Miroslav Marić

An efficient memetic algorithm for the uncapacitated single allocation hub location problem

In this paper, we present a memetic algorithm (MA) for solving the uncapacitated single allocation hub location problem (USAHLP). Two efficient local search heuristics are designed and implemented in the frame of an evolutionary algorithm in order to improve both the location and allocation part of the problem. Computational experiments, conducted on standard CAB/AP hub data sets (Beasley in J Global Optim 8:429–433, 1996) and modified AP data set with reduced fixed costs (Silva and Cunha in Computer Oper Res 36:3152–3165, 2009), show that the MA approach is superior over existing heuristic approaches for the USAHLP. For several large-scale AP instances up to 200 nodes, the MA improved the best-known solutions from the literature until now. Numerical results on instances with 300 and 400 nodes introduced in Silva and Cunha (Computer Oper Res 36:3152–3165, 2009) show significant improvements in the sense of both solution quality and CPU time. The robustness of the MA was additionally tested on a challenging set of newly generated large-scale instances with 520–900 nodes. To the best of our knowledge, these are the largest USAHLP problem dimensions solved in the literature until now. In addition, in this paper, we report for the first time optimal solutions for 30 AP and modified AP instances.

AN EFFICIENT EVOLUTIONARY ALGORITHM FOR LOCATING LONG-TERM CARE FACILITIES

This paper deals with a variant of a discrete location problem of establishing long-term care facilities in a given network. The objective is to determine optimal locations for these facilities in order to minimize the maximum number of assigned patients to a single facility. We propose an efficient evolutionary approach (EA) for solving this problem, based on binary encoding, appropriate objective function and standard genetic operators. Unfeasible individuals in the population are corrected to be feasible, while applied EA strategies keep the feasibility of individuals and preserve the diversity of genetic material. The algorithm is benchmarked on a real-life test instance with 33 nodes and the obtained results are compared with the existing ones from the literature. The EA is additionally tested on new problem instances derived from the standard ORLIB AP hub data set with up to 400 potential locations. For the first time in the literature we report verified optimal solutions for most of the tested problem instances with up to 80 nodes obtained by the standard optimization tool CPLEX. Exhaustive computational experiments show that the EA approach quickly returns all optimal solutions for smaller problem instances, while large-scale instances are solved in a relatively short CPU time. The results obtained on the test problems of practical sizes clearly indicate the potential of the proposed evolutionary-based method for solving this problem and similar discrete location problems. DOI: http://dx.doi.org/10.5755/j01.itc.41.1.1115

Memetic Algorithm for Solving the Multilevel Uncapacitated Facility Location Problem

We consider the Multilevel Uncapacitated Facility Location Problem (MLUFLP) and propose a new efficient integer programming formulation of the problem that provides optimal solutions for the MLUFLP test instances unsolved to optimality up to now. Further, we design a parallel Memetic Algorithm (MA) with a new strategy for applying the local search improvement within the MA frame. The conducted computational experiments show that the proposed MA quickly reaches all known optimal and best known solutions from the literature and additionally improves several solutions for large-scale MLUFLP test problems.

A hybridization of an evolutionary algorithm and a parallel branch and bound for solving the capacitated single allocation hub location problem

Graphical abstractDisplay Omitted HighlightsA well-known capacitated hub location problem CSAHLP is considered.We develop a hybrid of evolutionary algorithm and branch and bound (EA-BnB).Branch and bound is implemented by using parallelization techniques.The results of experimental study show reliability and efficiency of the EA-BnB.The EA-BnB achieved improvements regarding both solution quality and CPU time. In this study, we propose a hybrid optimization method, consisting of an evolutionary algorithm (EA) and a branch-and-bound method (BnB) for solving the capacitated single allocation hub location problem (CSAHLP). The EA is designed to explore the solution space and to select promising configurations of hubs (the location part of the problem). Hub configurations produced by the EA are further passed to the BnB search, which works with fixed hubs and allocates the non-hub nodes to located hubs (the allocation part of the problem). The BnB method is implemented using parallelization techniques, which results in short running times. The proposed hybrid algorithm, named EA-BnB, has been tested on the standard Australia Post (AP) hub data sets with up to 300 nodes. The results demonstrate the superiority of our hybrid approach over existing heuristic approaches from the existing literature. The EA-BnB method has reached all the known optimal solutions for AP hub data set and found new, significantly better, solutions on three AP instances with 100 and 200 nodes. Furthermore, the extreme efficiency of the implementation of this hybrid algorithm resulted in short running times, even for the largest AP test instances.

Hybrid metaheuristic method for determining locations for long-term health care facilities

Long-term health care facilities have gained an important role in today’s health care environments, due to the global trend of aging of human population. This paper considers the problem of network design in health-care systems, named the Long-Term Care Facility Location Problem (LTCFLP), which deals with determining locations for long-term care facilities among given potential sites. The objective is to minimize the maximal number of patients assigned to established facilities. We have developed an efficient hybrid method, based on combining the Evolutionary Approach (EA) with modified Variable Neighborhood Search method (VNS). The EA method is used in order to obtain a better initial solution that will enable the VNS to solve the LTCFLP more efficiently. The proposed hybrid algorithm is additionally enhanced by an exchange local search procedure. The algorithm is benchmarked on a data set from the literature with up to 80 potential candidate sites and on large-scale instances with up to 400 nodes. Presented computational results show that the proposed hybrid method quickly reaches all optimal solutions from the literature and in most cases outperforms existing heuristic methods for solving this problem.

Parallel VNS for Bus Terminal Location Problem

Graphical abstractDisplay Omitted HighlightsParallel variable neighborhood search (PVNS) is implemented for solving Bus Terminal Location Problem (BTLP).Improved local search based on the neighborhoods fast interchange is combined with reduced neighborhood size based on the covering characteristic of the problem.Parallelization gives significant time improvement based on processor core count.All existing results from the literature are improved by PVNS with notably less time.New larger instances based on rl instances from TSP library are introduced and computational results for those new instances are given. This paper considers the Bus Terminal Location Problem (BTLP) which incorporates characteristics of both the p-median and maximal covering problems. We propose a parallel variable neighborhood search algorithm (PVNS) for solving BTLP. Improved local search, based on efficient neighborhood interchange, is used for the p-median problem, and is combined with a reduced neighborhood size for the maximal covering part of the problem. The proposed parallel algorithm is compared with its non-parallel version. Parallelization yielded significant time improvement in function of the processor core count. Computational results show that PVNS improves all existing results from the literature, while using significantly less time. New larger instances, based on rl instances from the TSP library, are introduced and computational results for those new instances are reported.

The role of fuzzy sets in improving maximal covering location problem (MCLP)

In this paper an extension of fuzzy maximal covering location time problem (FMCLP) is presented. The travel times are considered to be linear, trapezoidal or Gaussian fuzzy numbers and the radius is considered to be a fuzzy set of a right shoulder type. For obtaining the distance a fuzzy ordering relation was used to compare distances to the radius. In order to solve the FMCLP problem we used discrete particle swarm optimization (DPSO) algorithm. Theoretical results show that the proposed DPSO algorithm is very competitive for FMCLP problem.

A note on the use of Choquet and Sugeno integrals in minimal and maximal covering location problems

The aim of this paper is to show a potential applicability of some well-known fuzzy integrals, i.e., of the Choquet integral and the Sugeno integral, in Minimal and Maximal Covering location problems, i.e., in MinCLP and MCLP. Possible benefits of the use of Choquet and Sugeno integrals lie in the flexibility of a monotone set function which is the core of the observed integrals and which is being used for modelling Decision Makers behavior. Mathematical models of Minimal and Maximal Covering location problems are given. Approach based on fuzzy integrals versus the standard two types of operators is discussed. Ideas for the future work and applications are presented.

Fuzzy GRASP with path relinking for the Risk-constrained Cash-in-Transit Vehicle Routing Problem

Abstract This paper considers a special case of famous vehicle routing problem with additional risk constraints, called the Risk-constrained Cash-in-Transit Vehicle Routing Problem (RCTVRP). We propose a fuzzy GRASP (Greedy Randomized Adaptive Search Procedure) hybridized with path relinking (PR) methodology for solving the RCTVRP. Introduced PR structure, which can be used for other vehicle routing problems, is implemented. To make the algorithms time complexity smaller, new data structure for the RCTVRP is incorporated. Proposed fuzzy GRASP with PR hybrid shows better computational performance compared to its non-fuzzy version. Furthermore, computational results on publicly available data sets indicate that proposed algorithm outperforms all existing methods from the literature for solving the RCTVRP.

Comparison of interpolation polynomials with divided differences, interpolation polynomials with finite differences, and quadratic functions obtained by the least squares method in modeling of chromatographic responses

A novel approach to mathematical modeling of chromatographic responses based on interpolation polynomials with divided differences and with finite differences is discussed. These interpolational techniques as well as traditionally applied second‐order polynomial models obtained by least squares are compared. Interpolation techniques can be useful in situations where commonly used linear or quadratic models are not applicable: when the nature of dependence is complex or the investigated factor intervals are broad. The three analyzed modeling techniques are incorporated in a design of experiments methodology for systematic development and optimization of liquid chromatographic methods. The direct modeling of retention factors is carried out first, while the objective function for final quality measurement is calculated last. An interpolation polynomial with divided differences resulted in a high quality fit compared with the results obtained by the other two modeling approaches and succeeded in locating the desired optimum. It is shown that this modeling technique can be a useful alternative for modeling of chromatographic responses. Copyright