# Political Optimizer (PO): Inspired by the Multi-Phased Political Process Efficiently Solving Classical Engineering Problems

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1. Introduction

Politics in different contexts holds different meanings. In political optimizer algorithm PO, we use the political system of a country as a reference point and mimic the behavior of politicians to achieve the end goal of optimization [1]. Politics is about the governance of a region, state or country. The party-based political systems can be categorized in four major types: One-party political system, two-party political system, dominant-party political system, and multi-party political system. Each of them is applicable in different countries/states with several variations. Moreover, the governance of a state/country can be practiced through either parliamentary system or presidential system [2]. We have generalized PO by incorporating a few commonalities from these systems, such as the concept of parties and constituencies, association of politicians with political parties, collaboration between the politicians associated with same party and competition between the politicians through inter-party election, change of affiliation of politicians to parties, campaigning before election for votes, and collaboration between the elected members in parliament.

Political Optimizer (PO) is structured as a sequence of five phases involving party formation and constituency allocation, election campaign, party switching, inter-party election, and parliamentary affairs [3]. The main objective of Political Optimizer (PO), which is inspired by the multi-phased political process. Although, the idea of using politics as an inspiration for optimization algorithms is not new but politics is a very diverse and complex process, which encourages us to map the inspiration from a totally different perspective.

2. Political Optimizer

PO is the mathematical mapping of all the major phases of politics such as constituency allocation, party switching, election campaign, inter-party election, and parliamentary affairs [4]. The politics being practiced in multi-party democracy is a complex political process, which covers a very wide range of social levels [5]. The process is illustrated in the below fig to comprises the following phases

• Party formation
• Party switching
• Seat allocation
• Election campaign
• Inter-party election
• Government formation and parliamentary affairs

3. Illustration of the multi –phased political process

A multi-party system is a political system in which multiple political parties across the political spectrum run for national election, and all have the capacity to gain control of government offices, separately or in coalition [6]. Apart from one-party-dominant and two-party systems, multi-party systems tend to be more common in parliamentary systems than presidential systems and far more common in countries that use proportional representation compared to countries that use first-past-the-post elections. Several parties compete for power and all of them have reasonable chance of forming government. A system where only two parties have the possibility of winning an election is called a two-party system [7]. A system where only three parties have a realistic possibility of winning an election or forming a coalition is sometimes called a “Third-party system”. But, in some cases the system is called a “Stalled Third-Party System,” when there are three parties and all three parties win a large number of votes, but only two have a chance of winning an election.

3. Inspiration of PO

PO is inspired by the idea of using politics as an inspiration for optimization algorithms is not new but politics is a very diverse and complex process [8], which encourages us to map the inspiration from a totally different perspective. Hence the multi-phased political process is the main inspiration for the PO Algorithm [9]. Politics itself is a process of optimization from two perspectives: each individual optimizes its goodwill to win the election and each party tries to maximize its number of seats in parliament to form a government. These aspects make politics an ideal inspiration for an optimization algorithm because an individual (a party member) may be considered a candidate solution [10], individual’s goodwill is considered the position of the candidate solution in the search space, and goodwill of a political member can be defined by many performance-related parameters which can be mimicked by design variables or components of the position vector of a candidate solution.

Election may be considered the evaluation (objective) function and the number of votes obtained by an individual in election is mapped by the fitness of the candidate solution [11]. Furthermore, following are the four major inspirational aspects of the politics that motivate us to propose a new optimization algorithm such as the election candidate’s campaign for votes. The intra-party collaboration and inter-party competitiveness. The analytical behavior of election candidates to improve their performance based on their experience in the past election. The interaction and cooperation of the winning candidates with each other to run the government in the post-election phase [12].

4. Mathematical Model of PO

5. A Comparative Performance of PO

5.1. Exploitation capability of PO

The true exploitation capability of PO is revealed when high-dimensional functions are solved.

5.2. Exploration capability of PO

The good exploratory behavior of PO is also attributed to its position updating mechanism because each solution explores different vicinity due to position updating with reference to a unique pair of party leader and constituency winner [15].

5.3. Convergence of PO

In PO, the balance between the exploration and exploitation is attained through party switching, which uses a parameter to control the diversity [16].

6. Flowchart of PO

7. Applications of PO

The Political algorithm is also tested on four well-known constrained engineering design problems such as

• Welded beam design (WBD)

In this problem, the optimal cost of welding a beam with a strong member is determined [17].

• Speed reducer design (SRD)

In SRD, the objective is to minimize the weight of a speed reducer subject to the constraints on stresses in the shafts, transverse deflection of the shafts, surface stress and bending stress of the gear teeth [18].

• Pressure vessel design (PVD)

The objective in this problem is to optimize the total cost to design a pressure vessel, which includes material, formation and welding of a cylindrical pressure vessel [19].

• Tension/compression spring design

This is the problem of optimally designing a tension/ compression spring having minimum weight [20].

Reference

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