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Here, an algorithm is presented for solving the minimum sum-of-squares clustering problems using their difference of convex representations. The proposed algorithm is based on an incremental approach and applies the well known DC algorithm at each iteration. The proposed algorithm is tested and compared with other clustering algorithms using large real world data sets.

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‎It is a well-known fact that finding a minimum dominating set and consequently the domination number of a general graph is an NP-complete problem‎. ‎In this paper‎, ‎we first model it as a nonlinear binary optimization problem and then extract two closely related semidefinite relaxations‎. ‎For each of these relaxations‎, ‎different rounding algorithm is exploited to produce a near-optimal dominating set‎. ‎Feasibility of the generated solutions and efficiency of the algorithms are analyzed as well‎.

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Air defense is a crucial area for all naval combat systems. In this study, we consider a warship equipped with an air-defense weapon that targets incoming threats using surface-to-air missiles. We define the weapon scheduling problem as the optimal scheduling of a set of surface-to-air missiles of a warship to a set of attacking air threats. The optimal scheduling of the weapon results in an increase in the probability of successful targeting of all incoming threats. We develop a heuristic method to obtain a very fast and acceptable solution for the problem. In addition, a branch and bound algorithm is developed to find the optimal solution. In order to increase the efficiency of this algorithm, a lower bound, an upper bound and a set of dominance rules have been developed. Using randomly generated test problems, the performance of the proposed solution approaches is analyzed. The results indicate that in all practical situations, the branch-and-bound algorithm is able to solve the problem optimally in less than a second.

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In this paper, we propose an arc-search corrector-predictor
interior-point method for solving $P_*(kappa)$-linear
complementarity problems. The proposed algorithm searches the
optimizers along an ellipse that is an approximation of the central
path. The algorithm generates a sequence of iterates in the wide
neighborhood of central path introduced by Ai and Zhang. The
algorithm does not depend on the handicap $kappa$ of the problem,
so that it can be used for any $P_*(kappa)$-linear complementarity
problem. Based on the ellipse approximation of the central path and
the wide neighborhood, we show that the proposed algorithm has
$O((1+kappa)sqrt{n}L)$ iteration complexity, the best-known
iteration complexity obtained so far by any interior-point method
for solving $P_*(kappa)$-linear complementarity problems.

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First, an integer programming model is proposed to find an α-labeling for quadratic graphs. Then, a Tabu search algorithm is developed to solve large scale problems. The proposed approach can generate α-labeling for special classes of quadratic graphs, not previously reported in the literature. Then, the main theorem of the paper is presented. We show how a problem in graph theory can be modeled and solved by an integer programming model and a metaheuristic approach.

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We present a bi-objective model for a green truck scheduling and routing problem at a cross-docking system. This model determines three key decisions at the cross dock: (1) defining a sequence and schedule of inbound trucks at the receiving door, (2) specifying a sequence and a schedule of outbound trucks at the shipping door, and (3) determining the routes of the outbound truck while serving customers. The first objective function is related to responsiveness of the network that minimizes time window violations and the second objective function minimizes total fuel consumption of trucks in order to consider the environmental factor of the network. Also, a learning effect is considered in loading and unloading process times. To solve the bi-objective model, an archived multi-objective simulated annealing (AMOSA) is used and modified. Finally, a number of test problems are solved and the efficiency of the proposed AMOSA is compared with the e-constraint method.

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Clustering problems with the similarity measure defined by the $𝐿_1$-norm are studied. Characterizations of different stationary points of these problems are given using their difference of convex representations. An algorithm for finding the Clarke stationary points of the clustering problems is designed and a clustering algorithm is developed based on it. The clustering algorithm finds a center of a data set at the first iteration and gradually adds one cluster center at each consecutive iteration. The proposed algorithm is tested using large real world data sets and compared with other clustering algorithms.

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In this paper bus scheduling problem under the constraints that the total number of buses needed to perform all trips is known in advance and the energy level of buses is limited, is considered. Each depot has a different time processing cost. The goal of this problem is to find a minimum cost feasible schedule for buses. A mathematical formulation of the problem is developed. When there are two depots, a polynomial time algorithm is developed for the problem and theoretical results about the complexity and correctness of the algorithm is presented. Also, several examples are introduced for illustrating validity of the algorithm.

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A new integer program is presented to model an independent resources assignment problem with resource shortages in the context of municipal fire service. When shortage in resources exists, a critical task for fire department's administrator in a city is to assign the available resources to the fire stations such that the effect of the shortage to cover (in providing service, in extinguishing fire and so on) is minimized. To solve the problem, we propose a polynomial time greedy algorithm.

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We deal with a recently proposed method of Chubanov [1], for solving linear homogeneous systems with positive variables. We use Nesterov's excessive gap method in the basic procedure. As a result, the iteration bound for the basic procedure is reduced by the factor $nsqrt{n}$. The price for this improvement is that the iterations are more costly, namely $O(n^2 )$ instead of $O(n)$. The overall gain in the complexity hence becomes a factor of $sqrt{n}$.

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Capacitated vehicle routing problem (CVRP) is one of the most well-known and applicable issues in the field of transportation. It has been proved to be an NP-Complete problem. To this end, it is needed to develop a high-performance algorithm to solve the problem, particularly in large scales. This paper develops a novel mathematical model for the CVRP considering the satisfaction level of demand nodes. Then, the proposed model is validated using a numerical example and sensitivity analyses that are implemented by CPLEX solver/GAMS software. To solve the problem efficiently, a Genetic Algorithm (GA) is designed and implemented. The obtained results demonstrate that the proposed GA can yield high-quality solutions compared to exact solutions.

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Here, we work on the problem of point estimation of the parameters of the Poisson-exponential distribution through the Bayesian and maximum likelihood methods based on complete samples. The point Bayes estimates under the symmetric squared error loss (SEL) function are approximated using three methods, namely the Tierney Kadane approximation method, the importance sampling method and the Metropolis-Hastings within Gibbs algorithm. The interval estimators are also obtained. The performance of the point and interval estimators are compared with each other by means of a Monte Carlo simulation. Several conclusions are given at the end.

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Ant colony optimization (ACOR) is a meta-heuristic algorithm for solving continuous optimization
problems (MOPs). In the last decades, some improved versions of ACOR have been proposed.
The UACOR is a unified version of ACOR that is designed for continuous domains. By adjusting
some specified components of the UACOR, some new versions of ACOR can be deduced. By doing
that, it becomes more practical for different types of MOPs. Based on the nature of meta-heuristic
algorithms, the performance of meta-heuristic algorithms are depends on the exploitation and
exploration, which are known as the two useful factors to generate solutions with different
qualities. Since all the meta-heuristic algorithms with random parameters use the probability
functions to generate the random numbers and as a result, there is no any control over the
amount of diversity; hence in this paper, by using the best parameters of UACOR and making
some other changes, we propose a new version of ACOR to increase the efficiency of UACOR.
These changes include using chaotic sequences to generate various random sequences and also
using a new local search to increase the quality of the solution. The proposed algorithm, the two
standard versions of UACOR and the genetic algorithm are tested on the CEC05 benchmark
functions, and then numerical results are reported. Furthermore, we apply these four algorithms
to solve the utilization of complex multi-reservoir systems, the three-reservoir system of Karkheh
dam, as a case study. The numerical results confirm the superiority of proposed algorithm over
the three other algorithms.
 

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Location theory is one of the most important topics in optimization and operations research. In location problems, the goal is to find the location of one or more facilities in a way such that some criteria such as transportation costs, customer traveling distance, total service time, and cost of servicing are optimized. In this paper, we investigate the goal Weber location problem in which the location of a number of demand points on a plane is given, and the ideal is locating the facility in the distance Ri , from the i-th demand point. However, in most instances, the solution of this problem does not exist. Therefore, the minimizing sum of errors is considered. The goal Weber location problem with the lp  norm is solved using the stochastic version of the LBFGS method, which is a second-order limited memory method for minimizing large-scale problems. According to the obtained numerical results, this algorithm achieves a lower optimal value in less time with comparing to other common and popular stochastic optimization algorithms. Note that although the investigated problem is not strongly convex, the numerical results show that the SLBFGS algorithm performs very well even for this type of problem.