Journal of Mathematical Sciences and Optimization

Comparison of the Dijkstra’s Algorithm and the Floyd-Warshall’s Algorithm to Determine the Shortest Path between Hospitals in Several Cities in Lampung Province

Alenia Daynur Putriani, Wamiliana, Siti Laelatul Chasanah — Thu, 30 May 2024 00:00:00 +0000

Determining the shortest route from one node to another is a problem we often encounter in everyday life. The routes obtained are intended to minimize costs, travel time or distance. In this study, we compare Dijkstra’s and Floyd-Warshall’s algorithms to determine the shortest route between hospitals in some cities in Lampung Province. The efficiency of the two algorithms in solving this problem is assessed based on the program running time. The results show that both Dijkstra’s algorithm and Floyd-Warshall’s algorithm provide the shortest path in the same distance. However, the running time of the Dijkstra’s algorithm takes less time than Floyd-Warshall’s algorithm.

Efficient Quadratic Programming Optimization via Staged Computational Procedures: Unconstrained Minimization and Constraint Exploration

Yosza Dasril, Nazarudin Bujang, R. Chandrashekar, Shahrul Nizam Salahudin — Wed, 31 Jan 2024 00:00:00 +0000

In this paper, we present a computational framework for finding optimal solutions to quadratic programming problems. Our computational process is divided into three steps. Initially, we derive unconstrained minimization of the quadratic programming problem by solving simultaneous equations involving objective function derivatives and confirming its feasibility. Using this discovered point, we identify the violated constraints and direct our search to these specific constraints. The next stage defines the process for determining the unconstrained point on each active constraint violated by the objective function's optimal point. Moving on to the next stage, we use the constraint exploration technique to systematically seek the optimal constrained point at the intersections of two or more violated active constraints as candidates for the optimal solution. The feasibility of the unconstrained point is systematically checked at each level. If the unconstrained point is deemed feasible, then the optimal solution is obtained, and the optimal value of the objective function is found.

TOTAL VERTEX IRREGULARITY STRENGTH OF HAYAT TREE GRAPH

Wed, 31 Jan 2024 00:00:00 +0000

Let G(V,E) be a finite, simple graph with no loop and parallel edges. V is a set of vertices in G and E is a set edges. Labeling a graf is mapping that sends some set of graph elements to a set of positive integers. If the domain is the vertex set then the labeling is call vertex labeling, if the domain is the edge set then the labeling is call edge labeling. Define a labeling as a vertex irregular total k - labeling if for every two different vertices x and y the vertex-weight where the vertex-weigth is defined by

The minimum value of label k for which G has a vertex irregular total labeling is called the total vertex irregularity strength of G and denoted by tvs(G) . We consider Hayat Tree Graph, a graph as symbol of Capital of Nusantara (IKN) which is ratified by president in June 2023. In this paper, we determined the total vertex irregularity strength of Hayat Tree Graph.

MODIFICATION OF PROSPECTIVE LIFE INSURANCE RESERVE PROSPECTIVE CALCULATIONS USING THE ZILLMER METHOD

Dea Setianingsih, Silvia Rosita, Siska Resti S — Wed, 31 Jan 2024 00:00:00 +0000

The calculation of the premium reserve can be modified to avoid losses in the early years because in the first year there are many expenses that must be borne by the company so that it has difficulties in calculating the amount of the premium reserve. Not a few insurers have suffered losses due to inaccurate calculations in the calculation of premium reserves. This study aims to modify the calculation of prospective whole life insurance premium reserves using the Zillmer method. Modification of premium reserves is calculated using the 2019 Indonesian Mortality Table with an interest rate of 3.50%. Based on the results of data analysis on the value of prospective premium reserves and the modified value of premium reserves using the Zillmer method, the results are the same, namely for male age (x) = 48 years, the prospective reserve value is IDR 213,253.05 and the modified premium reserve value using the Zillmer method is IDR 213,252.93 then for female age (y) = 69 years the prospective reserve value is IDR 8,698,949.01 and for the modified premium reserve value using the Zillmer method is IDR 8,698,948.89.

HAMILTONIAN AND HYPOHAMILTONIAN OF GENERALIZED PETERSEN GRAPH GPn,6

Putti Naura Adwita, Sri Gemawati — Wed, 31 Jan 2024 00:00:00 +0000

This article discusses the Hamiltonian and Hypohamiltonian properties of Generalized Petersen Graphs GP_n,6. A Hamiltonian graph is a graph that has a Hamiltonian cycle. So, a graph is called to be Hamiltonian and has a cycle that passes through each vertex exactly once. A Hypohamiltonian graph is if it is not a Hamiltonian graph, but if one vertex is removed it will be Hamiltonian. The Petersen graph is a cubic graph with ten vertices and fifteen edges and each vertex is of degree three. The generalized Petersen graph is denoted GP_n,k, for positive numbers n and k with 2 ≤ 2k < ????. The Petersen graph is not a Hamiltonian graph, but is Hypohamiltonian. In the Generalized Petersen graph for GP_n,6 for n ≡ 1(mod 13), n ≡ 3(mod 13), n ≡ 7(mod 13), n ≡ 9(mod 13) is a Hamiltonian, for n ≡ 0(mod 13) is a hypohamiltonian, and for n ≡ 2(mod 13), n ≡ 4(mod 13), n ≡ 5(mod 13), n ≡ 6(mod 13), n ≡ 8(mod 13) neither.