In this paper, the flashlight (FL) algorithm, which is categorized as a heuristic method, has been suggested to determine the ultimate pit limit (UPL). In order to apply the suggested algorithm and other common algorithms, such as the dynamic programming, the Korobov, and the Floating Cone, and to validate the capability of the proposed method, the ultimate pit limit was determined in a cross-section of the Korkora reserve, which is located in Kurdistan province, northwestern of Iran and consists of 3080 blocks. The comparison of the FL algorithm and other methods revealed that same as high accuracy dynamic programming methods, the proposed algorithm could find the optimum value, while the Korobov and the Floating Cone algorithms failed to determine the optimum limit.

The large-scale open-pit mine production planning problem is an NP-hard issue. That is, it cannot be solved in a reasonable computational time. To solve this problem, various methods, including metaheuristic methods, have been proposed to reduce the computation time. One of these methods is the genetic algorithm (GA) which can provide near-optimal solutions to the problem in a shorter time. This paper aims to evaluate the efficiency of the GA technique based on the pit values and computational times compared with other methods of designing the ultimate pit limit (UPL). In other words, in addition to GA evaluation in UPL design, other proposed methods for UPL design are also compared. Determining the UPL of an open-pit mine is the first step in production planning. UPL solver selects blocks whose total economic value is maximum while meeting the slope constraints. In this regard, various methods have been proposed, which can be classified into three general categories: Operational Research (OR), heuristic, and metaheuristic. The GA, categorized as a metaheuristic method, Linear Programming (LP) model as an OR method, and Floating Cone (FC) algorithm as a heuristic method, have been employed to determine the UPL of open-pit mines. Since the LP method provides the exact answer, consider the basics. Then the results of GA were validated based on the results of LP and compared with the results of FC. This paper used the Marvin mine block model with characteristics of 53271 blocks and eight levels as a case study. Comparing the UPL value's three ways revealed that the LP model received the highest value by comparing the value obtained from GA and the FC algorithm's lowest value. However, the GA provided the results in a shorter time than LP, which is more critical in large-scale production planning problems. By performing the sensitivity analysis in the GA on the two parameters, crossover and mutation probability, the GA's UPL value was modified to 20940. Its UPL value is only 8% less than LP's UPL value.

Background: The use of small fields has increased by the emergence of advanced radiotherapy. Dose calculations of these fields are complex and challenging for many reasons such as lack of electrical equilibrium even in homogeneous environments, and this complexity will increase in presence of heterogeneity. According to the importance of delivery the accurate prescription dose to the target volume in the patient’ s body, the dose calculation accuracy of used commercial algorithms in clinical treatment planning systems (TPS) should be evaluated. Objective: The present study aims to evaluate the accuracy of Collapsed-Cone dose measurement algorithm in Isogray treatment planning system. Material and Methods: In this analytical study, the measurements were made in tissue equivalent solid water phantom with lung and bone heterogeneities by Pinpoint dosimeter (0. 015 cm3 sensitive volume) in several radiation fields (1×1 to 5×5 cm2). The phantoms were irradiated with 6, 10 and 18 MV photon beams and finally, the results of experimental calculations were compared with treatment planning outputs. Results: In all setups, the maximum deviation occurred in the field of 1×1 cm2. Then, the maximum deviation was observed for 2×2 cm2 field size; however, it was up to 5% for homogeneous water phantom and lung heterogeneity. In 3×3 cm2 and larger fields, there was a good agreement between the results of the TPS and experimental dosimetry. The maximum deviation was observed in water-bone heterogeneity. Conclusion: This algorithm was able to pass the standard audit criteria, but it is better to be used more cautiously in bone heterogeneity, especially in low energies.

In this paper, we propose a feasible interior-point algorithm for mixed symmetric Cone linear complementarity problems which are a general class of complementarity problems. The symmetrization of the search directions used in this paper is based on Nesterov and Todd scaling scheme. By using Euclidean Jordan algebra, we prove the convergence analysis of the proposed algorithm and show that the complexity bound of the algorithm matches the currently best known iteration bound for feasible interior-point methods.

Background: Virtual wedge (VW) is used in radiotherapy to compensate for missing tissues and create a uniform dose distribution in tissues. According to TECDOC? 1583 and technical reports series no. 430, evaluating the dose calculation accuracy is essential for the quality assurance of treatment planning systems (TPSs). In this study, the dose calculation accuracy of the collapsed Cone superposition (CCS) algorithm in the postmastectomy radiotherapy of the chest wall for breast cancer was evaluated by comparing the calculated and measured dose in VW fields. Methods: Two tangential fields with the typical VW angles were planned using ISOgray TPS in a thorax phantom. The CCS algorithm was used for dose calculation at 6 and 15 MV photon beams. The obtained dose distributions from EBT3 film spaces and TPS were evaluated using the gamma index. Results: The measured and calculated dose values using VW in a heterogeneous medium with different beam energies were in a good agreement with each other (acceptance rate: 88. 0%-93. 4%). The calculated and measured data did not differ significantly with an increase/decrease in wedge angle. In addition, the results demonstrated that ISOgray overestimated and underestimated the dose of the soft tissue and lung in the planned volume, respectively. Conclusions: According to the results of gamma index analysis, the calculated dose distribution using VW model with the CCS algorithm in a heterogeneous environment was within acceptable limits

A full Nesterov-Todd (NT) step infeasible interior-point algorithm is proposed for solving monotone linear complementarity problems over symmetric Cones by using Euclidean Jordan algebra. Two types of full NT-steps are used, feasibility steps and centering steps. The algorithm starts from strictly feasible iterates of a perturbed problem, and, using the central path and feasibility steps, finds strictly feasible iterates for the next perturbed problem. By using centering steps for the new perturbed problem, strictly feasible iterates are obtained to be close enough to the central path of the new perturbed problem. The starting point depends on two positive numbers rp and rd. The algorithm terminates either by finding an e-solution or detecting that the symmetric Cone linear complementarity problem has no optimal solution with vanishing duality gap satisfying a condition in terms of rp and rd. The iteration bound coincides with the best known bound for infeasible interior-point methods.