This paper is motivated by high dose rate brachytherapy treatment planning problems which involve the specification of the movement schedule of a radiation source so that the target volumes are adequately covered with sufficient doses and organs at risk are not radiated beyond the clinical acceptance threshold. It utilizes four powerful multi-objective evolutionary algorithms (MOEA), which create a set of equally-weighted Pareto optimal solutions instead of only one and produce better results compared to other optimization methods. These algorithms include non-dominated sorting genetic algorithms, Pareto envelope-based selection algorithm, non-dominated ranking genetic algorithm, and strength Pareto evolutionary algorithm. The results indicate that the last algorithm uses the dependency between decision variables to solve them efficiently and is the best type of MOEA both in terms of convergence criteria and solution diversity maintenance for the brachytherapy problems.

Accurate prediction of third-party insurance claims is critical for pricing policies and managing risk. However, the highly imbalanced nature of insurance data—where non-claim cases vastly outnumber claim cases—poses significant challenges to standard predictive models. This study explores the use of machine learning algorithms to enhance claim prediction by directly addressing this imbalance. We use real data from the Insurance Research Center of Iran, incorporating variables such as driver characteristics, vehicle features, location, and claims history. Five models are evaluated: logistic regression, decision tree, bagging, random forest, and boosting. To handle the imbalance, we apply random undersampling, oversampling, and SMOTE. Model performance is assessed using accuracy, sensitivity, specificity, precision, and F-score. Results indicate that when data imbalance is properly treated, ensemble methods—particularly decision trees, bagging, and random forest—significantly outperform logistic regression and boosting, especially in detecting actual claim cases. The study underscores the importance of using appropriate resampling techniques and evaluation metrics in imbalanced settings. These findings can help insurers develop more reliable models for pricing and risk classification‏.

‎Graph coloring is the assignment of one color to each vertex of a graph so that two adjacent vertices are not of the same color‎. ‎The graph coloring problem (GCP) is a matter of combinatorial optimization‎, ‎and the goal of GCP is determining the chromatic number $\chi(G)$‎. ‎Since GCP is an NP-hard problem‎, ‎then in this paper‎, ‎we propose a new approximated algorithm for finding the coloring number (it is an approximation of chromatic number) by using a graph adjacency matrix to colorize or separate a graph‎. ‎To prove the correctness of the proposed algorithm‎, ‎we implement it in MATLAB software‎, ‎and for analysis in terms of solution and execution time‎, ‎we compare our algorithm with some of the best existing algorithms that are already implemented in MATLAB software‎, ‎and we present the results in tables of various graphs‎. ‎Several available algorithms used the largest degree selection strategy‎, ‎while our proposed algorithm uses the graph adjacency matrix to select the vertex that has the smallest degree for coloring‎. ‎We provide some examples to compare the performance of our algorithm to other available methods‎. ‎We make use of the Dolan-Mor\'e performance profiles to assess the performance of the numerical algorithms‎, ‎and demonstrate the efficiency of our proposed approach in comparison with some existing methods‎.

‎In this paper‎, ‎first‎, ‎we show how to define an algebraic hyperstructure by using algorithms‎. ‎Then‎, ‎we present algorithms that calculate specific elements in algebraic hyperstructures‎. ‎These specific elements are‎: ‎scalars‎, ‎scalar identities‎, ‎identities‎, ‎inverses‎, ‎zero elements‎, ‎right simplifiable elements‎, ‎left simplifiable elements‎, ‎left absorbing-like elements and right absorbing-like elements‎. ‎We also introduce some algorithms in algebraic hyperstructures to check properties or calculate specific members‎. ‎These algorithms are presented for algebraic hyperstructures with one hyperoperation‎, ‎i.e‎. ‎hypergroupoids‎. ‎However‎, ‎they can be developed for other algebraic hyperstructures‎.

‎In this paper‎, ‎combining the subgradient extragradient method with‎‎ inertial method‎, ‎we introduce a new iterative algorithm for solving equilibrium problems in real Hilbert spaces‎. ‎Moreover‎, ‎we present a new inertial self-adaptive scheme for solving variational inequalities in real Hilbert spaces‎, ‎which it is not necessary to know the Lipschitz constant of the mapping‎. ‎We prove the weak convergence of the generated iterates by presented algorithms‎. ‎To illustrate the usability of our results and also to show the efficiency of the proposed methods‎, ‎we present some comparative examples with several existing schemes in the literature.

The deterministic permutation flow shop scheduling problem with makespan criterion is not solvable in polynomial time‎. ‎Therefore‎, ‎researchers have thought about heuristic algorithms‎. ‎There are many heuristic algorithms for solving it that is a very important combinatorial optimization problem‎. ‎In this paper‎, ‎a new algorithm is proposed for solving the mentioned problem‎. ‎The presented algorithm chooses the weighted path that starts from the up-left corner and reaches the down-right in the matrix of jobs processing times and calculates the biggest sum of the times in the footprints of this path‎. ‎The row with the biggest sum permutes among all the rows of the matrix for locating the minimum of makespan‎. ‎This method was run on Taillard’s standard benchmark and the solutions were compared with the optimum or the best ones as well as 14 famous heuristics‎. ‎The validity and effectiveness of the algorithm are shown with tables and statistical evaluation‎.

‎A finite non-abelian group $G$ is said to be $(l,m,n)$-generated if it can be generated by two elements $x$ and $y$ such that $o(x)=l$‎, ‎$o(y)=m$ and $o(xy)=n$‎. ‎Also‎, ‎$G$ is said to be $nX$-complementary generated if given an arbitrary non-identity element $x\in G$‎, ‎there exists an element $y \in nX$ such that $G=\langle x,y\rangle$‎. ‎We studied the $(p,q,r)$-generation for the Chevalley group $G_{2}(3)$‎, ‎where $p$‎, ‎$q$ and $r$ are all the primes dividing the order of $G_{2}(3)$‎. ‎In the current paper‎, ‎we classify all the non-trivial conjugacy classes of $G_{2}(3)$ whether they are complementary generators or not‎. ‎To achieve this‎, ‎we mainly used the structure constant method together with other results applied to establish generation and non-generation of the group $G_{2}(3)$ by the $(p,q,r)$ triples‎. ‎Some particular algorithms‎, ‎as well as the (Gap) programming tool‎, ‎and the Atlas of finite groups have been exploited in our computations‎.

‎Quantile regression model and its generalizations‎, ‎including M-quantile regression model‎, ‎are analyzed usually via a nonparametric approach and their parameters are estimated using some iterative optimization algorithms‎. ‎For these reason‎, ‎in these models confidence intervals and hypotheses testing have done perforce using rank-based or bootstrapping approaches‎. ‎In this paper‎, ‎we consider parametric analysis of M-quantile model‎. ‎It is shown that‎, ‎the frequentist based approach of maximum likelihood estimation leads to results that are similar to the nonparametric approach‎. ‎Hence‎, ‎in order to achieve a more afficient model‎, ‎we have been used the Bayes theory and a‎ ‎hierarchical Bayes model has been developed‎. ‎The efficiency of the proposed model has been assessed via a simulation study and real word example‎. The ‎results ‎show ‎that ‎the ‎Bayesian ‎approach of ‎m-quantile ‎regression ‎analysis ‎is ‎more ‎efficient ‎than ‎the correspond ‎frequantist ‎appro‎ach, for all sample sizes. In addition, the proposed model truly takes into account the effect of the outlier observation, which causes skewness in response variable distribution, in modeling.