Optimizing Wiener and Randić Indices of Graphs

Wiener and Randić indices have long been studied in chemical graph theory as connection strength measures of graphs. Later, these indices were used in different fields such as network analysis. We consider two optimization problems related to these indices, with potential applications to network theory, in particular to epidemiological networks. Given a connected graph and a fixed total edge weight, we investigate how individual weights must be assigned to edges, minimizing the connection strength of the graph. In order to measure the connection strength, we use the weighted Wiener index and a modified version of the ordinary Randić index. Wiener index optimization is linear, while Randić index optimization turns out to be both nonlinear and nonconvex. Hence, we adopt the technique of separable programming to generate solutions. We present our experimental results by applying relevant algorithms to several graphs.

An optimal lockdown relaxation strategy for minimizing the economic effects of covid-19 outbreak in Sri Lanka

In order to recover the damage to the economy by the ongoing covid-19 pandemic, Sri Lanka is undergoing a gradual transition from strict lockdowns to partial lockdowns through relaxation of curfew and other moderated preventive measures. In this work, we propose an optimal lockdown relaxation strategy, which is aimed at minimizing the damage to the economy, while confining the covid-19 incidence to a level endurable by the available healthcare capacity in the country. The relevant optimization model turns out to be non-linear. We use the technique of separable programming to generate solutions and discuss the results.

A game-theoretic optimisation approach to fair customer allocation in oligopolies

Under the ever-increasing capital intensive environment that contemporary process industries face, oligopolies begin to form in mature markets where a small number of companies regulate and serve the customer base. Strategic and operational decisions are highly dependent on the firms’ customer portfolio and conventional modelling approaches neglect the rational behaviour of the decision makers, with regards to the problem of customer allocation, by assuming either static competition or a leader-follower structure. In this article, we address the fair customer allocation within oligopolies by employing the Nash bargaining approach. The overall problem is formulated as mixed integer program with linear constraints and a nonlinear objective function which is further linearised following a separable programming approach. Case studies from the industrial liquid market highlight the importance and benefits of the proposed game theoretic approach.

PERBANDINGAN METODE SEPARABLE PROGRAMMING DAN QUADRATIC PROGRAMMING DALAM PEMECAHAN MASALAH PEMROGRAMAN NONLINIER

The Separable programming method solves nonlinear programming problems by transforming a nonlinear shape that consists of a single variable into a linear function and resolved by the simplex method. Meanwhile, the quadratic programming method accomplishes the two degrees nonlinear model by transforming the nonlinear shape into linear function with the Kuhn Tucker Conditions and resolved by the simplex Wolfe method. Both of these methods are applied to the Markowitz’s portfolio model, which is to find the proportion of stock funds to obtain maximum profits by combination of three shares, such as BMRI, GGRM, and ICBP. The completion using the quadratic programming method is more effective and efficient with the same optimum value.