We expose and contrast the impact of landscape characteristics on the performance of search heuristics for black-box multiobjective combinatorial optimization problems. A sound and concise summary of features characterizing the structure of an arbitrary problem instance is identified and related to the expected performance of global and local dominance-based multiobjective optimization algorithms. We provide a critical review of existing features tailored to multiobjective combinatorial optimization problems, and we propose additional ones that do not require any global knowledge from the landscape, making them suitable for large-size problem instances. Their intercorrelation and their association with algorithm performance are also analyzed. This allows us to assess the individual and the joint effect of problem features on algorithm performance, and to highlight the main difficulties encountered by such search heuristics. By providing effective tools for multiobjective landscape analysis, we highlight that multiple features are required to capture problem difficulty, and we provide further insights into the importance of ruggedness and multimodality to characterize multiobjective combinatorial landscapes.

We describe a solution to tackle a common set of challenges in e-commerce, which arise from the fact that new products are continually being added to the catalogue. The challenges involve properly personalising the customer experience, forecasting demand and planning the product range. We argue that the foundational piece to solve all of these problems is having consistent and detailed information about each product, which is rarely available or consistent given the multitude of suppliers and types of products. We describe in detail the architecture and methodology implemented at ASOS, one of the world's largest fashion e-commerce retailers, to tackle this problem. We then show how this quantitative understanding of the products can be leveraged to improve recommendations in a hybrid recommender system approach.

Local Optima Networks were proposed to understand the structure of combinatorial landscapes at a coarse-grained level. We consider a compressed variant of such networks with features that are meaningful for the study of search difficulty in the context of local search. In particular, we investigate different landscapes of the Permutation Flowshop Scheduling Problem. The insert and 2-exchange neighbourhoods are considered, and two different objective functions are taken into account: the makespan and the total flow time. The aim is to analyse the network features in order to find differences between the landscape structures, giving insights about which features impact algorithm performance. We evaluate the correlation between landscape properties and the performance of an Iterated Local Search algorithm. Visualisation of the network structure is also given, where evident differences between the makespan and total flow time are observed.

Evolvability is a measure of the ability of an Evolutionary Algorithm (EA) to improve the fitness of an individual when applying a genetic operator. Other than the specific problem, many aspects of the EA may impact on the evolvability most notably the genetic operators and, if present, the genotype-phenotype mapping function. Grammatical Evolution (GE) is an EA in which the mapping function plays a crucial role since it allows to map any binary genotype into a program expressed in any user-provided language, defined by a context-free grammar. While GE mapping favored a successful application of GE to many different problems, it has also been criticized for scarcely adhering to the variational inheritance principle, which itself may hamper GE evolvability. In this paper, we experimentally study GE evolvability in different conditions, that is, problems, mapping functions, genotype sizes, and genetic operators. Results suggest that there is not a single factor determining GE evolvability: in particular, the mapping function alone does not deliver better evolvability regardless of the problem. Instead, GE redundancy, which itself is the result of the combined effect of several factors, has a strong impact on the evolvability.

The existence of sub-optimal funnels in combinatorial fitness landscapes has been linked to search difficulty. The exact nature of these structures --- and how commonly they appear --- is not yet fully understood. Improving our understanding of funnels could help with designing effective diversification mechanisms for a 'smoothing' effect, making optimisation easier. We model fitness landscapes as local optima networks. The relationship between communities of local optima found by network clustering algorithms and funnels is explored. Funnels are identified using the notion of monotonic sequences from the study of energy landscapes in theoretical chemistry. NK Landscapes and the Quadratic Assignment Problem are used as case studies. Our results show that communities are linked to funnels. The analysis exhibits relationships between these landscape structures and the performance of trajectory-based metaheuristics such as Simulated Annealing (SA) and Iterated Local Search (ILS). In particular, ILS gets trapped in funnels, and modular communities of optima slow it down. The funnels contribute to lower success for SA. We show that increasing the strength of ILS perturbation helps to 'smooth' the funnels and improves performance in multi-funnel landscapes.

In this article, we attempt to understand and to contrast the impact of problem features on the performance of randomized search heuristics for black-box multiobjective combinatorial optimization problems. At first, we measure the performance of two conventional dominance-based approaches with unbounded archive on a benchmark of enumerable binary optimization problems with tunable ruggedness, objective space dimension, and objective correlation ([Formula: see text]MNK-landscapes). Precisely, we investigate the expected runtime required by a global evolutionary optimization algorithm with an ergodic variation operator (GSEMO) and by a neighborhood-based local search heuristic (PLS), to identify a ([Formula: see text]approximation of the Pareto set. Then, we define a number of problem features characterizing the fitness landscape, and we study their intercorrelation and their association with algorithm runtime on the benchmark instances. At last, with a mixed-effects multilinear regression we assess the individual and joint effect of problem features on the performance of both algorithms, within and across the instance classes defined by benchmark parameters. Our analysis reveals further insights into the importance of ruggedness and multimodality to characterize instance hardness for this family of multiobjective optimization problems and algorithms.

Urban planners face increasing challenges to design and optimize sustainable cities. Evolutionary algorithms are an important tool for design optimization and can help urban planners finding alternative optimal designs to increase the sustainability of cities. Mobility and transportation are two important components of modern cities that are amenable to simulation and their design can be improved by evolutionary means. However, traffic simulation is computationally expensive and puts a serious constraint on the number of generations allowed to artificial evolution. In addition, to grasp the implication of traffic policies for sustainability usually a significant part of the traffic in the city must be simulated. This implies that we must design our evolutionary algorithms for an effective short-term evolution on large-scale problems. This paper investigates neighborhood mutation operators to explore efficiently in few generations a large space of cycle lengths, offsets and green time settings of traffic lights. Our aim is to find settings that allow a better coordination of signals. In addition, we analyze clusters of signal settings to gain knowledge about geographical coordination patterns to provide valuable information to city planners for micro-zonification.

Computationally hard multi-objective combinatorial optimization problems are common in practice, and numerous evolutionary multi-objective optimization (EMO) algorithms have been proposed to tackle them. Our aim is to understand which (and how) problem features impact the search performance of such approaches. In this paper, we consider two prototypical dominance-based algorithms: a global EMO strategy using an ergodic variation operator (GSEMO) and a neighborhood-based local search heuristic (PLS). Their respective runtime is estimated on a benchmark of combinatorial problems with tunable ruggedness, objective space dimension, and objective correlation ($\rho$MNK-landscapes). In other words, benchmark parameters define classes of instances with increasing empirical problem hardness; we enumerate and characterize the search space of small instances. Our study departs from simple performance comparison to systematically analyze the correlations between runtime and problem features, contrasting their association with search performance within and across instance classes, for both chosen algorithms. A mixed-model approach then allows us to further generalize from the experimental design, supporting a sound assessment of the joint impact of instance features on EMO search performance.

Inherent networks of potential energy surfaces proposed in physical chemistry inspired a compact network characterization of combinatorial fitness landscapes. In these so-called Local Optima Networks (LON), the nodes correspond to the local optima and the edges quantify a measure of adjacency - transition probability between them.

Local Optima Networks (LONs) have been recently proposed as an alternative model of combinatorial fitness landscapes. The model compresses the information given by the whole search space into a smaller mathematical object that is the graph having as vertices the local optima and as edges the possible weighted transitions between them. A new set of metrics can be derived from this model that capture the distribution and connectivity of the local optima in the underlying configuration space. This paper departs from the descriptive analysis of local optima networks, and actively studies the correlation between network features and the performance of a local search heuristic. The NK family of landscapes and the Iterated Local Search metaheuristic are considered. With a statistically-sound approach based on multiple linear regression, it is shown that some LONs' features strongly influence and can even partly predict the performance of a heuristic search algorithm. This study validates the expressive power of LONs as a model of combinatorial fitness landscapes.

Using a recently proposed model for combinatorial landscapes, Local Optima Networks (LON), we conduct a thorough analysis of two types of instances of the Quadratic Assignment Problem (QAP). This network model is a reduction of the landscape in which the nodes correspond to the local optima, and the edges account for the notion of adjacency between their basins of attraction. The model was inspired by the notion of `inherent network' of potential energy surfaces proposed in physical-chemistry. The local optima networks extracted from the so called uniform and real-like QAP instances, show features clearly distinguishing these two types of instances. Apart from a clear confirmation that the search difficulty increases with the problem dimension, the analysis provides new confirming evidence explaining why the real-like instances are easier to solve exactly using heuristic search, while the uniform instances are easier to solve approximately. Although the local optima network model is still under development, we argue that it provides a novel view of combinatorial landscapes, opening up the possibilities for new analytical tools and understanding of problem difficulty in combinatorial optimization.

Road Sign Detection is a major goal of Advanced Driving Assistance Systems (ADAS). Since the dawn of this discipline, much work based on different techniques has been published which shows that traffic signs can be first detected and then classified in video sequences in real time. While detection is usually performed using classical computer vision techniques based on color and/or shape matching, most often classification is performed by neural networks. In this work we present a novel approach based on both sign shape and color which uses Particle Swarm Optimization (PSO) for detection. Remarkably, a single fitness function can be used both to detect a sign belonging to a certain category and, at the same time, to estimate its actual position with respect to the camera reference frame. To speed up execution times, the algorithm exploits the parallelism offered by modern graphics cards and, in particular, the CUDA¿ architecture by nVIDIA. The effectiveness of the approach has been assessed on a synthetic video sequence, which has been successfully processed in real time at full frame rate.