Optimization of Demand and Supply Equilibrium equation by using Salp Swarm Algorithm

Abstract

The operation of demand and supply in a market is known as the market mechanism. The market will be in equilibrium at price (P), when quantity (Q) will be bought and sold. In equilibrium the quantity of a good supplied by producers equals the quantity demanded by consumers. Due to the fact that traditional deterministic methods or algorithms do not cope well to solve a large number of problems in practice; The aim of this paper is to solve approximately the demand and supply equilibrium equation which has an imperative role to describe the relation between consumers/ producers and price/quantity by means of the Salp Swarm Algorithm (SSA), inspired by the swarming behavior of salps when searching foods in deep oceans as well as the Genetic Algorithm (GA) inspired by the process of natural selection. The demand and supply equilibrium equation as an Initial Value Problem (IVP) is considered as an optimization problem, since it can almost be solved by classical mathematical tools with less precision. The effectiveness of the proposed method is tested via a simulation study between the exact results, the SSA and GA results. The comparison between these performances after many replications shows that SSA is a very powerful and can produce robust solutions on low dimensional problems with minimal error.