The Traffic assignment problem in the transport networks is formulated as a convex optimization problem using simplifier assumptions. Link based, path based and bush based algorithms have been presented to solve this problem, among which the link based algorithm have found more applications thanks to their low memory requirements. The link based algorithm of Frank-Wolf (FW) is yet amongst the most popular assignment algorithms, because of its simplicity as well as high convergence speed during the initial iterations. However, the low convergence rate of this algorithm near the optimal solution has driven many studies that focus on modifying the FW search direction, resulted in newer link based algorithms. Among them are conjugate direction algorithms which are more effective and simply implementable. These algorithms include PARTAN, conjugate FW (CFW) and bi-conjugate FW (BFW). This paper uses the Chicago Regional and Sioux-Falls test networks to make direct comparisons among these algorithms with respect to the CPU time and iteration number needed to reach various accurate solutions. The results for Chicago show that, compared with the FW algorithm, the three algorithms CFW, PARTAN increase the convergence speed to the relative error of 10-5 (i.e. a stable solution) by about 89, 72 and 63%, respectively, while only the BFW can reach to a 10-6 relative error. Comparing the results from Sioux-Fall with those of Chicago demonstrate that the performance of the conjugate directions Algorithms improves as network size decreases.

Radiotherapy is a high-energy ionizing radiation treatment for some kinds of cancers. Accuracy and the quality of radiotherapy treatment planning systems depend on the type of dose calculation algorithms that are utilized. There are uncertainties in the calculation of dose distribution, especially in a heterogeneous situation.
This study calculated and compared dose with model-based algorithms (superposition, collapsed cone convolution (CCC) and fast Fourier transform (FFT) and a measure-based algorithm (Clarkson in two modes: heterogeneity active and inactive).
A heterogeneous phantom was used based on a semi-anthropomorphic phantom CIRS thorax 002 LFC. All of the tests were planned according to IAEA TEC-DOC 1583. All measurements were performed with a 6 MV photon beam of a linear accelerator (ELEKTA Compact) and Farmer ionization chamber. Five methods were utilized to calculate dose and were compared with measurement results as the gold standard.
In the homogeneity media all algorithms had good accuracy and dose difference was below 3%, but in the inhomogeneity situation dose difference increased and in some cases did not achieve agreement criteria. The Superposition algorithm overall has minimum deviations in all cases. However in some cases CCC had better accuracy. The Clarkson algorithm had maximum differences, especially when inhomogeneity correction was inactive.
Dose calculation algorithms applied in radiotherapy treatment planning systems have different accuracy. Model-based algorithms have a better accuracy over measurement-based algorithms such as Clarkson. In the presence of large inhomogeneity, it is strongly recommended to activate manual inhomogeneity correction.

We present several heuristic algorithms based on tabu search for solving the multi-stage sequence-dependent group scheduling (SDGS) problem by considering minimization of makespan as the criterion. As the problem is recognized to be strongly NP-hard, several meta (tabu) search-based solution algorithms are developed to efficiently solve industry-size problem instances. Also, two different initial solution generators are developed to aid in the application of the tabu search-based algorithms. A lower bounding technique based on relaxing the mathematical model for the original SDGS problem is applied to estimate the quality of the heuristic algorithms. To find the best heuristic algorithm, random test problems, ranging in size from small, medium, to large are created and solved by the heuristic algorithms. A detailed statistical experiment, based on nested split-plot design, is performed to find the best heuristic algorithm and the best initial solution gen-erator. The results of the experiment show that the tabu search-based algorithms can provide high quality so-lutions for the problems with an average percentage error of only 1.00%.

As a real time process, in tuning the coefficients of PID controllers in AVRs, accuracy vs. speed is an important issue. Considering complexity of the problem and real systems requirements, various methods, including exact methods and approximation algorithms, have been implemented for this purpose. Since the conventional methods based on meta-heuristic algorithms solving this problem, generally use population-based algorithms such as GA and PSO, this paper aims to investigate the efficiency and performanceof single-solution based metaheuristics to solve this problem. So Simulated Annealing (SA) algorithm is proposed, and implemented for optimizing PID coefficients. In addition, an extension of SA is presented improving the search strategy based on neighborhood adjustment. The results indicate that the proposed algorithms as single based metaheuristics, have a good or even better performance vs. population based metaheuristics, in spite of simplicity in implementation and less computation requirements. Thisfact implies that the landscape complexity of these problems does notnecessarily require population-based algorithms. The presented method is also applied to multipleobjective functions regarding different time response criteria in output voltage and leads to better results in less time.

This paper addresses an unrelated multi-machine scheduling problem with sequence-dependent setup time, release date and processing set restriction to minimize the sum of weighted earliness/tardiness penalties and the sum of completion times, which is known to be NP-hard. A Mixed Integer Programming (MIP) model is proposed to formulate the considered multi-criteria problem. Also, to solve the model for real-sized applications, a Pareto-based algorithm, namely controlled elitism non-dominated sorting genetic algorithm (CENSGA), is proposed. To validate its performance, the algorithm is examined under six performance metric measures, and compared with a Pareto-based algorithm, namely NSGA-II. The results are statistically evaluated by the Mann–Whitney test and t-test methods. From the obtained results based on the t-test, the proposed CENSGA significantly outperforms the NSGA-II in four out of six terms. Additionally, the statistical results from Mann–Whitney test show that the performance of the proposed CENSGA is better than the NSGA- II in two out of six terms. Finally, the experimental results indicate the effectiveness of the proposed algorithm for different problems.

Nowadays, due to inherent complexity of real optimization problems, it has always been a challenging issue to develop a solution algorithm to these problems. Single row facility layout problem (SRFLP) is a NP-hard problem of arranging a number of rectangular facilities with varying length on one side of a straight line with aim of minimizing the weighted sum of the distance between all facility pairs. In this paper two new algorithms of cuckoo optimization and forest optimization are applied and compared to solve SRFLP for the first time. The operators of two algorithms are adapted according to the characteristics of SRFLP and results are compared for two groups of benchmark instances of the literature. These groups consist of instances with the number of facilities less and more than 30. Results on two groups of instances show that proposed cuckoo optimization based algorithm has better performance rather than proposed forest optimization based algorithm in both aspects of finding the best solution and Computational time.

Protection systems have vital role in network reliability in short circuit mode and proper operating for relays. Current transformer often in transient and saturation under short circuit mode causes mal-operation of relays which will have undesirable effects. Therefore, proper and quick identification of Current transformer saturation is so important. In this paper, an Artificial Neural Network (ANN) which is trained by two different swarm based algorithms; Gravitational Search Algorithm (GSA) and Particle Swarm Optimization (PSO) have been used to discriminate between Current transformer saturation and fault currents in power transformers. In fact, GSA operates based on gravity law and in opposite of other swarm based algorithms, particles have identity and PSO is based on behaviors of bird flocking. Proposed approach has two general stages. In first step, obtained data from simulation have been processed and applied to an ANN, and then in second step, using training data considered ANN has been trained by GSA & PSO. Finally, a proposed technique has been compared with one of the common training approach which is called Genetic algorithm (GA).

Metaheuristic algorithms are effective ways to solve optimization problems and use existing phenomena in nature to solve these problems. Due to the independence of metaheuristic algorithms from the gradient information, the objective function can be used to solve large-scale problems by optimization solutions. The organisms’ behavior in nature in their interaction with each other is one of the optimization methods that are modeled as swarm-based algorithms. Swarm-based algorithms are a set of metaheuristic algorithms which are modeled based on group behavior of their organisms and social interactions. The behavior of wildebeests in nature is considered as a swarm-based algorithm for survival because it can be seen that these organisms migrate in groups and try to survive for themselves and their own herd. In this paper, a new metaheuristic algorithm (WOA) based on migratory and displacement behavior of wildebeests is presented of solving optimization problems. In this algorithm, problem solutions are defined as wildebeest herds that search the problem space for appropriate habitat. The results of the implementation of a set of benchmark functions for solving optimization problems such as the Wildebeest Optimization Algorithm, Whale Optimization Algorithm, BAT, Firefly and Particle Swarm Optimization (PSO) algorithms show that the proposed algorithm is less error rate to find global optimum and also caught up rate in the local optimum is less than the methods.

The coordination and integration of efforts and activities of supply chain (SC) members that is a key component of supply chain management success has become a challenging activity due to conflicts in such systems. Lack of proper detection of conflicts in a SC and therefore mismanagement of them will increase disruption risk in the SC. In this article, a knowledge-based algorithm is presented based on the OTSM-TRIZ (general theory of powerful thinking) problem flow network approach to identify, formulate and solve the conflicts of SCs before they occur and cause harmful effects. The proposed algorithm involves analyzing and developing network of problems (NoP) in order to transfer it into a network of conflicts. This study validated the proposed algorithm through a case demonstration. Through the implementation and application, the result demonstrated that this knowledge- based algorithm was able to identify and formulate supply chain conflicts before they occur and more importantly it greatly increased the coordination between supply chain entities.

Sponge structure is a structure widely used in the design of cryptographic algorithms that reduces the design of the algorithms to the design of a permutation or pseudo-random function. The development of sponge-based algorithms and the selection of designs based on this structure in SHA3 and CAESAR competitions increase the need to examine its security against various types of attacks. In the previous article, we defined and examined the features of this structure, and in this article, with the focus on the security of sponge structures, we study general analysis methods on this structure and examine their complexities. Considering the complexities introduced for the general attacks, it is necessary to achieve a certain level of security, and therefore this article, both in terms of design and cryptanalysis of sponge-based algorithms plays important role. It is suggested that the article "Sponge structure; introduction and applications" published in this journal be reviewed before reading this article.