Multi-Species Cuckoo Search Algorithm for Global Optimization

Many optimization problems in science and engineering are highly nonlinear, and thus require sophisticated optimization techniques to solve. Traditional techniques such as gradient-based algorithms are mostly local search methods, and often struggle to cope with such challenging optimization problems. Recent trends tend to use nature-inspired optimization algorithms. This work extends the standard cuckoo search (CS) by using the successful features of the cuckoo-host co-evolution with multiple interacting species, and the proposed multi-species cuckoo search (MSCS) intends to mimic the multiple species of cuckoos that compete for the survival of the fittest, and they co-evolve with host species with solution vectors being encoded as position vectors. The proposed algorithm is then validated by 15 benchmark functions as well as five nonlinear, multimodal design case studies in practical applications. Simulation results suggest that the proposed algorithm can be effective for finding optimal solutions and in this case all optimal solutions are achievable. The results for the test benchmarks are also compared with those obtained by other methods such as the standard cuckoo search and genetic algorithm, which demonstrated the efficiency of the present algorithm. Based on numerical experiments and case studies, we can conclude that the proposed algorithm can be more efficient in most cases, leading a potentially very effective tool for solving nonlinear optimization problems.

Social Algorithms

This article concerns the review of a special class of swarm intelligence based algorithms for solving optimization problems and these algorithms can be referred to as social algorithms. Social algorithms use multiple agents and the social interactions to design rules for algorithms so as to mimic certain successful characteristics of the social/biological systems such as ants, bees, bats, birds and animals.

Why the Firefly Algorithm Works?

Firefly algorithm is a nature-inspired optimization algorithm and there have been significant developments since its appearance about ten years ago. This chapter summarizes the latest developments about the firefly algorithm and its variants as well as their diverse applications. Future research directions are also highlighted.

New directional bat algorithm for continuous optimization problems

Bat algorithm (BA) is a recent optimization algorithm based on swarm intelligence and inspiration from the echolocation behavior of bats. One of the issues in the standard bat algorithm is the premature convergence that can occur due to the low exploration ability of the algorithm under some conditions. To overcome this deficiency, directional echolocation is introduced to the standard bat algorithm to enhance its exploration and exploitation capabilities. In addition to such directional echolocation, three other improvements have been embedded into the standard bat algorithm to enhance its performance. The new proposed approach, namely the directional Bat Algorithm (dBA), has been then tested using several standard and non-standard benchmarks from the CEC2005 benchmark suite. The performance of dBA has been compared with ten other algorithms and BA variants using non-parametric statistical tests. The statistical test results show the superiority of the directional bat algorithm.

Cuckoo Search: State-of-the-Art and Opportunities

Since the development of cuckoo search (CS) by Yang and Deb in 2009, CS has been applied in a diverse range of applications. This paper first outlines the key features of the algorithm and its variants, and then briefly summarizes the state-of-the-art developments in many applications. The opportunities for further research are also identified.

Swarm Intelligence: Past, Present and Future

Many optimization problems in science and engineering are challenging to solve, and the current trend is to use swarm intelligence (SI) and SI-based algorithms to tackle such challenging problems. Some significant developments have been made in recent years, though there are still many open problems in this area. This paper provides a short but timely analysis about SI-based algorithms and their links with self-organization. Different characteristics and properties are analyzed here from both mathematical and qualitative perspectives. Future research directions are outlined and open questions are also highlighted.

Global Convergence Analysis of the Flower Pollination Algorithm: A Discrete-Time Markov Chain Approach

Flower pollination algorithm is a recent metaheuristic algorithm for solving nonlinear global optimization problems. The algorithm has also been extended to solve multiobjective optimization with promising results. In this work, we analyze this algorithm mathematically and prove its convergence properties by using Markov chain theory. By constructing the appropriate transition probability for a population of flower pollen and using the homogeneity property, it can be shown that the constructed stochastic sequences can converge to the optimal set. Under the two proper conditions for convergence, it is proved that the simplified flower pollination algorithm can indeed satisfy these convergence conditions and thus the global convergence of this algorithm can be guaranteed. Numerical experiments are used to demonstrate that the flower pollination algorithm can converge quickly in practice and can thus achieve global optimality efficiently.

LibOPT: An Open-Source Platform for Fast Prototyping Soft Optimization Techniques

Optimization techniques play an important role in several scientific and real-world applications, thus becoming of great interest for the community. As a consequence, a number of open-source libraries are available in the literature, which ends up fostering the research and development of new techniques and applications. In this work, we present a new library for the implementation and fast prototyping of nature-inspired techniques called LibOPT. Currently, the library implements 15 techniques and 112 benchmarking functions, as well as it also supports 11 hypercomplex-based optimization approaches, which makes it one of the first of its kind. We showed how one can easily use and also implement new techniques in LibOPT under the C paradigm. Examples are provided with samples of source-code using benchmarking functions.

A Discrete Firefly Algorithm to Solve a Rich Vehicle Routing Problem Modelling a Newspaper Distribution System with Recycling Policy

A real-world newspaper distribution problem with recycling policy is tackled in this work. In order to meet all the complex restrictions contained in such a problem, it has been modeled as a rich vehicle routing problem, which can be more specifically considered as an asymmetric and clustered vehicle routing problem with simultaneous pickup and deliveries, variable costs and forbidden paths (AC-VRP-SPDVCFP). This is the first study of such a problem in the literature. For this reason, a benchmark composed by 15 instances has been also proposed. In the design of this benchmark, real geographical positions have been used, located in the province of Bizkaia, Spain. For the proper treatment of this AC-VRP-SPDVCFP, a discrete firefly algorithm (DFA) has been developed. This application is the first application of the firefly algorithm to any rich vehicle routing problem. To prove that the proposed DFA is a promising technique, its performance has been compared with two other well-known techniques: an evolutionary algorithm and an evolutionary simulated annealing. Our results have shown that the DFA has outperformed these two classic meta-heuristics.

An Improved Discrete Bat Algorithm for Symmetric and Asymmetric Traveling Salesman Problems

Bat algorithm is a population metaheuristic proposed in 2010 which is based on the echolocation or bio-sonar characteristics of microbats. Since its first implementation, the bat algorithm has been used in a wide range of fields. In this paper, we present a discrete version of the bat algorithm to solve the well-known symmetric and asymmetric traveling salesman problems. In addition, we propose an improvement in the basic structure of the classic bat algorithm. To prove that our proposal is a promising approximation method, we have compared its performance in 37 instances with the results obtained by five different techniques: evolutionary simulated annealing, genetic algorithm, an island based distributed genetic algorithm, a discrete firefly algorithm and an imperialist competitive algorithm. In order to obtain fair and rigorous comparisons, we have conducted three different statistical tests along the paper: the Student's $t$-test, the Holm's test, and the Friedman test. We have also compared the convergence behaviour shown by our proposal with the ones shown by the evolutionary simulated annealing, and the discrete firefly algorithm. The experimentation carried out in this study has shown that the presented improved bat algorithm outperforms significantly all the other alternatives in most of the cases.