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1

A random search algorithm for cyclic delivery synchronization problem

Gdowska K., Książek R.

LogForum

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2017

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Vol. 13, no. 3

263--272

EN

Background: The paper is devoted to the cyclic delivery synchronization problem with vehicles serving fixed routes. Each vehicle is assigned to a fixed route: the series of supplier’s and logistic centers to be visited one after another. For each route the service frequency is fixed and known in advance. A vehicle loads at a supplier’s, then it delivers goods to a logistic center and either loads other goods there and delivers them to the next logistic center along the route or goes to another logistic center. Each logistic center can belong to several routes, so goods are delivered there with one vehicle and then they departure for the further journey with another truck. The objective of this cyclic delivery synchronization problem is to maximize the total number of synchronizations of vehicles arrivals in logistic centers and their load times, so that it is possible to organize their arrivals in repeatable blocks. Methods: Basing on the previously developed mathematical model for the cyclic delivery synchronization problem we built a random search algorithm for cyclic delivery synchronization problem. The random heuristic search utilizes objective-oriented randomizing. In the paper the newly-developed random search algorithm for cyclic delivery synchronization problem is presented. Results: A computational experiment consisted of employing the newly-developed random search algorithm for solving a series of cyclic delivery synchronization problems. Results obtained with the algorithm were compared with solutions computed with the exact method. Conclusions: The newly-developed random search algorithm for cyclic delivery synchronization problem gives results which are considerably close to the ones obtained with mixed-integer programming. The main advantage of the algorithm is reduction of computing time; it is relevant for utilization of this method in practice, especially for large-sized problems.

PL

Wstęp: W pracy przedstawiono problem synchronizowania dostaw cyklicznych do centrów przeładunkowych. Dostawy realizowane są na stałych trasach: pojazd, obsługujący daną trasę ma dostarczyć towar do centrum przeładunkowego, załadować tam inny towar i przewieźć go do kolejnego punktu trasy lub wykonać pusty przejazd do punktu załadunku. Punktami synchronizacji obsługi tras są centra logistyczne, w których niejednokrotnie towar przywieziony przez jeden pojazd, wyrusza w dalszą drogę innym. Dostawy na każdej trasie realizowane są ze stałą częstotliwością. Trasy dostaw oraz ilości przewożonego towaru są znane. Celem w zadaniu synchronizacji dostaw cyklicznych jest maksymalizacja liczby synchronizacji przyjazdów i pobytu pojazdów w centrach logistycznych tak, aby możliwe było grupowanie ich obsługi w bloki rozładunkowo-załadunkowe. Metody: Na podstawie opracowanego wcześniej modelu matematycznego dla problemu synchronizowania dostaw cyklicznych do centrów przeładunkowych został zbudowany algorytm heurystyczny poszukujący rozwiązań poprzez ukierunkowane losowanie. W artykule przedstawiono opracowany algorytm losowego przeszukiwania. Wyniki: Eksperyment obliczeniowy polegał na rozwiązaniu zestawu zadań synchronizowania dostaw cyklicznych przy pomocy opracowanego algorytmu i porównaniu uzyskanych wyników ze znanymi rozwiązaniami dokładnymi. Wnioski: Przedstawiony algorytm heurystyczny dla zadania synchronizowania dostaw cyklicznych pozwala na uzyskanie rozwiązań zbliżonych do wyników otrzymanych przy zastosowaniu modelu programowania matematycznego. Zaletą zastosowanego algorytmu jest znaczne skrócenie czasu poszukiwania rozwiązania, co może mieć znaczenie dla praktycznego wykorzystania zaproponowanej metody.

2

Optimization of linear functions on a cyclic permutation. Based on the random search

Grebennik I., Baranov O., Chorna A., Gorbacheva E.

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

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2016

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Vol. 5, No 3

211--216

EN

For creating adequate mathematical models of combinatorial problems of constructing optimal cyclic routes, mathematical modeling and solving a number of planning and control tasks solutions of optimization problems on the set of cyclic permutations are required. Review of the publications on combinatorial optimization demonstrates that the optimization problem on the cyclic permutations have not been studied sufficiently. This paper is devoted to solving optimization problem of a linear function with linear constraints on the set of cyclic permutations. For solving problems of this class using of known methods, taking into account the properties of a combinatorial set of cyclic permutations, is proposed. For this purpose we propose a method based on the ideology of random search. Heuristic method based on the strategy of the branch and bound algorithm is proposed to solve auxiliary optimization problem of a linear function without constraints on the set of cyclic permutations. Since application of the branch and bound algorithm immediately leads to an exponential growth of the complexity with increasing the dimension of the problem a number of modifications are suggested. Modifications allow reducing computational expenses for solving higher dimension problems. The effectiveness of the proposed improvements is demonstrated by computational experiments.

3

A Short Introduction to Stochastic Optimization

Ombach J.

Schedae Informaticae

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2014

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Vol. 23

9--20

EN

We present some typical algorithms used for finding global minimum/ maximum of a function defined on a compact finite dimensional set, discuss commonly observed procedures for assessing and comparing the algorithms’ performance and quote theoretical results on convergence of a broad class of stochastic algorithms.

4

Simulation-based optimization; methods and practical application

Niewiadomska-Szynkiewicz E.

Prace Naukowe Politechniki Warszawskiej. Elektronika

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2006

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z. 156

291-300

EN

The paper is concerned with computational research for complex systems. The simulation-based optimization approach, which is widely used in applied science and engineering, is formulated and discussed. The numerical techniques that optimize performance of system by using simulation to evaluate the objective value are reviewed. The focus is on random search and metaheuristics. The practical example - application of simulation optimization to calculate the optimal decisions for controlling the river-basin reservoir system during flood period is presented and discussed.

5

Parallel and distributed Controlled Random Search algorithms; case study results

Marks M., Niewiadomska-Szynkiewicz E.

Prace Naukowe Politechniki Warszawskiej. Elektronika

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2006

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z. 156

263-272

EN

CRS (Controlled Random Search) algorithms for global optimization are considered. The main objective is to present the advantages of developing the parallel and distributed random search algorithms to search for the global solution. A practical example, application of parallel CRS2, CRS4, CRS6, CRSI algorithms and distributed CRS2 algorithm to calculate the optimal prices of products that are sold in the market, are presented. In the final part of the paper the results of numerical experiments performed on the historical data are described and discussed.

6

Hybrid search for optimum in a small implicitly defined region

Zilinskas A.

Control and Cybernetics

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2004

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Vol. 33, no 4

599-609

EN

We consider optimization problems with a small implicitly denned feasible region, and with an objective function corrupted by irregularities, e.g. small noise added to the function values. Known mathematical programming methods with high convergence rate can not, lie applied to such problems. A hybrid technique is developed combining random search for the feasible region of a considered problem, and evolutionary search for the minimum over the found region. The solution results of two test problems and of a difficult real world problem are presented.