Adding Negative Learning to Ant Colony Optimization: A Comprehensive Study

Abstract

Ant colony optimization is a metaheuristic that is mainly used for solving hard combinatorial optimization problems. The distinctive feature of ant colony optimization is a learning mechanism that is based on learning from positive examples. This is also the case in other learning-based metaheuristics such as evolutionary algorithms and particle swarm optimization. Examples from nature, however, indicate that negative learning—in addition to positive learning—can beneficially be used for certain purposes. Several research papers have explored this topic over the last decades in the context of ant colony optimization, mostly with limited success. In this work we present and study an alternative mechanism making use of mathematical programming for the incorporation of negative learning in ant colony optimization. Moreover, we compare our proposal to some well-known existing negative learning approaches from the related literature. Our study considers two classical combinatorial optimization problems: the minimum dominating set problem and the multi dimensional knapsack problem. In both cases we are able to show that our approach significantly improves over standard ant colony optimization and over the competing negative learning mechanisms from the literature.

A Knowledge-Based Hybrid Approach on Particle Swarm Optimization Using Hidden Markov Models

“…In [70], an incremental learning technique was applied to constrained optimization problems. Finally, in [71], an alternative mechanism for the incorporation of negative learning on the ant colony optimization is proposed.…”

A LQR Neural Network Control Approach for Fast Stabilizing Rotary Inverted Pendulums

“…An interesting problem is how to control the pendulum so that it can keep its equilibrium upward state in various conditions [8][9][10]. Recently, there are many algorithms in controlling the RIP systems such as LQR [6], PID [11,12], sliding mode [1,[13][14][15][16][17], backstepping [18], semi-optimal [8,19], fuzzy logic [9,20,21], and reinforcement learning controllers [22], etc. Due to the unique instability nature, the pendulum will fall instantly if affected by any strong external disturbance.…”

“…Due to the unique instability nature, the pendulum will fall instantly if affected by any strong external disturbance. Adoption of PID control methods [19,23,24] in this case is possible but it is not easy to figure out the best control gains to strongly suppress uncertain nonlinearities in the system dynamics. To cope with such the shortcoming, a vast of nonlinear control approaches have been promptly studied.…”

“…Since the fuzzy-control mechanism is mostly based on experience of the operators, this approach could be limited in universal applicability. Another research direction of the intelligent nominal controller series is biologically inspired with Artificial Neural Network [24,30], Genetic Algorithm [31,32] and Bacterial Foraging Optimization Algorithm (BFOA), that mimic natural processes such as hybridization, reproduction, natural selection, mutation, etc., [19,28,[31][32][33][34]. In [35], the optimal LQR control performance was enhanced by intelligent control effect of an Adaline neural network, which was adopted for learning control behaviors of another linear controller based on a basic backpropagation adaptation method.…”

Special Issue “Mathematical Methods for Operations Research Problems”

“…The second paper [2] studies an alternative mechanism for using mathematical programming to incorporate negative learning into a widely used ant colony optimization. The authors compare their approach with existing negative learning approaches from the literature on two combinatorial optimization problems: the minimum dominating set problem and the multi-dimensional knapsack problem.…”