Finding multiple global optima for unconstrained discrete location problems

Global optimization problems widely exist in the fields of economic model, finance, engineering design and control. Since it is easy to fall into multiple local optimal solutions that are different from the global optimal solution, how to obtain the global optimal solution is a very important subject. Inspired by the recently proposed deterministic global optimization method – Granular Sieving (GrS) algorithm, this paper proposes a parallel method for global optimization – P-GrS. Supported by the mathematical theory of GrS, P-GrS can theoretically guarantee to find the global optimum and the complete set of global optimal solutions through the parallel design of GrS. The method has better performance than the traditional GrS in most bench mark functions, and the results show the feasibility and effectiveness of the algorithm.

A quadtree-based allocation method for a class of large discrete Euclidean location problems

To model flexible objectives for discrete location problems, ordered median functions can be applied. These functions multiply a weight to the cost of fulfilling the demand of a customer which depends on the position of that cost relative to the costs of fulfilling the demand of the other customers. In this paper a reformulated and more compact version of a covering model for the discrete ordered median problem (DOMP) is considered. It is shown that by using this reformulation better solution times can be obtained. This is especially true for some objectives that are often employed in location theory. In addition, the covering model is extended so that ordered median functions with negative weights are feasible as well. This type of modeling weights has not been treated in the literature on the DOMP before. We show that several discrete location problems with equity objectives are particular cases of this model. As a result, a mixed-integer linear model for this type of problems is obtained for the first time.

Discrete facility location problems are classified as types of facility location problems, wherein decisions on choosing facilities in specific locations are made to serve the demand points of customers, thus minimizing the total cost. The covering- and median-based problems are the common classified types of discrete facility location problems, which both comprise different classes of discrete problems as reviewed in this research. However, the discrete facility location problems shown in deterministic and known information and data under uncertain, vague, and ambiguous environments have usually been solved using intuitionistic fuzzy approaches. Neutrosophic is recently applied to tackle the uncertainty and ambiguity of information and data. This paper considered solving the discrete facility location problems under the neutrosophic environment, wherein the information of the locations, distances, times, and costs is uncertain. The mathematical models for the main types of neutrosophic discrete facility location problems, which remain unclear till now despite previous related works, are formulated in this study. Numerical examples demonstrated testing of the neutrosophic discrete models and comparison with the optimization solutions obtained from the normal situations.

On solving the discrete location problems when the facilities are prone to failure

Global optimization of Savonius-type vertical axis wind turbine with multiple circular-arc blades using validated 3D CFD model

A hybrid global optimization method: The multi-dimensional case

Virulence Optimization Algorithm

One of the most important things in evolutional algorithms is to find global solution as stable as possible. As we know that it cost too much computational cost, even if we are not sure the results is really global or not, we do not want to re-run evolutional algorithms to make sure its final results. Therefore, evolutional algorithms need to include as much effort as possible to let the user feel relieved that they got close to global solution. In this paper, development of range juggling in Genetic Range Genetic Algorithms (GRGA) for better convergence is described. Genetic Range Genetic Algorithms is updated version of Adaptive Range Genetic Algorithms (ARGA). In ARGA, searching range differ every generation, in the initial stages, searching range try to find the range that include global optimum solution. In the very last stages, it tries to converge to global solution, and the searching range is beginning to shrink in order to raise the accuracy of the solution. Therefore it is very important to choose system parameter especially for the initial stage not to trap into local solution and also not to move too fast to overshoot global solution. Not like ARGA, GRGA is free from critical settings of parameters, but it has some short comings in first convergence, because once searching range is given it does not change before the range is diminished. For better convergence, techniques of range juggling is proposed and examined in this paper. Through numerical experiments, it turned out that it has better convergence and accuracy in simple problem. Even in the case that has a large number of design variables, it can reach close to global optimum solutions.

The Discrete Ordered Median Problem (DOMP) unifies discrete facility location problems in the sense that classical location problems, such as the N-median, N-centre and Uncapacitated Facility Location problems, are particular cases of the DOMP. In addition, new location problems, which are interesting from a practical point of view (e.g. the k 1 + k 2 trimmed mean problem, see Section 2.1.1), can be formulated as special cases of the DOMP. Therefore, the study of the DOMP is interesting not only from a theoretical point of view (unification of discrete facility location problems) but also from a practical one (possibility to formulate new interesting problems).KeywordsLocation ProblemVariable Neighbourhood SearchFacility Location ProblemSupply Chain PlanningUncapacitated Facility LocationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Researchers have studied discrete location problems for a long time because of their importance in practice. The Discrete Ordered Median Problem (DOMP) generalizes discrete facility location problems. The DOMP generalizes the main facility location problems' objective functions such as the p-median, p-center and p-centdian location problems. As these problems, also known as the problems of location-allocation, have NP-hard structure, it is inevitable to use heuristic methods for solution. In this study, a metaheuristic algorithmic suggestion will be put forward by examining the DOMP to find optimal solutions. For that purpose, we proposed a Simulated Annealing (SA) metaheuristic with K-means Clustering Algorithm in initialization for the DOMP. Novel approaches for initial solution and K-exchange algorithm-based neighborhoods for local search were analysed. In addition, best level of selected parameters were determined by Taguchi method. Forty common p-median instances derived from OR-LIB were used to test the SA performance, and the results were compared with three state-of-art algorithms in the literature. According to the computational results, 21 best solutions were obtained on instances despite gap values and CPU times increasing proportionally to the scale of the instances. In a conclusion, the proposed clustering-based SA algorithm is competitive and can be a robust alternative for the DOMP.

This paper considers the locally and globally optimal solutions of the global optimisation problem whose objective function is a max‐plus vector‐valued function and constraint function is a real affine function. The formulas about global optimisation in the existing work are further explained and simplified. The necessary and sufficient conditions for the existence and uniqueness of locally optimal solutions of a single objective are established, which are then used to deduce these of globally optimal solutions. Furthermore, the general formulas of locally and globally optimal solutions are presented, respectively. The local optimisation is then applied to solve the load distribution problem of distributed systems with no globally optimal solution, and the optimal allocation scheme is proposed to complete the overall task at the earliest time. The proposed method is constructive, and the obtained results are illustrated by the numerical examples.

Global optimization of MSF seawater desalination processes

A non-parametric heuristic algorithm for convex and non-convex data clustering based on equipotential surfaces

Location Problems with Multiple Criteria