A New Optimization Algorithm For Combinatorial Problems

Abstract

Abstract-Combinatorial optimization problems are those problems that have a finite set of possible solutions. The best way to solve a combinatorial optimization problem is to check all the feasible solutions in the search space. However, checking all the feasible solutions is not always possible, especially when the search space is large. Thus, many meta-heuristic algorithms have been devised and modified to solve these problems. The meta-heuristic approaches are not guaranteed to find the optimal solution since they evaluate only a subset of the feasible solutions, but they try to explore different areas in the search space in a smart way to get a near-optimal solution in less cost and time. In this paper, we propose a new meta-heuristic algorithm that can be used for solving combinatorial optimization problems. The method introduced in this paper is named the Global Neighborhood Algorithm (GNA). The algorithm is principally based on a balance between both the global and local search. A set of random solutions are first generated from the global search space, and then the best solution will give the optimal value. After that, the algorithm will iterate, and in each iteration there will be two sets of generated solutions; one from the global search space and the other set of solutions will be generated from the neighborhood of the best solution. Throughout the paper, the algorithm will be delineated with examples. In the final phase of the research, the results of GNA will be discussed and compared with the results of Genetic Algorithm (GA) as an example of another optimization method.

Optimization Algorithm’s Problems: Comparison Study

“…Combinatorial optimization emerged from more than 50 years ago, [6][15] [12] [7]. It not only helps to solve real-life problems but also tends to give efficient algorithms, especially in working with the large and complex data.…”

A Tabu Search hyper-heuristic strategy for t-way test suite generation

“…Like TLBO, the Global Neighborhood Algorithm (GNA) [15], is a population based meta-heuristic. GNA has only two control parameters; population size and the maximum number of iterations.…”

“…HHH employs Tabu Search (TS) as its high level metaheuristic (HLH) and leverages on the strength of four low level meta-heuristics (LLH), comprising Teaching Learning based Optimization (TLBO) [14], Global Neighborhood Algorithm (GNA) [15], Particle Swarm Optimization (PSO) [16], and Cuckoo Search Algorithm (CS) [17]. To the best of our knowledge, HHH is the first hyper-heuristic based strategy that addresses the problem of t-way test suite generation.…”

Grass Fibrous Root Optimization Algorithm

“…In order to test the proposed metaheuristic GRA, seven standard test functions will be used. The obtained results will be compared with other nine well-known, and recently proposed algorithms which are Particle Swarm Optimization (PSO) [4], Differential Evolutionary algorithm (DEA) [5], Bee Colony Optimization (BCO) [6], Cuckoo Search Algorithm (CSO) [7], Wind Driven Algorithm (WDA) [8], Stochastic Fractal Search (SFS) [9], Symbiotic Organisms Search (SOS) [10], Grey Wolf Optimizer (GWO) [11], and Novel Bat Algorithm (NBA) [12]. This work proposes and implements a general grass root optimization algorithm GRA, comparing it with other meta-heuristic algorithms through using a variety of test function to evaluate the average mean absolute error, average number of effective iteration, and average effective processing time.…”