A Non-Dominated Sorting Based Customized Random-Key Genetic Algorithm for the Bi-Objective Traveling Thief Problem

In this paper, we propose a method to solve a bi-objective variant of the well-studied Traveling Thief Problem (TTP). The TTP is a multi-component problem that combines two classic combinatorial problems: Traveling Salesman Problem (TSP) and Knapsack Problem (KP). In the TTP, a thief has to visit each city exactly once and can pick items throughout their journey. The thief begins their journey with an empty knapsack and travels with a speed inversely proportional to the knapsack weight. We address the BI-TTP, a bi-objective version of the TTP, where the goal is to minimize the overall traveling time and to maximize the profit of the collected items. Our method is based on a genetic algorithm with customization addressing problem characteristics. We incorporate domain knowledge through a combination of near-optimal solutions of each subproblem in the initial population and a custom repair operation to avoid the evaluation of infeasible solutions. Moreover, the independent variables of the TSP and KP components are unified to a real variable representation by using a biased random-key approach. The bi-objective aspect of the problem is addressed through an elite population extracted based on the non-dominated rank and crowding distance of each solution. Furthermore, we provide a comprehensive study which shows the influence of hyperparameters on the performance of our method and investigate the performance of each hyperparameter combination over time. In addition to our experiments, we discuss the results of the BI-TTP competitions at EMO-2019 and GECCO-2019 conferences where our method has won first and second place, respectively, thus proving its ability to find high-quality solutions consistently.

Design optimisation of a multi-mode wave energy converter

A wave energy converter (WEC) similar to the CETO system developed by Carnegie Clean Energy is considered for design optimisation. This WEC is able to absorb power from heave, surge and pitch motion modes, making the optimisation problem nontrivial. The WEC dynamics is simulated using the spectral-domain model taking into account hydrodynamic forces, viscous drag, and power take-off forces. The design parameters for optimisation include the buoy radius, buoy height, tether inclination angles, and control variables (damping and stiffness). The WEC design is optimised for the wave climate at Albany test site in Western Australia considering unidirectional irregular waves. Two objective functions are considered: (i) maximisation of the annual average power output, and (ii) minimisation of the levelised cost of energy (LCoE) for a given sea site. The LCoE calculation is approximated as a ratio of the produced energy to the significant mass of the system that includes the mass of the buoy and anchor system. Six different heuristic optimisation methods are applied in order to evaluate and compare the performance of the best known evolutionary algorithms, a swarm intelligence technique and a numerical optimisation approach. The results demonstrate that if we are interested in maximising energy production without taking into account the cost of manufacturing such a system, the buoy should be built as large as possible (20 m radius and 30 m height). However, if we want the system that produces cheap energy, then the radius of the buoy should be approximately 11-14~m while the height should be as low as possible. These results coincide with the overall design that Carnegie Clean Energy has selected for its CETO 6 multi-moored unit. However, it should be noted that this study is not informed by them, so this can be seen as an independent validation of the design choices.

Is perturbation an effective restart strategy?

Premature convergence can be detrimental to the performance of search methods, which is why many search algorithms include restart strategies to deal with it. While it is common to perturb the incumbent solution with diversification steps of various sizes with the hope that the search method will find a new basin of attraction leading to a better local optimum, it is usually not clear how big the perturbation step should be. We introduce a new property of fitness landscapes termed "Neighbours with Similar Fitness" and we demonstrate that the effectiveness of a restart strategy depends on this property.

A Hybrid Cooperative Co-evolution Algorithm Framework for Optimising Power Take Off and Placements of Wave Energy Converters

Wave energy technologies have the potential to play a significant role in the supply of renewable energy on a world scale. One of the most promising designs for wave energy converters (WECs) are fully submerged buoys. In this work, we explore the optimisation of WEC arrays consisting of a three-tether buoy model called CETO. Such arrays can be optimised for total energy output by adjusting both the relative positions of buoys in farms and also the power-take-off (PTO) parameters for each buoy. The search space for these parameters is complex and multi-modal. Moreover, the evaluation of each parameter setting is computationally expensive -- limiting the number of full model evaluations that can be made. To handle this problem, we propose a new hybrid cooperative co-evolution algorithm (HCCA). HCCA consists of a symmetric local search plus Nelder-Mead and a cooperative co-evolution algorithm (CC) with a backtracking strategy for optimising the positions and PTO settings of WECs, respectively. Moreover, a new adaptive scenario is proposed for tuning grey wolf optimiser (AGWO) hyper-parameter. AGWO participates notably with other applied optimisers in HCCA. For assessing the effectiveness of the proposed approach five popular Evolutionary Algorithms (EAs), four alternating optimisation methods and two modern hybrid ideas (LS-NM and SLS-NM-B) are carefully compared in four real wave situations (Adelaide, Tasmania, Sydney and Perth) with two wave farm sizes (4 and 16). According to the experimental outcomes, the hybrid cooperative framework exhibits better performance in terms of both runtime and quality of obtained solutions.

Algorithm Selection for Image Quality Assessment

Subjective perceptual image quality can be assessed in lab studies by human observers. Objective image quality assessment (IQA) refers to algorithms for estimation of the mean subjective quality ratings. Many such methods have been proposed, both for blind IQA in which no original reference image is available as well as for the full-reference case. We compared 8 state-of-the-art algorithms for blind IQA and showed that an oracle, able to predict the best performing method for any given input image, yields a hybrid method that could outperform even the best single existing method by a large margin. In this contribution we address the research question whether established methods to learn such an oracle can improve blind IQA. We applied AutoFolio, a state-of-the-art system that trains an algorithm selector to choose a well-performing algorithm for a given instance. We also trained deep neural networks to predict the best method. Our results did not give a positive answer, algorithm selection did not yield a significant improvement over the single best method. Looking into the results in depth, we observed that the noise in images may have played a role in why our trained classifiers could not predict the oracle. This motivates the consideration of noisiness in IQA methods, a property that has so far not been observed and that opens up several interesting new research questions and applications.

Adaptive Neuro-Surrogate-Based Optimisation Method for Wave Energy Converters Placement Optimisation

The installed amount of renewable energy has expanded massively in recent years. Wave energy, with its high capacity factors has great potential to complement established sources of solar and wind energy. This study explores the problem of optimising the layout of advanced, three-tether wave energy converters in a size-constrained farm in a numerically modelled ocean environment. Simulating and computing the complicated hydrodynamic interactions in wave farms can be computationally costly, which limits optimisation methods to have just a few thousand evaluations. For dealing with this expensive optimisation problem, an adaptive neuro-surrogate optimisation (ANSO) method is proposed that consists of a surrogate Recurrent Neural Network (RNN) model trained with a very limited number of observations. This model is coupled with a fast meta-heuristic optimiser for adjusting the model's hyper-parameters. The trained model is applied using a greedy local search with a backtracking optimisation strategy. For evaluating the performance of the proposed approach, some of the more popular and successful Evolutionary Algorithms (EAs) are compared in four real wave scenarios (Sydney, Perth, Adelaide and Tasmania). Experimental results show that the adaptive neuro model is competitive with other optimisation methods in terms of total harnessed power output and faster in terms of total computational costs.

A new insight into the Position Optimization of Wave Energy Converters by a Hybrid Local Search

Renewable energy, such as ocean wave energy, plays a pivotal role in addressing the tremendous growth of global energy demand. It is expected that wave energy will be one of the fastest-growing energy resources in the next decade, offering an enormous potential source of sustainable energy. This research investigates the placement optimization of oscillating buoy-type wave energy converters (WEC). The design of a wave farm consisting of an array of fully submerged three-tether buoys is evaluated. In a wave farm, buoy positions have a notable impact on the farm's output. Optimizing the buoy positions is a challenging research problem because of very complex interactions (constructive and destructive) between buoys. The main purpose of this research is maximizing the power output of the farm through the placement of buoys in a size-constrained environment. This paper proposes a new hybrid approach of the heuristic local search combined with a numerical optimization method that utilizes a knowledge-based surrogate power model. We compare the proposed hybrid method with other state-of-the-art search methods in five different wave scenarios -- one simplified irregular wave model and four real wave climates. Our method considerably outperforms all previous heuristic methods in terms of both quality of achieved solutions and the convergence-rate of search in all tested wave regimes.

A Hybrid Evolutionary Algorithm Framework for Optimising Power Take Off and Placements of Wave Energy Converters

Ocean wave energy is a source of renewable energy that has gained much attention for its potential to contribute significantly to meeting the global energy demand. In this research, we investigate the problem of maximising the energy delivered by farms of wave energy converters (WEC's). We consider state-of-the-art fully submerged three-tether converters deployed in arrays. The goal of this work is to use heuristic search to optimise the power output of arrays in a size-constrained environment by configuring WEC locations and the power-take-off (PTO) settings for each WEC. Modelling the complex hydrodynamic interactions in wave farms is expensive, which constrains search to only a few thousand model evaluations. We explore a variety of heuristic approaches including cooperative and hybrid methods. The effectiveness of these approaches is assessed in two real wave scenarios (Sydney and Perth) with farms of two different scales. We find that a combination of symmetric local search with Nelder-Mead Simplex direct search combined with a back-tracking optimization strategy is able to outperform previously defined search techniques by up to 3\%.

On resampling vs. adjusting probabilistic graphical models in estimation of distribution algorithms

The Bayesian Optimisation Algorithm (BOA) is an Estimation of Distribution Algorithm (EDA) that uses a Bayesian network as probabilistic graphical model (PGM). Determining the optimal Bayesian network structure given a solution sample is an NP-hard problem. This step should be completed at each iteration of BOA, resulting in a very time-consuming process. For this reason most implementations use greedy estimation algorithms such as K2. However, we show in this paper that significant changes in PGM structure do not occur so frequently, and can be particularly sparse at the end of evolution. A statistical study of BOA is thus presented to characterise a pattern of PGM adjustments that can be used as a guide to reduce the frequency of PGM updates during the evolutionary process. This is accomplished by proposing a new BOA-based optimisation approach (FBOA) whose PGM is not updated at each iteration. This new approach avoids the computational burden usually found in the standard BOA. The results compare the performances of both algorithms on an NK-landscape optimisation problem using the correlation between the ruggedness and the expected runtime over enumerated instances. The experiments show that FBOA presents competitive results while significantly saving computational time.

A characterisation of S-box fitness landscapes in cryptography

Substitution Boxes (S-boxes) are nonlinear objects often used in the design of cryptographic algorithms. The design of high quality S-boxes is an interesting problem that attracts a lot of attention. Many attempts have been made in recent years to use heuristics to design S-boxes, but the results were often far from the previously known best obtained ones. Unfortunately, most of the effort went into exploring different algorithms and fitness functions while little attention has been given to the understanding why this problem is so difficult for heuristics. In this paper, we conduct a fitness landscape analysis to better understand why this problem can be difficult. Among other, we find that almost each initial starting point has its own local optimum, even though the networks are highly interconnected.