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Multi-Objective Data Analysis is a method of exploring conflicting patterns in static data. This method is used to explore complex relationships commonly found in medical data, where human body systems often have overlapping variables, creating a complex web of relationships. Within multi-objective optimization, a relationship is usually described as conflicting if an increase in optimality in one objective leads to a subsequent decrease in the other. This relationship is difficult to extract from static data, where no optimization is taking place. Multi-Objective Data Analysis extracts conflicting relationships using non-dominated sorting to find multiple fronts that represent the gradient of the fitness landscape between the decision and objective spaces, and checks to see if this gradient is related to variables in the decision space that are of interest. In this work, we showcase the use of the Wilcoxon (or Proportions) test and the Pearson Correlation test as objective measures of the usefulness of a found conflicting pair of objectives by comparing the distributions of a chosen response variable relative to the sorting. The shown examples include a clean synthetic dataset, a synthetic dataset with noise in the objective space, and a real-world dataset consisting of breast cancer data. From these examples, the argument is made that the statistical tests are compatible with Multi-Objective Data Analysis.

The crossover operator is a fundamental component of genetic algorithms, combining genetic material from parent solutions to generate offspring. Traditionally, crossover is performed in the search space using the genotype. However, it can also be executed in the solution space on the phenotype, offering potential advantages such as improved feasibility preservation, faster convergence, and greater explainability. These benefits, however, come with tradeoffs, including increased implementation complexity, higher computational costs, and a likely reduction in solution diversity. This study examines the properties of search space and solution space crossover operators in the context of a multi-objective, weighted, and continuous coverage path planning problem. Three crossover strategies are tested: two of which operate directly on the genotype and one that uses intersections of the phenotype.

This paper explores multi-objective pathfinding in path-influenced environments. These environments contain movable obstacles which can be shifted by the agents. This way, the agents actively change their environment while traversing on their path. Therefore, pathfinding takes on a new dimension. While it has been extensively studied across various domains, finding an optimal path in a path-influenced environment introduces new challenges. In this paper, we propose several real-world inspired problem instances. Then we formally describe this sort of problem as a multi-objective optimization problem and finally evaluate the performance of seven state-of-the-art multi-objective evolutionary algorithms on our problem instances. The results indicate that the evolutionary approach can generate sets of non-dominated solutions for this new problem. The performance of the algorithms in terms of convergence and diversity of the Pareto front highly depends on the way the encountered obstacles are handled, as well as the obstacle distribution on the map. Among the algorithms, AGE-MOEA and SPEA-II demonstrate the best convergence across the majority of problem instances.

Traditional facility layout planning (FLP) typically assumes predictable, static or periodic material flows, which no longer applies to modern mass-customization assembly systems. Optimizing these systems requires a complex integration of unequal-area FLP with the dynamic flexible assembly job-shop scheduling problem (DFA-JSP), and adaptable material handling provided by multiple-load automated guided vehicle (AGV) dispatching. Due to high variability in material flows, stochastic processing times, and dynamic AGV availability, traditional methods fail to address the new problem effectively. This paper introduces the first solution approach to integrate these three NP-hard problems through a combination of multi-objective evolutionary algorithms and advanced dispatching rule systems, thus offering a significant advancement in addressing the planning challenges of mass-customization assembly systems. We evaluate three optimization architectures in 12 configurations and demonstrate that a mutation-only NSGA-II with adaptive parameter adjustment outperforms multi-stage optimization slightly, and cooperative coevolution approaches substantially on this problem. The results suggest that transitioning between early exploration and late exploitation is essential for optimal results, while coevolutionary search space division has little benefit. For the same scenario and budget, the proposed algorithm improves flow time by approximately 5% and reduces idle time by 9% compared to the coevolutionary algorithms.

Unmanned aerial vehicles have become affordable and adaptable tools for various real-world applications, in which path planning is often a crucial component. Consequently, this paper introduces a novel approach to Coverage Path Planning for UAVs, aiming to optimize paths without restricting their shape. Unlike existing methods, the proposed approach focuses on generating free-form paths. The method employs a multi-objective evolutionary algorithm grounded in graph-based path planning principles. The application scenario involves a search and rescue mission in forestry terrain, considering prior knowledge about forest density and the target's probable location. The optimization goal is twofold: minimize the chance of not finding the target, while keeping the resulting paths short.

The goal of the paper is to address the need for methods to handle time-sensitive, human-centered, multi-criteria decision-making problems. In the current literature, prevalent methods rely on expressing decision-maker/stakeholder preferences through weights, ideal points, and trade-off matrices. However, these conventional approaches prove unsuitable for time-constrained, atypical, and stressful situations, such as emergencies. In such scenarios, where both time and additional factors significantly affect decision-making abilities, the effective utilization of advanced decision-making techniques becomes chal-lenging. Therefore, this paper explores the possibility of how an intelligent agent might be used to provide possible courses of action to human decision-makers/stakeholders. The agent will be put to the test to tackle the dynamic alternate airport selection problem. In emergency and time-critical situations, like an engine fire or a medical emergency, there is often a need to select an alternate airport destination dynamically midflight. During such emergencies, a lot of information must be collected and evaluated by the pilots as a basis for the decision-making process. The pilots need to compare multiple characteristics of the available airports and weigh the pros and cons of each. Given the need for clear and interpretable retroactive analysis in decision-making in general and in the aviation field in particular, the focus was placed on more interpretable and explainable models from the field of AI. Due to this, the Learning Classifier System (LCS) is to be the primary model explored. The LCS is trained on a custom dataset composed of various decision-making scenarios. The approach shows promising results and appears to merit further investigation.

Computer aided drug design is a promising approach to reduce the tremendous costs, i.e. time and resources, for developing new medicinal drugs. It finds application in aiding the traversal of the vast chemical space of potentially useful compounds. In this paper, we deploy multi-objective evolutionary algorithms, namely NSGA-II, NSGA-III, and MOEA/D, for this purpose. At the same time, we used the SELFIES string representation method. In addition to the QED and SA score, we optimize compounds using the GuacaMol benchmark multi-objective task sets. Our results indicate that all three algorithms show converging behavior and successfully optimize the defined criteria whilst differing mainly in the number of potential solutions found. We observe that novel and promising candidates for synthesis are discovered among obtained compounds in the Pareto-sets.

Renewable energy resources (RES) are closely linked to grid stability problems. The main challenge of RES is the uncertainty caused by parameters such as irradiation, wind velocity, or temperature. In this connection, Multi-Objective Optimization (MOO) Algorithms can be used as an intelligent control system for a microgrid by ensuring continuity of power supply in case of grid failures. Based on grid reliability and local demand, MOO can make real-time decisions about disconnecting from the primary grid (islanding) and when to reconnect. It can help in MG control systems by optimizing energy storage systems (ESS) operation by determining when to charge and discharge them based on electricity prices, grid demand, and renewable energy availability. This survey discusses an MG and its different challenges with RES with Photovoltaic (PV) as a primary component and prominent energy sources such as a utility grid, Diesel Genset (DG), Wind Turbine (WT) and ESS. In this research, a unique classification approach of different problems in Microgrid (MG) is identified and discussed. This paper focuses on the MOO algorithms used in MG for their energy management systems (EMS) and technical and economic problems and investigates how MOO can play a significant role in solving such problems.

The high demand for energy in communication technologies is posing a major challenge in many future applications. Highly dynamic systems, such as mobile networks and renewable energy sources, are interconnected and subject to constant change, requiring situation-aware optimization. Alternative solutions necessary for decision-making based on temporary requirements can be obtained by multi-objective optimization. This paper considers a resource allocation problem related to the beamforming technology of the upcoming 6G standard and explores the feasibility of using an evolutionary algorithm (EA) in a dynamic network scenario to optimize power consumption and quality of service (QoS) simultaneously while assigning a user equipment (UE) to a base station (BS) beam. The proposed approach includes an information carry-over mechanism within the optimization process, enabling convergence despite the constantly changing network topology. The evaluation focuses on three factors that may limit applicability: network utilization, portion of moving users, and movement speed. It is conducted in a simulation environment in comparison to a heuristic approach that only takes QoS into account. The results indicate that, even in a fully dynamic network instance, the EA outperforms the heuristic approach in all experimental instances, although the performance gain decreases depending on certain combinations of influencing factors.

Many works in the domain of artificial intelligence in games focus on board or video games due to the ease of reimplementing their mechanics [1], [2]. Decision-making problems in real-world sports share many similarities to such domains. Nevertheless, not many frameworks on sports games exist. In this paper, we present the tennis match simulation environment Match Point AI, in which different agents can compete against real-world data-driven bot strategies. Next to presenting the framework, we highlight its capabilities by illustrating, how MCTS can be used in Match Point AI to optimize the shot direction selection problem in tennis. While the framework will be extended in the future, first experiments already reveal that generated shot-by-shot data of simulated tennis matches show realistic characteristics when compared to real-world data. At the same time, reasonable shot placement strategies emerge, which share similarities to the ones found in real-world tennis matches.

Objective ranking and clustering of behavioral data that utilized different metrics is an important foundation for understanding the relationship between behavior and physiological as well as neurological processes in medicine and neuroscience. Fortunately, similar problems have been extensively studied in multi-objective optimization, where a population of solutions needs to be ranked in terms of performance within a high dimensional objective space. In this paper, we take advantage of the ordinal nature of behavioral metrics, and propose a non-dominated ranking-based approach to perform Pareto dominance-based partial ranking on the test subjects of behavioral studies regarding their performances with respect to multiple metrics. We have also proposed two indicators, interfront hypervolume and intrafront spread, to measure the separation between and diversity within non-dominated fronts. They serve to gauge the validity of the produced fronts as a basis for clustering analysis. Our approach is then applied to two different datasets and its functionalities and potentials are demonstrated.

Coverage path planning is one of the main challenges in precision farming. Here the goal is to compute a continuous optimal working path by combining individual tracks such that the entire field can be cultivated in the most efficient way. Various 2D and 3D approaches have already been presented in the literature. However, these are lacking in two major aspects: In each case, a seed curve is determined and offsetted to generate the individual tracks, but the seed curve is usually selected from a predefined set of alternatives. Additionally, the utilized objectives do not consider the efficiency of the tools used to work on the field, which typically depends on the path angle and the field's inclination. In this paper, we propose a scheme to cope with both aspects through an evolutionary multi-objective optimization approach. Three objectives are used, namely coverage, energy based on anisotropic friction and gravity, and precession, which describes the angle between the path direction and the gradient of the terrain.

Chemical industry provides a multitude of intermediaries and final products essential to society, ranging from fertilizers and plastics to sophisticated pharmaceuticals. The underlying production processes are typically linear, utilizing finite resources in an unsustainable manner and creating unnecessary waste over a products lifetime. While a shift towards sustainability and circular economy is desired, the current market and political framework lead to conflicting objectives ranging from sustainability to profit maximization. In this article, we build upon a first minimal multi-objective MILP model and extend thereupon, reducing the overall level of required abstraction compared to the first model. Thereafter, we present a multi-agent based distributed optimization approach for a sequence of the extended MILP formulation.

Abstract Many real-world multi-objective optimization problems inherently have multiple multi-modal solutions and it is in fact very important to capture as many of these solutions as possible. Several crowding distance methods have been developed in the past few years to approximate the optimal solution in the search space. In this paper, we discuss some of the shortcomings of the crowding distance-based methods such as inaccurate estimates of the density of neighboring solutions in the search space. We propose a new classification for the selection operations of Pareto-based multi-modal multi-objective optimization algorithms. This classification is based on utilizing nearby solutions from other fronts to calculate the crowding values. Moreover, to address some of the drawbacks of existing crowding methods, we propose two algorithms whose selection mechanisms are based on each of the introduced types of selection operations. These algorithms are called NxEMMO and ES-EMMO. Our proposed algorithms are evaluated on 14 test problems of various complexity levels. According to our results, in most cases, the NxEMMO algorithm with the proposed selection mechanism produces more diverse solutions in the search space in comparison to other competitive algorithms.

Abstract Pathfinding, also known as route planning, is one of the most important aspects of logistics, robotics, and other applications where engineers must balance many competing interests. There is a significant challenge in pathfinding problems with multiple objectives because many paths can map to the same objective value. Such multi-modal solutions cannot easily be found in multi-objective optimisation algorithms, which are typically geared towards selection mechanisms in the objective space. A niching approach for preserving good diverse solutions in the decision space is proposed in this paper, which is tailored for pathfinding problems. The criteria used to compare the solutions within the decision space are path similarity metrics, which we extend from a previous study, and are used instead of the well-established crowding distance. In two variations, we investigate the proposed meta-heuristic approach on a range of benchmark instances and compare the methodology to a deterministic optimisation approach.

Context steering is a local approach to control an agent’s movement in a dynamically changing scene. Recent works have formalized the context-steering approach by Fray and presented a multiobjective view of the context-steering problem. Combining a variety of different behaviors, which can be used multiple times in different configurations for different context maps, introduces a large number of parameters that need to be tuned to obtain well-performing agents. This work aims to use evolutionary algorithms to optimize context-steering agents for various environments. A special focus lies on the evolution of agents that perform robustly across multiple variations of the same environment. To this end, we develop a real-valued encoding for a context-steering agent along with three different fitness functions to represent different goals of the agent. Our experimental evaluation shows that an evolutionary optimization can produce agent configurations that perform well with respect to different tasks and show a high intratask robustness. The proposed approach based on evolutionary optimization enables the user to optimize context-steering agents such that they can explore environments while avoiding dynamic obstacles.

In this paper, we investigate multi-objective opti-mization of roadmaps for multi-robot path planning. We propose a new representation for roadmaps based on polygons and explore its potentials on various scenarios. In addition, we define three objective functions to estimate the suitability of each roadmap for navigation, and propose a modification of the well-known NSGA-II algorithm to optimize the roadmaps. In our experiments, we compare the quality of the proposed optimized roadmaps with those based on regular grids. The results show that in complex environments with obstacles, the optimized roadmaps perform much more efficient than those on regular grids. In addition, the performance of the optimization can be significantly improved by using the regular grids to initialize the optimization process.

The simulation of particle-laden flows is a crucial task in fluid dynamics, requiring high computational cost owing to the complex interactions between numerous particles. Typically, the flow velocity is described with the equations proposed by Stokes. While there is an analytical solution for the Stokes flows around a single spherical particle, the Stokes flows around many particles are still unsolved. In this paper, we study Genetic Programming (GP) for symbolic regressions to explore the potentials of multi-objective GP in recovering analytical expressions for two and, in the future, N particles. We propose a new GP approach containing building blocks to scale up the problem and provide a new benchmark with 22 cases for this application. To identify the strengths and limitations of GP, we generate fully resolved training data from simulations. We compare the results of our algorithm to the superimposition method and a multi-layer perceptron as two baseline methods. The results show that GP can find comparable and sometimes better solutions with smaller failure rates than the two baseline methods. In addition, the produced solutions by GP are explainable and certain function patterns inline with physical laws can be identified across the benchmark problems.

In facility layout planning (FLP) for shop floor optimization, the goal is to find an optimal arrangement for a number of machines in a given space. Despite the significance of machine selection for the FLP, the integration of arrangement and selection problems is neglected in the literature. This paper presents a methodology for solving an extended facility layout problem where not only the arrangement of machines is con-sidered, but also how many machines should be allocated and of which type. We assume the context of a modern brownfield planning project, where an initial layout already exists, which is to be re-purposed for manufacture of products with high variability. We apply our methodology in a case study where three objectives are to be minimized simultaneously. The results demonstrate that a standard NSGA-II introduces bias for this problem type that leads to an inadequate search space exploration. We test adapted mutation and crossover operators to overcome this challenge. While modified crossover had little impact, the new mutation operator was key to outperform the standard approach in all computed metrics. With this operator, we obtain diverse Pareto sets which strictly dominate up to 80% of the solutions found by the standard approach on average.

Implementing and conducting reproducible experiments on multi-robot hardware platforms are challenging tasks due to variations in hardware, software, and most importantly the intensive implementation effort. In this paper, we aim to present the Driving Swarm software framework which is developed to facilitate the implementation, deployment, supervision, and analysis of multi-robot experiments. We use this framework with the TurtleBot3 hardware platform and measure its performance for two example scenarios: trajectory tracking and flocking behavior, with 5 and 6 robots. The goal of our experiments is to validate the simulation comparing to hardware implementations and to provide a baseline data for further experiments. While the simulated and real robots show similar behavior, we could observe that the simulated behavior is more robust than the real behavior in both scenarios. This effect is observed in the lower tracking error and better obstacle avoidance in both experiments. While the simulation proved to be a valuable tool during the development of the behaviors, the results confirm the importance of conducting experiments on a real-world test bed.

Node failures are known to be among the generic problems in Internet of Things (IoT) networks. These failures can be caused by communication disturbances, battery depletion, or even hardware faults. The larger the IoT network and the larger the task to be executed in the network, the higher is the probability of a node failure in the relevant part of the network. This article studies the node failures and proposes a new task allocation algorithm based on multiobjective optimization to address this issue. This article proposes a specialized archive-selection mechanism to enhance diversity in the search space of the so-called multiobjective task allocation algorithm (MOTA). High diversity in the archive allows a reliable selection of alternative task assignments in the case of node failures in the IoT network. We evaluate the performance of the proposed approach regarding the network lifetime, its latency, and its availability, using a network simulation model and compare the results with the baseline MOTA and the dynamic task allocation scheduler (DTAS). The results show that the proposed approach provides significant performance improvements over the existing algorithms, especially in scenarios with high task-to-node ratios.

Route planning, also known as pathfinding, is one of the key elements in logistics, mobile robotics, and other applications, where engineers face many conflicting objectives. Most route planning algorithms consider only up to three objectives. In this article, we propose a scalable many-objective benchmark problem covering most of the important features for routing applications based on real-world data. We define five objective functions representing distance, traveling time, delays caused by accidents, and two route-specific features, such as curvature and elevation. We analyze several different instances for this test problem and provide their true Pareto front to analyze the problem difficulties. Additionally, we apply four well-known evolutionary multiobjective algorithms. Since this test benchmark can be easily transferred to real-world routing problems, we construct a routing problem from OpenStreetMap data. We evaluate the three optimization algorithms and observe that we are able to provide promising results for such a real-world application. The proposed benchmark represents a scalable many-objective route planning optimization problem enabling researchers and engineers to evaluate their many-objective approaches.

This paper aims to introduce a methodology to trace the influence of the initial population of an evolutionary algorithm to the final population. The major challenge concerns tracking the heritage of multiple parent operators. In this paper, we propose a new encoding for tracking purposes. In addition, we propose modifications to the corresponding metrics for measuring the impact of individuals. With this approach, we provide several tools to not only track the influence of the initial population on the results but also to study the effects of different crossover and mutation operators. In our experiments, we evaluate the differences between two selected crossover and mutation operators and provide insight into the proposed approach.

Non-pharmaceutical interventions (NPIs) are effective measures to contain a pandemic. Yet, such control measures commonly have a negative effect on the economy. Here, we propose a macro-level approach to support resolving this Health-Economy Dilemma (HED). First, an extension to the well-known SEIR model is suggested which includes an economy model. Second, a bi-objective optimization problem is defined to study optimal control policies in view of the HED problem. Third, four multi-objective evolutionary algorithms are applied to perform a study on the health-economy performance trade-offs that are inherent to the obtained optimal policies. Finally, the results from the applied algorithms are compared to select a preferred algorithm for future studies. As expected, for the proposed models and strategies, a clear conflict between the health and economy performances is found. Furthermore, the results suggest that the guided usage of NPIs is preferable as compared to refraining from employing such strategies at all. This study contributes to pandemic modeling and simulation by providing a novel concept that elaborates on integrating economic aspects while exploring the optimal moment to enable NPIs.

This work concentrates on decision-making for autonomous movement of agents to simultaneously optimize several objectives which occur in their local environment. Such behavior can be achieved with steering algorithms, which have originally been designed for moving numerous agents simultaneously where occasional uncertainties are not noticeable by players. Nevertheless, concentrating on single individuals can reveal major flaws in their movement patterns such as oscillatory movement. For avoiding such problems, game makers are forced to develop higher-level abstractions for handling game-relevant special cases. Thus, eliminating the initial benefit of steering behaviors to be highly modular, lightweight, and controllable. This work enhances the context steering approach by Fray, which introduced discretized contextual information in the aggregation of a steering behavior's components. We combine this method with multi-criteria decision-making for controlling the agent's velocity direction and magnitude. The resulting approach is tested based on selected scenarios which show that the resulting approach is well suited to improve the agent's smooth and natural movement. Based on our observations we propose suitable parameterizations of the designed method and discuss advantages and disadvantages of made enhancements.

Role Based Access Control is a widely spread concept in cyber security. Thus, the (NP-complete) Role Mining Problem (RMP), which consists of finding an optimal set of roles and a corresponding assignment of those roles to users, is of great scientific interest. Over the last years, different algorithms have been developed to search for good solutions to the RMP. However, conclusive benchmarks for thorough comparison of the developed methods are rarely known. This paper introduces to RMPlib, a library for the Role Mining Problem, containing a set of new industry-oriented benchmark instances partly taken from real-world use cases, partly created synthetically. Access to RMPlib is provided through a platform where researchers can actively contribute new benchmark instances and best solutions, such that the library adapts to the changing requirements in science. The current version of RMPlib can be found at https://github.com/RMPlib/RMPlib.

Preserving diversity in decision space plays an important role in Multimodal Multi-objective Optimization problems (MMOPs). Due to the lack of mechanisms to keep different solutions with the same fitness value, most of the available Multi-objective Evolutionary Algorithms (MOEAs) perform poorly when applied to MMOPs. To deal with these problems, this paper proposes a novel method for diversity preserving in the decision space. To this end, the concept of grid-based crowding distance for decision space is introduced. Furthermore, to keep a good diversity of solutions in both decision and objective spaces, we propose different frameworks by combining this method with crowding distance in decision space, crowding distance in objective space, and the weighted sum of both crowding distances. In order to evaluate the performance of these frameworks, we integrate them into the diversity preserving part of the NSGA-II algorithm, and compare them with the NSGA-II (as the baseline algorithm) and the state-of-the-art multimodal multi-objective optimization algorithms on ten different MMOPs with different levels of complexity.

In this paper, the influence of the initial population into successive generations in Evolutionary Algorithms (EAs) is studied as a problem-independent approach. For this purpose, the Traceable Evolutionary Algorithm (T-EA) is proposed. This algorithm keeps track of the influence of the individuals from the initial population over the generations of the algorithm. The algorithm has been implemented for both bit-string and integer vector representations. In addition, in order to study the general influence of each individual, new impact factor metrics have been proposed. In this way, we aim to provide tools to measure the influence of initial individuals on the final solutions. As a proof of concept, three classical optimization problems (One Max, 0/1 Knapsack and Unbounded Knapsack problems) are used. We provide a framework that allows to explain why some individuals in the initial population work better than others in relation with the corresponding fitness values.

The Multi-Agent Pathfinding problem (MAPF) has several applications in industry and robotics. The aim of a MAPF-solver is to find a set of optimal and non-overlapping paths for a number of agents in a navigation scenario. Existing approaches are shown to successfully deal with MAPF, where either the makespan or flow-time is used as a single objective. In this article, we treat the MAPF as a multi-objective optimisation problem (MOMAPF). In this paper, we consider three different objective functions, called makespan, flow-time and path-overlaps which are to be optimised at the same time. The MOMAPF problem in this paper is designed to be a scalable test problem for multi-objective optimisation algorithms, where we can scale up the variable space to reflect different real-world scenarios. We propose a new problem formulation for MOMAPF optimisation algorithms and implement it into the NSGA-II and NSGA-III and provide an experimental evaluation of the optimisation results.

In this paper, we classify Kaizen (production process related best practices) from Volkswagen internal knowledge database into their adaptability status over other Volkswagen production plants with help of supervised machine learning. Different criteria's like Return on Investment, implementation time-frame, impact on various other key performance indicators, plant-specific technical details, etc. are used to evaluate Kaizens and eventually cluster them into two categories. Empirical results show that the Decision tree model can predict the degree of adaptability (Success/Denied) with 85% accuracy.

Predictive analytics is seen as one of the emerging technology in this digital age of big data. Computational processing power and speed has grown exponentially in the last few years that has made predictive analytic practical for application in different organization. Manufacturing industries has huge amount of data in different shapes and forms, and keep regular track of their performance by monitoring key performance indicators defined under business strategy. Prioritizing and predicting these key performance indicators provide organization cutting edge as compared to competitors by being proactive rather than reactive. As compared to traditional business intelligence tools where focus is on static report or dashboards about past data, predictive analysis focuses on estimating outcomes with the objective of driving better business performance. Moreover, it is also being adopted for decision-making tools. Different data mining techniques are applied in the field of performance management system as per individual or project need. Many researches has developed different ideas to understand and evaluate complex intervened key performance indicator relationships in performance measurement system. The aim of the paper is to present comprehensive version of predictive key performance indicator analysis from its background to state of the art, describing various data mining standards, methodologies as well as industrial and research application. The paper also studies various surveys regarding predictive analytic for business application to identify different best practices in this field.

This paper investigates the effect of learning a forward model on the performance of a statistical forward planning agent. We transform Conway's Game of Life simulation into a single-player game where the objective can be either to preserve as much life as possible or to extinguish all life as quickly as possible. In order to learn the forward model of the game, we formulate the problem in a novel way that learns the local cell transition function by creating a set of supervised training data and predicting the next state of each cell in the grid based on its current state and immediate neighbours. Using this method we are able to harvest sufficient data to learn perfect forward models by observing only a few complete state transitions, using either a look-up table, a decision tree, or a neural network. In contrast, learning the complete state transition function is a much harder task and our initial efforts to do this using deep convolutional auto-encoders were less successful.We also investigate the effects of imperfect learned models on prediction errors and game-playing performance, and show that even models with significant errors can provide good performance.

Real-time games often require a combination of long-term and short-term planning as well as interleaved planning and execution. In our previous work, we introduced a hybrid planning and execution approach, in which high-level strategical planning is performed by a Hierarchical Task Network Planner and micro-management is done through Monte Carlo Tree Search. We use evaluation functions that represent weighted sums of selected game features as an interface between the two hierarchy levels.In this work, we present a way of automatically evolving the weights of these evaluation functions in order to improve the efficiency of the execution of high-level tasks. We compare the agent using the evolved evaluation functions with the one using manually created evaluation functions against state-of-theart controllers in the Real Time Strategy game environment microRTS.

In the last decade, many commercial video games have used planners instead of classical behavior trees or finite state machines to define agent behaviors. Planners allow looking ahead in time and can prevent some problems of purely reactive systems. Furthermore, some of them allow coordination of multiple agents. However, implementing a planner for highly dynamic environments such as video games is a difficult task. This paper aims to provide an overview of different elements of planners and the problems that developers might have when dealing with them. We identify the major areas of plan creation and execution, trying to guide developers through the process of implementing a planner and discuss possible solutions for problems that may arise in the following areas: environment, planning domain, goals, agents, actions, plan creation, and plan execution processes. Giving insights into multiple commercial games, we show different possibilities of solving such problems and discuss which solutions are better suited under specific circumstances, and why some academic approaches find a limited application in the context of commercial titles.

While it is relatively easy to imitate and evolve natural swarm behavior in simulations, less is known about the social characteristics of simulated, evolved swarms, such as the optimal (evolutionary) group size, why individuals in a swarm perform certain actions, and how behavior would change in swarms of different sizes. To address these questions, we used a genetic algorithm to evolve animats equipped with Markov Brains in a spatial navigation task that facilitates swarm behavior. The animats' goal was to frequently cross between two rooms without colliding with other animats. Animats were evolved in swarms of various sizes. We then evaluated the task performance and social behavior of the final generation from each evolution when placed with swarms of different sizes in order to evaluate their generalizability across conditions. According to our experiments, we find that swarm size during evolution matters: animats evolved in a balanced swarm developed more flexible behavior, higher fitness across conditions, and, in addition, higher brain complexity.

In large-scale optimisation, most algorithms require a separation of the variables into multiple smaller groups and aim to optimise these variable groups independently. In single-objective optimisation, a variety of methods aim to identify best variable groups, most recently the Differential Grouping 2. However, it is not trivial to apply these methods to multiple objectives, as the variable interactions might differ between objective functions. In this work, we introduce four different transfer strategies that allow to use any single-objective grouping mechanisms directly on multi-objective problems. We apply these strategies to a popular single-objective grouping method (Differential Grouping 2) and compare the performance of the obtained groups inside three recent large-scale multi-objective algorithms (MOEA/DVA, LMEA, WOF). The results show that the performance of the original MOEA/DVA and LMEA can in some cases be improved by our proposed grouping variants or even random groups. At the same time the computational budget is dramatically reduced. In the WOF algorithm, a significant improvement in performance compared to random groups or the standard version of the algorithm can on average not be observed.

In this paper, we propose a new method for solving multiobjective optimization problems with a large number of decision variables. The proposed method called weighted optimization framework is intended to serve as a generic method that can be used with any population-based metaheuristic algorithm. After explaining some general issues of large-scale optimization, we introduce a problem transformation scheme that is used to reduce the dimensionality of the search space and search for improved solutions in the reduced subspace. This involves so-called weights that are applied to alter the decision variables and are also subject to optimization. Our method relies on grouping mechanisms and employs a population-based algorithm as an optimizer for both original variables and weight variables. Different grouping mechanisms and transformation functions within the framework are explained and their advantages and disadvantages are examined. Our experiments use test problems with 2-3 objectives 40-5000 variables. Using our approach on three well-known algorithms and comparing its performance with other large-scale optimizers, we show that our method can significantly outperform most existing methods in terms of solution quality as well as convergence rate on almost all tested problems for many-variable instances.

This paper presents the Vector Field Map PSO (VFM-PSO) as a collective search algorithm for aerial micro-robots in environments with unknown external dynamics (such as wind). The proposed method is based on a multi-swarm approach and allows to cope with unknown disturbances arising by the vector fields in which the positions and the movements of the particles are highly affected. VFM-PSO requires gathering the information regarding the vector fields and one of our goals is to investigate the amount of the required information for a successful search mechanism. The experiments show that VFM-PSO can reduce the drift and improves the performance of the PSO algorithm despite incomplete information (awareness) about the structure of considered vector fields.

In evolutionary swarms adaptability and diversity are closely related concepts. In order to get a better understanding of their codependency we study a heterogeneous evolutionary multi-agent system with different rates of redundancy within the genetic material. The agents process a dynamic multi-objective task, where their genetic material defines their efficiency concerning the different objective functions of that task. One focus of this study is the influence of an elitist behavior performed by the agents during the evolutionary process, where an agent can decline the genetic material of another agent if it does not meet specific requirements. Further we analyze the impact of three different methods to aggregate the objective values into a single fitness value that is applicable for the evolutionary mechanism of the system. The results show that heterogeneity in the optimization behavior of the agents is very beneficial as it maintains a higher diversity in the system. The elitist behavior of the agents slows the evolutionary process but gives it a stronger pull towards qualitatively higher positions in the objective space. Indeed, the pace of the evolutionary process ultimately has a higher impact on the adaptability of the system than the amount of redundancy in the genetic information.

In this article we propose a new dynamic multi-objective optimization problem. This dynamic Distance Minimization Problem (dDMP) functions as a benchmark problem for dynamic multi-objective optimization and is based on the static versions from the literature. The dDMP introduces a useful property and challenge for dynamic multi-objective algorithms. Not only the positions of the Pareto-optimal solutions in the search space change over time, but also the complexity of the problem can be adjusted dynamically. In addition the problem is based on a simple geometric structure, which makes it useful to visualize the search behaviour of algorithms. We describe the basic principles of the problem, and introduce the possible dynamic changes and their implementation and effects of the Pareto-optimal areas. Our experiments show how a possible instance of the dynamic DMP can be defined and how different algorithms react to the dynamic changes.

The current boom of Unmanned Aerial Vehicles (UAVs) is increasing the number of potential industrial and research applications. One of the most demanded topics in this area is related to the automated planning of a UAVs swarm, controlled by one or several Ground Control Stations (GCSs). In this context, there are several variables that influence the selection of the most appropriate plan, such as the makespan, the cost or the risk of the mission. This problem can be seen as a Multi-Objective Optimization Problem (MOP). On previous approaches, the problem was modelled as a Constraint Satisfaction Problem (CSP) and solved using a Multi-Objective Genetic Algorithm (MOGA), so a Pareto Optimal Frontier (POF) was obtained. The main problem with this approach is based on the large number of obtained solutions, which hinders the selection of the best solution. This paper presents a new algorithm that has been designed to obtain the most significant solutions in the POF. This approach is based on Knee Points applied to MOGA. The new algorithm has been proved in a real scenario with different number of optimization variables, the experimental results show a significant improvement of the algorithm performance.

This paper proposed the method to reduce the calculating time to reveal the functional brain network associated with a task using a genetic algorithm and functional near-infrared spectroscopy (fNIRS) data. Changes in the cerebral blood flow during a task are obtained as time series data is analyzed using fNIRS, and a correlation matrix for multiple fNIRS channels is created for each subject. The subject group is divided into two groups, and a classifier of the two groups learns the correlation matrix as a feature quantity. The correlation matrix changes as the feature quantity changes with the combinations of channels, which affects classifier accuracy. If the combination of channels with the best classifier accuracy is identified, these channels can be considered important to the creation of the functional brain network for a target task. In our study, a genetic algorithm (GA) is used for channel selection. However, learning the classifier to calculate the evaluation value and optimization by the GA requires significant time. Thus, to increase search efficiency, we propose the kick-out method to skip the evaluation value calculation for poor individuals according to a previous evaluation value. We evaluated the effectiveness of the proposed method using fNIRS data recorded during a mental rotation test. Results show that important channels that express the functional brain network were selected and that processing time was reduced significantly by the proposed method.

This paper proposes a new multi-objective optimization algorithm that is called Fitness-Proportional Attraction with Weights (F-PAW). In contrast to many other approaches, this work was inspired by physics rather than biology. It is based on concepts from several methods, including the attraction principle of gravity from the Gravitational Search Algorithm (GSA), the weight sum approach from Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) as well as particle swarm optimization methods. These and other algorithms that were providing inspiration are introduced during the text and their techniques are investigated for the use in F-PAW. The performance of F-PAW is compared to three well-known multi-objective algorithms through an experiment on 16 common test problems taken from the WFG and DTLZ benchmarks. The results indicate two conclusions. On the one side, the proposed approach with the weight sum obtains a good diversity. On the other side, the currently implemented local search is lacking reliability and speed.

The design of algorithms for Game AI agents usually focuses on the single objective of winning, or maximizing a given score. Even if the heuristic that guides the search (for reinforcement learning or evolutionary approaches) is composed of several factors, these typically provide a single numeric value (reward or fitness, respectively) to be optimized. Multi-Objective approaches are an alternative concept to face these problems, as they try to optimize several objectives, often contradictory, at the same time. This paper proposes for the first time a study of Multi-Objective approaches for General Video Game playing, where the game to be played is not known a priori by the agent. The experimental study described here compares several algorithms in this setting, and the results suggest that Multi-Objective approaches can perform even better than their single-objective counterparts.

Evolutionary systems can be very adaptable to dynamic environments. If the systems input changes, it either has to remember or (re-)invent an efficient behavior fitting to a new or recurring situation. In this study we propose a haplodiploid system where haploid agents have one set of properties and diploid agents have two sets of properties. In the studied system agents process tasks which add to their fitness values. Once their fitness values exceed a certain threshold, they pass a copy of their property set to randomly chosen other agents. The agents property set defines the fitness value it gains by processing a task. Diploid agents apply the property set providing the higher fitness. While haploid agents enforce a fast and straight forwards adaptation and convergence, diploid agents maintain a higher diversity in the system. However, mixed systems are most suitable in highly dynamic environments. The focus of our simulation experiments is the adaptability of systems with specific distributions of haploids and diploids in various dynamic environments.

In multi-objective optimization, scalable test problems are required to test and compare the search abilities of the algorithms in solving large and small-dimensional problems. In this paper, we analyze a generalized Distance Minimization Problem (DMP) that is scalable in the number of decision variables and objectives and can be used with any distance function. Since previous research mostly regarded the behaviour of algorithms for Euclidean distances, in this work, we propose to use the Manhattan metric to measure the distances of solutions towards a set of predefined locations in the decision space. The structure of the Pareto-fronts of this problem widely differ from those of the euclidean problem. We perform an analytical analysis exemplary for low-dimensional instances of the problem to provide an understanding of the general properties and structure, and the challenges that might arise in many-objective many-variable instances. The negative effects on the search behaviour of algorithms are theoretically described, and three different optimization methods (MOEA/D, NSGA-II, SMPSO) are tested to give an understanding of different instances of the problem. The experimental results support our expectations and show that the proposed Manhattan metric DMP is difficult to solve for optimization algorithms even in low-dimensional spaces.

General Video Game Playing is a sub-field of Game Artificial Intelligence, where the goal is to find algorithms capable of playing many different real-time games, some of them unknown a priori. In this scenario, the presence of domain knowledge must be severely limited, or the algorithm will overfit to the training games and perform poorly on the unknown games of the test set. Research in this area has been of special interest in the last years, with emerging contests like the General Video Game AI (GVG-AI) Competition. This paper introduces three different open loop techniques for dealing with this problem. First, a simple directed depth first search algorithm is employed as a baseline. Then, a tree search algorithm with a multi-armed bandit based tree policy is presented, followed by a Rolling Horizon Evolutionary Algorithm (RHEA) approach. In order to test these techniques, the games from the GVG-AI Competition framework are used as a benchmark, evaluation on a training set of 29 games, and submitting to the 10 unknown games at the competition website. Results show how the general game-independent heuristic proposed works well across all algorithms and games, and how the RHEA becomes the best evolutionary technique in the rankings of the test set.

Multiobjective optimization has been traditionally a matter of study in domains like engineering or finance, with little impact on games research. However, action-decision based on multiobjective evaluation may be beneficial in order to obtain a high quality level of play. This paper presents a multiobjective Monte Carlo tree search algorithm for planning and control in real-time game domains, those where the time budget to decide the next move to make is close to 40 ms. A comparison is made between the proposed algorithm, a single-objective version of Monte Carlo tree search and a rolling horizon implementation of nondominated sorting evolutionary algorithm II (NSGA-II). Two different benchmarks are employed, deep sea treasure (DST) and the multiobjective physical traveling salesman problem (MO-PTSP). Using the same heuristics on each game, the analysis is focused on how well the algorithms explore the search space. Results show that the algorithm proposed outperforms NSGA-II. Additionally, it is also shown that the algorithm is able to converge to different optimal solutions or the optimal Pareto front (if achieved during search).

For real-world problems, the task of decision-makers is to identify a solution that can satisfy a set of performance criteria, which are often in conflict with each other. Multi-objective evolutionary algorithms tend to focus on obtaining a family of solutions that represent the trade-offs between the criteria; however ultimately a single solution must be selected. This need has driven a requirement to incorporate decision-maker preference models into such algorithms - a technique that is very common in the wider field of multiple criteria decision making. This paper reviews techniques which have combined evolutionary multi-objective optimization and multiple criteria decision making. Three classes of hybrid techniques are presented: a posteriori, a priori, and interactive, including methods used to model the decision-makers preferences and example algorithms for each category. To encourage future research directions, a commentary on the remaining issues within this research area is also provided.

Usually, Multi-Objective Evolutionary Algorithms face serious challengers in handling many objectives problems. This work presents a new Particle Swarm Optimization algorithm, called Iterated Multi-Swarm (I-Multi Swarm), which explores specific characteristics of PSO to face Many-Objective Problems. The algorithm takes advantage of a Multi-Swarm approach to combine different archiving methods aiming to improve convergence to the Pareto-optimal front and diversity of the non-dominated solutions. I-Multi Swarm is evaluated through an empirical analysis that uses a set of many-Objective problems, quality indicators and statistical tests.

This paper presents a new decentralized approach for evacuating a large number of people from a building using mobile devices which can communicate locally with each other. We investigate the impact of the local communication between the devices on the evacuation by proposing a new distributed evacuation planning algorithm called Distributed Swarm Evacuation Planning. The main challenge in this approach concerns the local communication, which can be unreliable, incomplete, and delayed. Experiments show that we can significantly reduce the evacuation time compared to a modeled panic-like evacuation scenario and that the results are better than those of a shortest-path evacuation plan.

Many practical optimization problems are constrained and have a bounded search space. In this paper, we propose and compare a wide variety of bound handling techniques for particle swarm optimization. By examining their performance on flat landscapes, we show that many bound handling techniques introduce significant search bias. Furthermore, we compare the performance of many bound handling techniques on a variety of test problems, demonstrating that the bound handling technique can have a major impact on the algorithm performance, and that the method recently proposed as the standard does not, in general, perform well.

All existing stochastic optimisers such as Evolutionary Algorithms require parameterisation which has a significant influence on the algorithm's performance. In most cases, practitioners assign static values to variables after an initial tuning phase. This parameter tuning method requires experience the practitioner may not have and, when done conscientiously, is rather time-consuming. Also, the use of parameter values that remain constant over the optimisation process has been observed to achieve suboptimal results. This work presents a parameter control method which redefines variables repeatedly based on a separate optimisation process which receives its feedback from the primary optimisation algorithm. The feedback is used for a projection of the value performing well in the future. The parameter values are sampled from intervals which are adapted dynamically, a method which has proved particularly effective and outperforms all existing adaptive parameter controls significantly.

State-of-the art constrained multiobjective optimisation methods are often explored and demonstrated with the help of function optimisation problems from these accounts. It is sometimes hard for practitioners to extract good approaches for practical problems. In this paper we apply an evolutionary algorithm to a factual problem with realistic constraints and compare the effects of different operators and constraint handling methods. We observe that in spite of an apparently very insular search space, we consistently obtain the best results when using a repair mechanism, effectively eliminating infeasible solutions. This runs contrary to some recommendations in the optimisation literature which propose penalty functions for search spaces where feasible solutions are sparse.

In this paper, we review several proposals for guide selection in Multi-Objective Particle Swarm Optimization (MOPSO) and compare them with each other in terms of convergence, diversity and computational times. The new proposals made for guide selection, both personal best (dasiapbestpsila) and global best (dasiagbestpsila), are found to be extremely effective and perform well compared to the already existing methods. The combination of selection methods for choosing dasiagbestpsila and dasiapbestpsila is also studied and it turns out that there exist certain combinations which yield an overall superior performance outperforming the others on the tested benchmark problems. Furthermore, two new proposals namely velocity trigger (as a substitute for ldquoturbulence operatorrdquo) and a new scheme of boundary handling is made.

Peer-to-peer based distributed computing environments can be expected to be dynamic to greater of lesser degree. While node losses will not usually lead to catastrophic failure of a population-based optimisation algorithm, such as particle swarm optimisation, performance will be degraded unless the lost computational power is replaced. When resources are replaced, one must consider how to utilise newly available nodes as well as the loss of existing nodes. In order to take advantage of newly available nodes, new particles must be generated to populate them. This paper proposes two methods of generating new particles during algorithm execution and compares the performance of each approach, then investigates a hybridised approach incorporating both mechanisms.

In this paper, we study parallelization of multi-objective optimization algorithms on a set of heterogeneous resources based on the Master-Slave model. The Master-Slave model is known to be the simplest parallelization paradigm, where a master processor sends function evaluations to several slave processors. The critical issue when using the standard methods on heterogeneous resources is that in every iteration of the optimization, the master processor has to wait for all of the computing resources (including the slow ones) to deliver the evaluations. In this paper, we study a new algorithm where all of the available computing resources are efficiently utilized to perform the multi-objective optimization task independent of the speed (fast or slow) of the computing processors. For this we propose a hybrid method using Multi-objective Particle Swarm optimization and Binary search methods. The new algorithm has been tested on a scenario containing heterogeneous resources and the results show that not only does the new algorithm perform well for parallel resources, but also when compared to a normal serial run on one computer.

This paper examines the performance characteristics of both asynchronous and synchronous parallel particle swarm optimisation algorithms in heterogeneous, fault-prone environments. Algorithm convergence is measured as a function of both iterations completed and time elapsed, allowing the two particle update mechanisms to be comprehensively evaluated and compared in such an environment. Asynchronous particle updates are shown to negatively impact the convergence speed in regards to iterations completed, however the increased parallel efficiency of the asynchronous model appears to counter this performance reduction, ensuring the asynchronous update mechanism performs comparably to the synchronous mechanism in fault-free environments. When faults are introduced, the synchronous update method is shown to suffer significant performance drops, suggesting that at least partly asynchronous algorithms should be used in real-world environments where faults can regularly occur.

Abstract. In recent years, a number of authors have successfully extended particle swarm optimization to problem domains with multiple objectives. This paper addresses the issue of parallelizing multi-objective particle swarms. We propose and empirically compare two parallel versions which differ in the way they divide the swarm into subswarms that can be processed independently on different processors. One of the variants works asynchronously and is thus particularly suitable for heterogeneous computer clusters as occurring e.g. in modern grid computing platforms. 1

In this paper we study a real-world optimization problem in mineralogy which contains a large number of parameters and several objective functions. The problem has been described through a thermodynamic model for which the parameters have to be quantified. Due to non-linear chemical reactions and the characteristics of the problem, we developed a Bilevel Optimization approach in which the parameters that need to be determined can be split in two levels. The lower level contains three non linear equations and two linear charge and mass balance constraints. We use Linear Multi-Objective Particle Swarm Optimization (LMO PSO) to solve this problem for a general case. We then use the results in the upper level. This Bilevel Optimization has been used to find the thermodynamic parameters of the Na2O − SiO2 system. The results are analytically analyzed and compared with the reference data. This shows that the thermodynamic model is accurate and that the termination of thermodynamic properties using a Bilevel Optimization method based on PSO algorithms is reliable and efficient.

This paper presents quantitative comparison of the performance of different methods for selecting the guide particle for multi-objective particle swarm optimization (MOPSO). Two principal methods are compared: the recently described Sigma method, and a new "Centroid" method. Drawing on the different dominant behaviors exhibited by the different selection methods, a variety of hybridizations of these is proposed to develop a more robust optimization algorithm. Statistical analysis of the hybrid methods demonstrates their contribution to improved performance of the optimization algorithm.

We suggest a novel tool for the parametrization of molecular force fields by using multi-objective optimization algorithms with a new set of physically motivated objective functions. The new approach is validated in the parametrization of the bonded terms for the homologous series of primary alcohols. Multi-objective evolutionary algorithms (MOEAs) and particularly multi-objective particle swarm optimization (MOPSO) are applied. The results show that in this case MOPSO finds solutions with higher convergence than the MOEA method. Physical analysis of the results confirms the performance of the MOPSO method and the choice of objective functions.

Covering the whole set of Pareto-optimal solutions is a desired task of multiobjective optimization methods. Because in general it is not possible to determine this set, a restricted amount of solutions are typically delivered in the output to decision makers. We propose a method using multiobjective particle swarm optimization to cover the Pareto-optimal front. The method works in two phases. In phase 1 the goal is to obtain a good approximation of the Pareto-front. In a second run subswarms are generated to cover the Pareto-front. The method is evaluated using different test functions and compared with an existing covering method using a real world example in antenna design.

In this paper, the influence of /spl epsi/-dominance on multi-objective particle swarm optimization (MOPSO) methods is studied. The most important role of /spl epsi/-dominance is to bound the number of non-dominated solutions stored in the archive (archive size), which has influences on computational time, convergence and diversity of solutions. Here, /spl epsi/-dominance is compared with the existing clustering technique for fixing the archive size and the solutions are compared in terms of computational time, convergence and diversity. A new diversity metric is also suggested. The results show that the /spl epsi/-dominance method can find solutions much faster than the clustering technique with comparable and even in some cases better convergence and diversity.

In multi-objective particle swarm optimization (MOPSO) methods, selecting the best local guide (the global best particle) for each particle of the population from a set of Pareto-optimal solutions has a great impact on the convergence and diversity of solutions, especially when optimizing problems with high number of objectives. This paper introduces the Sigma method as a new method for finding best local guides for each particle of the population. The Sigma method is implemented and is compared with another method, which uses the strategy of an existing MOPSO method for finding the local guides. These methods are examined for different test functions and the results are compared with the results of a multi-objective evolutionary algorithm (MOEA).

In MOEAs with elitism, the data structures and algorithms for storing and updating archives may have a great impact on the CPU time, especially when optimizing continuous problems with larger population sizes. In this paper, we introduce quadtrees as an efficient data structure for storing Pareto-points. Apart from conventional linear lists, we have implemented three kinds of quadtrees for the archives. These data structures were examined for different examples. The results presented show that linear lists perform better in terms of CPU time for small population sizes whereas tree structures perform better for large population sizes.