The traveling salesman problem (TSP) is one of the most important combinational optimization problems that have nowadays received much attention because of its practical applications in industrial and service problems. In this paper, a hybrid two-phase meta-heuristic algorithm called MACSGA used for solving the TSP is presented. At the first stage, the TSP is solved by the modified ant colony s...

In this paper, we provide local and global convergence guarantees for recovering CP (Candecomp/Parafac) tensor decomposition. The main step of the proposed algorithm is a simple alternating rank-1 update which is the alternating version of the tensor power iteration adapted for asymmetric tensors. Local convergence guarantees are established for third order tensors of rank k in d dimensions, wh...

A while loop tests a termination condition on every iteration. On quantum computer, such measurements perturb the evolution of algorithm. We define primitive using weak measurements, offering trade-off between perturbation caused and amount information gained per This is adjusted with parameter set by programmer. provide sufficient conditions that let us determine, arbitrarily high probability,...

We develop a new algorithm for scheduling the charging process of large number electric vehicles (EVs) over finite horizon. assume that EVs arrive at stations with different charge levels and flexibility windows. The arrival is assumed to have known distribution can be preemptive. pose problem as dynamic program constraints. show resulting formulation leads monotone Lipschitz continuous value f...

Many instances of NP-hard problems can be solved efficiently if the treewidth of their corresponding graph is small. Finding the optimal tree decompositions is an NP-hard problem and different algorithms have been proposed in the literature for generation of tree decompositions of small width. In this paper we propose a novel iterated local search algorithm to find good upper bounds for treewid...

We introduce a new method, namely, the Optimal Iteration Perturbation Method OIPM , to solve nonlinear differential equations of oscillators with cubic and harmonic restoring force. We illustrate that OIPM is very effective and convenient and does not require linearization or small perturbation. Contrary to conventional methods, in OIPM, only one iteration leads to high accuracy of the solution...

In this paper, the Sawada-Kotera equation is solved by using the Adomian’s decomposition method, modified Adomian’s decomposition method, variational iteration method, modified variational iteration method, homotopy perturbation method, modified homotopy perturbation method and homotopy analysis method. The approximate solution of this equation is calculated in the form of series which its comp...

The Nelder-Mead algorithm can stagnate and converge to a non-optimal point, even for very simple problems. In this note we propose a test for sufficient decrease which, if passed for the entire iteration, will guarantee convergence of the Nelder-Mead iteration to a stationary point if the objective function is smooth. Failure of this condition is an indicator of potential stagnation. As a remed...

In this article, we apply the modified variational iteration method for solving the (1+1)dimensional Ramani equations and the (1+1)-dimensional Joulent Moidek (JM) equations together with the initial conditions. The proposed method is modified the variational iteration method by the introducing He’s polynomials in the correction functional. The analytical results are calculated in terms of conv...