Chaotic Quantum Double Delta Swarm Algorithm using Chebyshev Maps: Theoretical Foundations, Performance Analyses and Convergence Issues

Quantum Double Delta Swarm (QDDS) Algorithm is a new metaheuristic algorithm inspired by the convergence mechanism to the center of potential generated within a single well of a spatially co-located double-delta well setup. It mimics the wave nature of candidate positions in solution spaces and draws upon quantum mechanical interpretations much like other quantum-inspired computational intelligence paradigms. In this work, we introduce a Chebyshev map driven chaotic perturbation in the optimization phase of the algorithm to diversify weights placed on contemporary and historical, socially-optimal agents' solutions. We follow this up with a characterization of solution quality on a suite of 23 single-objective functions and carry out a comparative analysis with eight other related nature-inspired approaches. By comparing solution quality and successful runs over dynamic solution ranges, insights about the nature of convergence are obtained. A two-tailed t-test establishes the statistical significance of the solution data whereas Cohen's d and Hedge's g values provide a measure of effect sizes. We trace the trajectory of the fittest pseudo-agent over all function evaluations to comment on the dynamics of the system and prove that the proposed algorithm is theoretically globally convergent under the assumptions adopted for proofs of other closely-related random search algorithms.Comment: 27 pages, 4 figures, 19 table

Improvements in meta-heuristic algorithms for minimum cost design of reinforced concrete rectangular sections under compression and biaxial bending

A numerical procedure is proposed in this paper for achieving the minimum cost design of reinforced concrete rectangular sections under compression and biaxial bending by using biologically-inspired meta-heuristic optimization algorithms. The problem formulation includes the costs of concrete, reinforcement and formwork, obtaining the detailed optimum design in which the section dimensions and the reinforcement correspond to values used in practice. The formulation has been simplified in order to reduce the computational cost while ensuring the rigor necessary to achieve safe designs. The numerical procedure includes the possibility of using high-strength concrete and several design constraints, such as mínimum reinforcement and limiting the neutral axis depth. Two numerical examples are presented, drawing comparisons between the results obtained by ACI318 and EC2 standards

Short-term scheduling of hybrid thermal, pumped-storage, and wind plants using firefly optimization algorithm

This paper presents a novel method based on an enhanced firefly algorithm (EFA) to solve scheduling hybrid thermal, pumped-storage, and wind plants. Since the scheduling problem is inherently discrete, basic EFA and binary encoding/decoding techniques are used in the proposed EFA approach. Optimal power values of thermal and pumped-storage units are determined separately in the presence of uncertainty caused by wind speed. The proposed method is applied to a real plant, including four pumped-storage units, 34 thermal units with different characteristics, and one wind turbine plant. In addition, dynamic constraints of upstream and downstream sources and constraints regarding thermal and wind units are also considered for finding the optimal solution. In addition, the proposed EFA is successfully applied to a real plant, and the results are compared with those of the three available methods. The results show that the proposed method has converted to a more optimal cost than the other methods

A Comprehensive Review of Recent Variants and Modifications of Firefly Algorithm

Swarm intelligence (SI) is an emerging field of biologically-inspired artificial intelligence based on the behavioral models of social insects such as ants, bees, wasps, termites etc. Swarm intelligence is the discipline that deals with natural and artificial systems composed of many individuals that coordinate using decentralized control and self-organization. Most SI algorithms have been developed to address stationary optimization problems and hence, they can converge on the (near-) optimum solution efficiently. However, many real-world problems have a dynamic environment that changes over time. In the last two decades, there has been a growing interest of addressing Dynamic Optimization Problems using SI algorithms due to their adaptation capabilities. This paper presents a broad review on two SI algorithms: 1) Firefly Algorithm (FA) 2) Flower Pollination Algorithm (FPA). FA is inspired from bioluminescence characteristic of fireflies. FPA is inspired from the the pollination behavior of flowering plants. This article aims to give a detailed analysis of different variants of FA and FPA developed by parameter adaptations, modification, hybridization as on date. This paper also addresses the applications of these algorithms in various fields. In addition, literatures found that most of the cases that used FA and FPA technique have outperformed compare to other metaheuristic algorithms

Reconstructing Rational Functions with FireFly\texttt{FireFly}

We present the open-source $\texttt{C++}$ library $\texttt{FireFly}$ for the reconstruction of multivariate rational functions over finite fields. We discuss the involved algorithms and their implementation. As an application, we use $\texttt{FireFly}$ in the context of integration-by-parts reductions and compare runtime and memory consumption to a fully algebraic approach with the program $\texttt{Kira}$.Comment: 46 pages, 3 figures, 6 tables; v2: matches published versio