An analysis of the Taguchi method for tuning a memetic algorithm with reduced computational time budget

Determining the best initial parameter values for an algorithm, called parameter tuning, is crucial to obtaining better algorithm performance; however, it is often a time-consuming task and needs to be performed under a restricted computational budget. In this study, the results from our previous work on using the Taguchi method to tune the parameters of a memetic algorithm for cross-domain search are further analysed and extended. Although the Taguchi method reduces the time spent finding a good parameter value combination by running a smaller size of experiments on the training instances from different domains as opposed to evaluating all combinations, the time budget is still larger than desired. This work investigates the degree to which it is possible to predict the same good parameter setting faster by using a reduced time budget. The results in this paper show that it was possible to predict good combinations of parameter settings with a much reduced time budget. The good final parameter values are predicted for three of the parameters, while for the fourth parameter there is no clear best value, so one of three similarly performing values is identified at each time instant

An investigation of F-Race training strategies for cross domain optimisation with memetic algorithms

Parameter tuning is a challenging and time-consuming task, crucial to obtaining improved metaheuristic performance. There is growing interest in cross-domain search methods, which consider a range of optimisation problems rather than being specialised for a single domain. Metaheuristics and hyper-heuristics are typically used as high-level cross-domain search methods, utilising problem-specific low-level heuristics for each problem domain to modify a solution. Such methods have a number of parameters to control their behaviour, whose initial settings can influence their search behaviour significantly. Previous methods in the literature either fix these parameters based on previous experience, or set them specifically for particular problem instances. There is a lack of extensive research investigating the tuning of these parameters systematically. In this paper, F-Race is deployed as an automated cross-domain parameter tuning approach. The parameters of a steady-state memetic algorithm and the low-level heuristics used by this algorithm are tuned across nine single-objective problem domains, using different training strategies and budgets to investigate whether F-Race is capable of effectively tuning parameters for cross-domain search. The empirical results show that the proposed methods manage to find good parameter settings, outperforming many methods from the literature, with different configurations identified as the best depending upon the training approach used

Parameter tuning for cross-domain search

Metaheuristics usually have algorithmic parameters whose initial settings can influence their search behaviour and arbitrarily setting these values often leads to poor performance. Parameter tuning, i.e. determining the best initial parameter values, is a challenging and time-consuming task, but is one which is crucial to obtaining improved meta-heuristic performance. Memetic algorithms, which hybridise evolutionary algorithms with local search, are well-known metaheuristics for solving combinatorial optimisation problems. There are various methods available for parameter tuning and these have been widely used to tune the parameters of metaheuristics for individual optimisation problems. There is a growing interest towards designing general-purpose problem-independent search methodologies which produce good quality solutions for cross-domain search; which means that they consider a broad range of optimisation problems rather than being specialised for a solution method for a single problem. Metaheuristics can be used as a high-level cross-domain search method, utilising the available low level heuristics for each of the problem domains to modify a solution. The cross-domain search methods have ‘algorithm parameters’ to control the behaviour of the algorithms, while the low level heuristics have ‘heuristic parameters’ to determine the extent of the change that they make when used. Previous cross-domain search methods in the literature generally either fixed these parameters to some values based on previous experience or adapted them to the specific instances being solved. However, there has been a lack of extensive research in tuning these parameters for cross-domain search. In this thesis, two parameter tuning methods are adapted as cross-domain parameter tuning approaches. The parameters of a steady state memetic algorithm (SSMA) and the low level heuristics which are used in this algorithm are tuned across nine problem domains using the training instances from only a limited number of problems. One of the issues with the cross-domain parameter tuning is that the instances are characteristically different in nature and that their objective function values are often not comparable; therefore, a Formula 1 ranking based Taguchi method is proposed as the first approach. Four strategies are also presented to illustrate and contrast the capability of an F-Race parameter tuning method for cross-domain search. Due to the potential for excessive runtime for these problems, an analysis of parameter tuning with reduced computational time budget is also presented. The empirical results show that both of the methods managed to find good parameter settings which outperform the untuned SSMA as well as many of the previous CHeSC2011 competitors. Moreover, comparisons of the two methods show that Taguchi method found the same best configuration more easily and consistently with different run time budgets, while F-Race identified different configurations as the best one in some of the strategies, depending on the configuration budget and in what order instances are introduced to the tuning process

Move Acceptance in Local Search Metaheuristics for Cross-domain Heuristic Search

Many real-world combinatorial optimisation problems (COPs) are computationally hard problems and search methods are frequently preferred as solution techniques. Traditionally, an expert with domain knowledge designs, and tailors the search method for solving a particular COP. This process is usually expensive, requiring a lot of effort and time and often results in problem specific algorithms that can not be applied to another COP. Then, the domain expert either needs to design a new search method, or reconfigure an existing search method to solve that COP. This prompted interest into developing more general, problem-domain-independent high-level search methods that can be re-used, capable of solving not just a single problem but multiple COPs. The cross-domain search problem is a relatively new concept and represents a high-level issue that involves designing a single solution method for solving a multitude of COPs preferably with the least or no expert intervention. Cross-domain search methods are algorithms designed to tackle the cross-domain search problem. Such methods are of interest to researchers and practitioners worldwide as they offer a single off-the-shelf go-to approach to problem solving. Furthermore, if a cross-domain search method has a good performance, then it can be expected to solve `any' given COP well and in a reasonable time frame. When a practitioner is tasked with solving a new or unknown COP, they are tasked with a decision-making dilemma. This entails the decision of what algorithm they should use, what parameters should be used for that algorithm, and whether any other algorithm can outperform it. A well designed cross-domain search method that performs well and does not require re-tuning can fulfil this dilemma allowing practitioners to find good-enough solutions to such problems. Researchers on the other hand strive to find high-quality solutions to these problems; however, such a cross-domain search method provides them with a good benchmark to which they can compare their solution methods to, and should ultimately aim to outperform. In this work, move acceptance methods, which are a component of traditional search methods, such as metaheuristics and hyper-heuristics, are explored under a cross-domain search framework. A survey of the existing move acceptance methods as a part of local search metaheuristics is conducted based on the hyper-heuristic literature as solution methods to the cross-domain search problem. Furthermore, a taxonomy is provided for classifying them based on their design characteristics. The cross-domain performance of existing move acceptance methods, covering the taxonomy, is compared across a total of 45 problem instances spanning 9 problem domains, and the effects of parameter tuning versus choice of the move acceptance method are explored. A novel move acceptance method (HAMSTA) is proposed to overcome the shortcomings of the existing methods to improve the cross-domain performance of a local search metaheuristic. HAMSTA is capable of outperforming the cross-domain performances of existing methods that are re-tuned for each domain, despite itself using only a single cross-domain parameter configuration derived from tuning experiments that considers 2 instances each from 4 domains; hence, HAMSTA requires no expert intervention to re-configure it to perform well for solving multiple COPs with 37 problem instances unseen by HAMSTA, 25 of which are from unseen domains. HAMSTA is therefore shown to have the potential to fulfil the aforementioned decision-making dilemma

Diversity Control in Evolutionary Computation using Asynchronous Dual-Populations with Search Space Partitioning

Diversity control is vital for effective global optimization using evolutionary computation (EC) techniques. This paper classifies the various diversity control policies in the EC literature. Many research works have attributed the high risk of premature convergence to sub-optimal solutions to the poor exploration capabilities resulting from diversity collapse. Also, excessive cost of convergence to optimal solution has been linked to the poor exploitation capabilities necessary to focus the search. To address this exploration-exploitation trade-off, this paper deploys diversity control policies that ensure sustained exploration of the search space without compromising effective exploitation of its promising regions. First, a dual-pool EC algorithm that facilitates a temporal evolution-diversification strategy is proposed. Then a quasi-random heuristic initialisation based on search space partitioning (SSP) is introduced to ensure uniform sampling of the initial search space. Second, for the diversity measurement, a robust convergence detection mechanism that combines a spatial diversity measure; and a population evolvability measure is utilised. It was found that the proposed algorithm needed a pool size of only 50 samples to converge to optimal solutions of a variety of global optimization benchmarks. Overall, the proposed algorithm yields a 33.34% reduction in the cost incurred by a standard EC algorithm. The outcome justifies the efficacy of effective diversity control on solving complex global optimization landscapes. Keywords: Diversity, exploration-exploitation tradeoff, evolutionary algorithms, heuristic initialisation, taxonomy

Move Acceptance in Local Search Metaheuristics for Cross-domain Heuristic Search

Many real-world combinatorial optimisation problems (COPs) are computationally hard problems and search methods are frequently preferred as solution techniques. Traditionally, an expert with domain knowledge designs, and tailors the search method for solving a particular COP. This process is usually expensive, requiring a lot of effort and time and often results in problem specific algorithms that can not be applied to another COP. Then, the domain expert either needs to design a new search method, or reconfigure an existing search method to solve that COP. This prompted interest into developing more general, problem-domain-independent high-level search methods that can be re-used, capable of solving not just a single problem but multiple COPs. The cross-domain search problem is a relatively new concept and represents a high-level issue that involves designing a single solution method for solving a multitude of COPs preferably with the least or no expert intervention. Cross-domain search methods are algorithms designed to tackle the cross-domain search problem. Such methods are of interest to researchers and practitioners worldwide as they offer a single off-the-shelf go-to approach to problem solving. Furthermore, if a cross-domain search method has a good performance, then it can be expected to solve `any' given COP well and in a reasonable time frame. When a practitioner is tasked with solving a new or unknown COP, they are tasked with a decision-making dilemma. This entails the decision of what algorithm they should use, what parameters should be used for that algorithm, and whether any other algorithm can outperform it. A well designed cross-domain search method that performs well and does not require re-tuning can fulfil this dilemma allowing practitioners to find good-enough solutions to such problems. Researchers on the other hand strive to find high-quality solutions to these problems; however, such a cross-domain search method provides them with a good benchmark to which they can compare their solution methods to, and should ultimately aim to outperform. In this work, move acceptance methods, which are a component of traditional search methods, such as metaheuristics and hyper-heuristics, are explored under a cross-domain search framework. A survey of the existing move acceptance methods as a part of local search metaheuristics is conducted based on the hyper-heuristic literature as solution methods to the cross-domain search problem. Furthermore, a taxonomy is provided for classifying them based on their design characteristics. The cross-domain performance of existing move acceptance methods, covering the taxonomy, is compared across a total of 45 problem instances spanning 9 problem domains, and the effects of parameter tuning versus choice of the move acceptance method are explored. A novel move acceptance method (HAMSTA) is proposed to overcome the shortcomings of the existing methods to improve the cross-domain performance of a local search metaheuristic. HAMSTA is capable of outperforming the cross-domain performances of existing methods that are re-tuned for each domain, despite itself using only a single cross-domain parameter configuration derived from tuning experiments that considers 2 instances each from 4 domains; hence, HAMSTA requires no expert intervention to re-configure it to perform well for solving multiple COPs with 37 problem instances unseen by HAMSTA, 25 of which are from unseen domains. HAMSTA is therefore shown to have the potential to fulfil the aforementioned decision-making dilemma

A prescription of methodological guidelines for comparing bio-inspired optimization algorithms

Bio-inspired optimization (including Evolutionary Computation and Swarm Intelligence) is a growing research topic with many competitive bio-inspired algorithms being proposed every year. In such an active area, preparing a successful proposal of a new bio-inspired algorithm is not an easy task. Given the maturity of this research field, proposing a new optimization technique with innovative elements is no longer enough. Apart from the novelty, results reported by the authors should be proven to achieve a significant advance over previous outcomes from the state of the art. Unfortunately, not all new proposals deal with this requirement properly. Some of them fail to select appropriate benchmarks or reference algorithms to compare with. In other cases, the validation process carried out is not defined in a principled way (or is even not done at all). Consequently, the significance of the results presented in such studies cannot be guaranteed. In this work we review several recommendations in the literature and propose methodological guidelines to prepare a successful proposal, taking all these issues into account. We expect these guidelines to be useful not only for authors, but also for reviewers and editors along their assessment of new contributions to the field.This work was supported by grants from the Spanish Ministry of Science (TIN2016-8113-R, TIN2017-89517-P and TIN2017-83132-C2- 2-R) and Universidad Politécnica de Madrid (PINV-18-XEOGHQ-19- 4QTEBP). Eneko Osaba and Javier Del Ser-would also like to thank the Basque Government for its funding support through the ELKARTEK and EMAITEK programs. Javier Del Ser-receives funding support from the Consolidated Research Group MATHMODE (IT1294-19) granted by the Department of Education of the Basque Government

Heuristic sequence selection for inventory routing problem

In this paper, an improved sequence-based selection hyper-heuristic method for the Air Liquide inventory routing problem, the subject of the ROADEF/EURO 2016 challenge, is described. The organizers of the challenge have proposed a real-world problem of inventory routing as a difficult combinatorial optimization problem. An exact method often fails to find a feasible solution to such problems. On the other hand, heuristics may be able to find a good quality solution that is significantly better than those produced by an expert human planner. There is a growing interest toward self-configuring automated general-purpose reusable heuristic approaches for combinatorial optimization. Hyper-heuristics have emerged as such methodologies. This paper investigates a new breed of hyper-heuristics based on the principles of sequence analysis to solve the inventory routing problem. The primary point of this work is that it shows the usefulness of the improved sequence-based selection hyper-heuristic, and in particular demonstrates the advantages of using a data science technique of hidden Markov model for the heuristic selection

A Comprehensive Survey on Particle Swarm Optimization Algorithm and Its Applications

Particle swarm optimization (PSO) is a heuristic global optimization method, proposed originally by Kennedy and Eberhart in 1995. It is now one of the most commonly used optimization techniques. This survey presented a comprehensive investigation of PSO. On one hand, we provided advances with PSO, including its modifications (including quantum-behaved PSO, bare-bones PSO, chaotic PSO, and fuzzy PSO), population topology (as fully connected, von Neumann, ring, star, random, etc.), hybridization (with genetic algorithm, simulated annealing, Tabu search, artificial immune system, ant colony algorithm, artificial bee colony, differential evolution, harmonic search, and biogeography-based optimization), extensions (to multiobjective, constrained, discrete, and binary optimization), theoretical analysis (parameter selection and tuning, and convergence analysis), and parallel implementation (in multicore, multiprocessor, GPU, and cloud computing forms). On the other hand, we offered a survey on applications of PSO to the following eight fields: electrical and electronic engineering, automation control systems, communication theory, operations research, mechanical engineering, fuel and energy, medicine, chemistry, and biology. It is hoped that this survey would be beneficial for the researchers studying PSO algorithms