Stefan Mišković

Solving the robust two-stage capacitated facility location problem with uncertain transportation costs

In this study, we start from a multi-source variant of the two-stage capacitated facility location problem (TSCFLP) and propose a robust optimization model of the problem that involves the uncertainty of transportation costs. Since large dimensions of the robust TSCFLP could not be solved to optimality, we design a memetic algorithm (MA), which represents a combination of an evolutionary algorithm (EA) and a modified simulated annealing heuristic (SA) that uses a short-term memory of undesirable moves from previous iterations. A set of computational experiments is conducted to examine the impact of different protection levels on the deviation of the objective function value. We also investigate the impact of variations of transportation costs that may occur on both transhipment stages on the total cost for a fixed protection level. The obtained results may help in identifying a sustainable and efficient strategy for designing a two stage capacitated transportation network with uncertain transportation costs, and may be applicable in the design and management of similar transportation networks.

Novel formulations and VNS-based heuristics for single and multiple allocation p-hub maximal covering problems

This paper deals with uncapacitated single and multiple allocation p-hub maximal covering problems (USApHMCP and UMApHMCP) with binary and partial covering criteria. We present new mixed-integer programming formulations of the considered problems, which are valid for both binary and partial coverage cases. The efficiency of the proposed formulations is evaluated through computational experiments on smaller-size instances, and compared with the state-of-the art models from the literature. The obtained results indicate that the new UMApHMCP formulation outperforms the existing one for both coverage criteria in the sense of solutions’ quality and running times. In order to solve instances of larger problem dimension, we develop two heuristic methods based on variable neighborhood search: general VNS (GVNS) for USApHMCP and basic VNS (BVNS) for UMApHMCP. The proposed GVNS and BVNS involve the same shaking procedure in order to hopefully escape local minima traps, while local search phases in GVNS and BVNS use different neighborhood structures in accordance with applied allocation schemes. Computational experiments conducted on smaller-size instances showed that both GVNS and BVNS almost instantly reach all known optimal solutions. In addition, the proposed GVNS and BVNS showed to be very efficient when solving large and large-scale hub instances with up to 1000 nodes, which were not previously considered as test instances for the considered problems. Both GVNS and BVNS provided best solutions on challenging USApHMCP and UMApHMCP instances for both coverage cases in short running times, which indicates their potential to be applied to similar problems.

A VNS-LP algorithm for the robust dynamic maximal covering location problem

This study introduces a robust variant of the well-known dynamic maximal covering location problem (DMCLP) and proposes an integer linear programming formulation of the robust DMCLP. A hybrid approach for solving both deterministic and robust variant of the DMCLP is developed, which is based on hybridization of a Variable neighborhood search and a linear programming technique. The main idea is to split the problem into subproblems and to combine optimal solutions of the obtained subproblems in order to construct solution of the initial problem. The results of the proposed hybrid approach on instances of the deterministic DMCLP are presented and compared with the results of the state-of-the-art approach from the literature and with the results of commercial CPLEX solver. The presented computational analysis shows that the proposed hybrid algorithm outperforms other approaches for the DMCLP. In addition, the algorithm was tested on the instances of the robust variant of DMCLP, and obtained results are discussed in detail.

An efficient variable neighborhood search for solving a robust dynamic facility location problem in emergency service network

Abstract In this study, we propose a robust variant of a dynamic facility location problem that arises from optimizing the emergency service network of Police Special Forces Units (PSFUs) in the Republic of Serbia. We present for the first time a mathematical programming formulation of the problem under consideration. We further propose a Variable Neighborhood Search (VNS) method with an efficient local search procedure for solving real-life problem instances that remained out of reach of CPLEX solver. The results presented in this paper may help in optimizing the network of PSFUs and other security networks as well.

A Two-Phase Optimization Method for Solving the Multi-Type Maximal Covering Location Problem in Emergency Service Networks

This study introduces the Multi-Type Maximal Covering Location Problem (MTMCLP) that arises from the design of emergency service networks, and represents a generalization of the well-known Maximal Covering Location Problem (MCLP). Differently from the basic MCLP, several types of incidents and emergency units are considered and hierarchy of emergency units of different types is assumed in the MTMCLP. The numbers of available emergency units of each type are limited to some constants. The objective of the MTMCLP is to choose locations for establishing emergency units of each type, such that the total number of covered incidents is maximized. In order to provide a decision maker with optimal solutions in an efficient manner, a two-phase optimization approach to the MTMCLP is designed. In the first phase, a variant of Reduced Variable Neighborhood Search (RVNS) is applied to quickly find a high-quality solution. The obtained RVNS solution is used as a good starting point for the Linear Programming method in the second phase, which returns the optimal solution to the MTMCLP. All constructive elements of the proposed two-phase method, denoted as RVNS-LP, are adapted to the characteristics of the considered problem. The RVNS-LP approach is evaluated on real-life instances obtained from two networks of police units in Montenegro and Serbia, and randomly generated test instances of larger dimensions. Experimental evaluation shows that the proposed RVNS-LP reached all optimal solutions on all real-life test instances in very short CPU time. On generated test instances, the RVNS-LP also returned optimal solutions in all cases, within short running times and significant time savings compared to CPLEX solver. The mathematical model and the proposed two-phase optimization method may be applicable in the design and management of various emergency-service networks.DOI: http://dx.doi.org/10.5755/j01.itc.46.1.13853

Modeling of HILIC retention behavior with theoretical models and new spline interpolation technique

When it is taken into account that hydrophilic interaction liquid chromatography (HILIC) as an analytical method is relatively young compared with the other techniques, retention modeling could still bring scientifically valuable data to the field. Therefore, in this paper, olanzapine and its 8 impurities were selected as a test mixture, considering that they have never been analyzed in HILIC before. Their investigation on 4 different HILIC columns (bare silica, cyanopropyl, diol and zwitterionic) has been performed. The mixture of 9 structurally similar substances allows the examination of complex HILIC retention behavior depending on the chemical properties of the analytes, as well as of the stationary phase. To describe the nature of the relationship between the retention and the stronger eluent content in the mobile phase, we fitted experimentally obtained data to several theoretical (localized adsorption, nonlocalized partition, quadratic, and mixed) models. Results show that the best fit is the quadratic model with the highest R2 and cross‐validated coefficient of determination (Q2) values, but its usage has some drawbacks. With the aim to improve the possibility to predict retention behavior in HILIC, a new empirical model was proposed. For that purpose, a spline interpolation technique was performed, by dividing the experimental range into several subdivisions. This type of interpolation was performed for the first time in the chromatographic field. The estimation of the polynomial equations was performed using Q2 values. Obtained Q2 values pointed out the goodness of fit of the model, as well as its good predictive capabilities. In the end, the prediction capabilities were experimentally verified, under randomly chosen conditions from the experimental range. The errors in prediction were all under 10%, which is satisfying for HILIC.

A hybrid metaheuristic method for the deterministic and robust uncapacitated multiple allocation p-hub centre problem

This study considers the well-known uncapacitated multiple allocation p-hub centre problem (UMApHCP) and introduces its robust variant (UMApHCP-R) by involving flow variations with unknown distributions. As a solution method to both UMApHCP and UMAPHCP-R, a hybrid metaheuristic algorithm (HMA) is proposed, which successfully combines particle swarm optimisation and a local search heuristic. Constructive elements of the HMA are adapted to the considered problems and its parameters are experimentally adjusted. Experimental results obtained for the UMApHCP show the superiority of the proposed HMA over the existing methods from the literature on standard hub instances in the sense of solution quality or running times. The results obtained by the HMA on large-scale hub instances with up to 900 nodes are also presented. The analysis of the HMA results for the UMApHCP-R on selected problem instances shows the impact of flow variations on the objective function value. [Received 11 September 2016; Revised 23 March 2017; Accepted 7 July 2017]

Hybrid metaheuristic method for solving a multi-period emergency service location problem

This study deals with the problem of establishing the network of emergency service units. The goal of the basic problem proposed in the literature is to locate certain number of units at given discrete points of the region and to allocate cities to established units, in order to balance the load of established emergency units. Having in mind that emergency units work in shifts, we extend the basic model to a multi-period model and involve additional constraints on the number of units to be located. Since, in practice, the number of emergency incidents varies on daily or monthly basis, we consider the uncertainty of the number of incidents and propose a robust integer programming formulation of the multi-period model, which controls the deviation of objective value under uncertainty of input data. In order to solve both deterministic and robust variant of the problem, we design an efficient hybrid metaheuristic method based on combination of Particle Swarm Optimization method (PSO) and Reduced Variable Neighborhood Search (RVNS). Computational results show that the proposed hybrid PSO-RVNS method quickly reaches all known optimal solutions obtained by CPLEX solver, and provides solutions for instances that remained out of reach of CPLEX. In the single-period case, PSO-RVNS outperforms existing metaheuristic method from the literature in the sense of CPU time. Short running times of PSO-RVNS and high-quality solutions indicate the efficiency of the proposed hybrid metaheuristic approach when solving the considered problem. Results presented in this study may help security experts and emergency managers to design an efficient and sustainable emergency system. DOI: http://dx.doi.org/10.5755/j01.itc.45.3.14041