrócono uwagę na wystąpienie relacji trade-off, związanych z zachowaniem odpowiednich standardów obsługi klienta przy minimalizacji łącznych kosztów zapasów i przy zachowaniu ciągłości procesu produkcyjnego.

EN

The article presents the opportunity of use of the process analysis and nonlinear programming to determine the optimum batch production. Attention was drawn te the occurrence of trade-off relationship, associated with appropriate standards of customer service while minimizing the total cost of inventory and maintaining the continuity of the production process.

12

Inventory stocks management under the limited capital conditions – nonlinear analysis

Ślaski P.

Gospodarka Materiałowa i Logistyka

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2015

|

nr 5

27--31

EN

The article presents the use of Lagrange multipliers functions to inventory stocks management under the limited capital conditions. The example verified the method based on the process analysis, the nonlinear programming and the Solver application.

PL

W artykule przedstawiono możliwość wykorzystania mnożników Lagrangea do zarządzania zapasami w warunkach ograniczonego kapitału. Zaproponowano weryfikację ww. metody w oparciu o programowanie nieliniowe i aplikację Solver.

13

Inventory stocks management under the limited capital conditions – nonlinear analysis

Ślaski P.

Gospodarka Materiałowa i Logistyka

|

2015

|

nr 5

678--686

EN

The article presents the use of Lagrange multipliers functions to inventory stocks management under the limited capital conditions. The example verified the method based on the process analysis, the nonlinear programming and the SOLVER application.

PL

W artykule przedstawiono możliwość wykorzystania mnożników Lagrangea do zarządzania zapasami w warunkach ograniczonego kapitału. Zaproponowano weryfikację ww. metody w oparciu o programowanie nieliniowe i aplikację SOLVER.

14

Teoria badań operacyjnych jako narzędzie zarządzania optymalizacyjnego

Ficoń K., Krasnodębski G.

Logistyka

|

2014

|

nr 6

622--635, CD 2

PL

W pracy przedstawiono rolę i znaczenie teorii i metod badań operacyjnych w procesie zarządzania optymalizacyjnego występującego szczególnie aktywnie w zarządzaniu logistycznym. We wstępie omówiono genezę i podstawowe pojęcia i definicje badań operacyjnych. Zgodnie z zarysowaną taksonomią metod stosowanych tradycyjnie w badaniach operacyjnych zaprezentowano ich ogólną charakterystykę. W szerokim nurcie programowania matematycznego omówiono metody programowania liniowego i nieliniowego, a także heurystycznego, dynamicznego, stochastycznego i sieciowego. Na zakończenie przedstawiono podstawy teorii grafów, teorii gier, teorii masowej obsługi oraz grupę nowoczesnych metod sztucznej inteligencji należących do tzw. inteligencji obliczeniowej.

EN

The paper presents the role and importance of the theory and methods of operations research in the optimization management process occurs particularly active in the management of logistics. In the introduction discusses the origins and basic concepts and definitions of operational research. According to the taxonomy applied methods traditionally in operations research's presented their general characteristics. In the broad mainstream of mathematical programming the paper discusses methods of linear and nonlinear programming, as well as heuristic, dynamic, stochastic and network programming. At the end are discussed the fundamentals of graph theory, game theory, queuing theory, and a group of modern artificial intelligence methods belonging to the so-called computational intelligence.

15

Ekonomiczna wielkość zamówienia w aplikacji SOLVER

Mitkow Sz., Śląski P., Waśniewski T., Zelkowski J.

Logistyka

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2014

|

nr 6

PL

W artykule przedstawiono rozwiązanie problemu ekonomicznej wielkości zamówienia w oparciu o aplikację SOLVER i programowanie nieliniowe. W oparciu o metodykę projektowania procesów zaproponowano algorytm sterowania zapasem jednorodnym w środowisku deterministycznym.

EN

The article presents the solution of the economic size of the order based on the application SOLVER and nonlinear programming. Based on the methodology of designing process control algorithm, there is proposed a supply of uniform deterministic environment.

16

Loopshaping of motor torque controller

Sieklucki G.

Archives of Control Sciences

|

2013

|

Vol. 23, no. 2

213--228

EN

The controller synthesis problem of the motor torque is presented. The tuning of the II2 controller parameters of the electromagnetic motor torque is introduced. The results are obtained by applying the weighted sensitivity method (nominal performance) which is the optimization in H∞ space. The waterbed effect for some weighting functions is presented. The results, which are obtained by a parametric optimization (nonlinear programming), are analysed by the calculations of the stability margins.

17

A modified filter SQP method as a tool for optimal control of nonlinear systems with spatio-temporal dynamics

Rafajłowicz E., Styczeń K., Rafajłowicz W.

International Journal of Applied Mathematics and Computer Science

|

2012

|

Vol. 22, no. 2

313-326

EN

Our aim is to adapt Fletcher's filter approach to solve optimal control problems for systems described by nonlinear Partial Differential Equations (PDEs) with state constraints. To this end, we propose a number of modifications of the filter approach, which are well suited for our purposes. Then, we discuss possible ways of cooperation between the filter method and a PDE solver, and one of them is selected and tested.

18

Steady state optimisation of gas networks

Osiadacz A. J.

Archives of Mining Sciences

|

2011

|

Vol. 56, no 3

335-352

EN

The algorithm for steady-state optimisation of large gas networks, based upon The Generalised Reduced Gradient method (GRG) is described. The networks can be of any configuration. The optimization is treated as a non-linear problem with non-linear constraints. It is assumed that the structure of the network is known, and such a network consists of compressor stations, valves and regulators, all of which must be on. The main goal of the described algorithms is to minimise running costs of the operating compressors. The investigation results are given and these have shown that the GRG is very effective method.

PL

W artykule opisano algorytm optymalizacji sieci gazowych w stanie ustalonym wykorzystujący metodę gradientu zredukowanego. Algorytm pozwala na optymalizację sieci o dowolnej strukturze topologicznej. Zadanie optymalizacji zostało sformułowane jako zadanie nieliniowe z nieliniowymi ograniczeniami. Przyjęto założenie, że struktura sieci optymalizowanej jest znana, tzn. jest wiadome które tłocznie, zawory, i regulatory pracują. Funkcją celu omawianego algorytmu jest minimalizacja kosztów eksploatacji tłoczni. Badania wykazały, że prezentowany algorytm cechuje się dużą efektywnością obliczeniową.

19

Optimal production of electrolytic copper determined by the concentration and distribution of copper concentrates to smelters on the example of KGHM

Saramak D.

Archives of Metallurgy and Materials

|

2011

|

Vol. 56, iss. 3

619-626

EN

The issues of copper production strategy for the Polish copper industry are presented in the article. The problem is considered within the scope of the ore extraction, ore concentration and metallurgical processing of the copper concentrate and the main aim is to produce the specific amount of copper, which generates maximum technological and economic benefits. In order to determine the strategy of production for a company an optimisation approach may be applied with the target function defined as either the maximization of metal recovery or the maximization of profit. The real operating conditions are implemented into the model, together with existing limitation resulting from the concentration technology and metallurgical treatment. The problem verification was possible with using of non-linear programming theory. Two variants were considered: the first for lower production costs, and the second for low stock market prices. The presented optimal strategies determine the copper grades of concentrates as well as the system of concentrates distribution between three smelters. Generally smelters should receive concentrates with higher copper grades for low stock market metal prices and for low processing costs the mass of concentrates delivered to smelters should be higher together with decreased the copper grades.

PL

W pracy przedstawiono zagadnienia dotyczące strategii produkcji miedzi elektrolitycznej dla polskich warunków produkcji miedzi w układzie kopalnia-zakład przeróbczy-huta miedzi. Problem jest rozpatrywany głównie z punktu widzenia hut miedzi, ale determinowany jest jakością i ilością koncentratów miedziowych wyprodukowanych przez zakłady przeróbcze. Celem jest osiągniecie maksymalnych efektów technologicznych i ekonomicznych. Podejście optymalizacyjne zakłada zbudowanie odpowiedniego modelu ekonometrycznego z funkcja celu zdefiniowaną jako maksymalny odzysk metalu oraz uwzględnieniem istniejących realnych ograniczeń technologicznych Weryfikacja modelu jest możliwa z wykorzystaniem oprogramowania działającego w oparciu o teorię programowania nielinowego. W artykule przedstawiono analizę dla dwóch wariantów produkcji miedzi: niskich kosztów produkcyjnych oraz niskich cen giełdowych miedzi. Aby maksymalizować funkcję celu w zaprezentowanym modelu, w okresie niskich cen produkcji huty powinny otrzymywać mniej koncentratów o wyższej zawartości miedzi, natomiast przy niskich giełdowych cenach miedzi, huty powinny przerabiać większe ilości koncentratu o zmniejszonej zawartości miedzi.

20

Optimization of the emission and economic dispatch by the genetic algorithm

Abdelhakem Koridak L., Rahli M.

Przegląd Elektrotechniczny

|

2010

|

R. 86, nr 11a

363-366

EN

This paper presents an efficient and reliable technique of optimization with combined economic emission dispatch. This problem has been formulated as a multi-objective problem by considering both economy and emission simultaneously. The bi-objective problem is converted into single objective function using hybrid factor in the proposed approach. The optimal solution of problem is determined by genetic algorithm. This approach has been tested on Indian utility-62 bus systems consisting of 19 generators with line flow constraints. The solutions obtained are quite encouraging and useful in the present deregulated environment.

PL

W artykule zaprezentowano skuteczną i niezawodną metodę optymalizacji rozsyłu energii z uwzględnieniem aspektów ekonomicznych i środowiskowych. Zadanie potraktowano jako problem wieloskładnikowy rozważając oba aspekty równocześnie. Zaproponowano przekształcenie problemu dwuskładnikowego w jednoskładnikowy przy wykorzystaniu współczynnika hybrydowego. Do rozwiązania problemu zastosowano algorytmy genetyczne. Metoda została przetestowana w systemie 62-szynowym składającym się z 19 generatorów. Otrzymano zadawalające wyniki.