The Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) is a model-based EA framework that has been shown to perform well in several domains, including Genetic Programming (GP). Differently from traditional EAs where variation acts blindly, GOMEA learns a model of interdependencies within the genotype, that is, the linkage, to estimate what patterns to propagate. In this article, we study the role of Linkage Learning (LL) performed by GOMEA in Symbolic Regression (SR). We show that the non-uniformity in the distribution of the genotype in GP populations negatively biases LL, and propose a method to correct for this. We also propose approaches to improve LL when ephemeral random constants are used. Furthermore, we adapt a scheme of interleaving runs to alleviate the burden of tuning the population size, a crucial parameter for LL, to SR. We run experiments on 10 real-world datasets, enforcing a strict limitation on solution size, to enable interpretability. We find that the new LL method outperforms the standard one, and that GOMEA outperforms both traditional and semantic GP. We also find that the small solutions evolved by GOMEA are competitive with tuned decision trees, making GOMEA a promising new approach to SR.

The importance and potential of Gray-Box Optimization (GBO) with evolutionary algorithms is becoming increasingly clear lately both for benchmark and real-world problems. We consider the GBO setting where partial evaluations are possible, meaning that sub-functions of the evaluation function are known and can be exploited to improve optimization efficiency. In this paper, we show that the efficiency of GBO can be greatly improved through large-scale parallelism, exploiting the fact that each evaluation function requires the calculation of a number of independent sub-functions. This is especially interesting for real-world problems where often the majority of the computational effort is spent on the evaluation function. Moreover, we show how the best parallelization technique largely depends on factors including the number of sub-functions and their required computation time, revealing that for different parts of the optimization the best parallelization technique should be selected based on these factors. As an illustration, we show how large-scale parallelization can be applied to optimization of high-dose-rate brachytherapy treatment plans for prostate cancer. We find that use of a modern Graphics Processing Unit (GPU) was the most efficient parallelization technique in all realistic scenarios, leading to substantial speed-ups up to a factor of 73.

The recently introduced Gene-pool Optimal Mixing Evolutionary Algorithm for Genetic Programming (GP-GOMEA) has been shown to find much smaller solutions of equally high quality compared to other state-of-the-art GP approaches. This is an interesting aspect as small solutions better enable human interpretation. In this paper, an adaptation of GP-GOMEA to tackle real-world symbolic regression is proposed, in order to find small yet accurate mathematical expressions, and with an application to a problem of clinical interest. For radiotherapy dose reconstruction, a model is sought that captures anatomical patient similarity. This problem is particularly interesting because while features are patient-specific, the variable to regress is a distance, and is defined over patient pairs. We show that on benchmark problems as well as on the application, GP-GOMEA outperforms variants of standard GP. To find even more accurate models, we further consider an evolutionary meta learning approach, where GP-GOMEA is used to construct small, yet effective features for a different machine learning algorithm. Experimental results show how this approach significantly improves the performance of linear regression, support vector machines, and random forest, while providing meaningful and interpretable features.

The recently introduced Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) has been shown to be among the state-of-the-art for solving discrete optimization problems. Key to the success of GOMEA is its ability to efficiently exploit the linkage structure of a problem. Here, we introduce the Real-Valued GOMEA (RV-GOMEA), which incorporates several aspects of the real-valued EDA known as AMaLGaM into GOMEA in order to make GOMEA well-suited for real-valued optimization. The key strength of GOMEA to competently exploit linkage structure is effectively preserved in RV-GOMEA, enabling excellent performance on problems that exhibit a linkage structure that is to some degree decomposable. Moreover, the main variation operator of GOMEA enables substantial improvements in performance if the problem allows for partial evaluations, which may be very well possible in many real-world applications. Comparisons of performance with state-of-the-art algorithms such as CMA-ES and AMaLGaM on a set of well-known benchmark problems show that RV-GOMEA achieves comparable, excellent scalability in case of black-box optimization. Moreover, RV-GOMEA achieves unprecedented scalability on problems that allow for partial evaluations, reaching near-optimal solutions for problems with up to millions of real-valued variables within one hour on a normal desktop computer.

The recently introduced Multi-Objective Gene-pool Optimal Mixing Evolutionary Algorithm (MO-GOMEA) exhibits excellent scalability in solving a wide range of challenging discrete multi-objective optimization problems. In this paper, we address scalability issues in solving multi-objective optimization problems with continuous variables by introducing the Multi-Objective Real-Valued GOMEA (MO-RV-GOMEA), which combines MO-GOMEA with aspects of the multi-objective estimation-of-distribution algorithm known as MAMaLGaM. MO-RV-GOMEA exploits linkage structure in optimization problems by performing distribution estimation, adaptation, and sampling as well as solution mixing based on an explicitly-defined linkage model. Such a linkage model can be defined a priori when some problem-specific knowledge is available, or it can be learned from the population. The scalability of MO-RV-GOMEA using different linkage models is compared to the state-of-the-art multi-objective evolutionary algorithms NSGA-II and MAMaLGaM on a wide range of benchmark problems. MO-RV-GOMEA is found to retain the excellent scalability of MO-GOMEA through the successful exploitation of linkage structure, scaling substantially better than NSGA-II and MAMaLGaM. This scalability is even further improved when partial evaluations are possible, achieving strongly sub-linear scalability in terms of the number of evaluations.

The Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) is a recently introduced model-based EA that has been shown to be capable of outperforming state-of-the-art alternative EAs in terms of scalability when solving discrete optimization problems. One of the key aspects of GOMEA's success is a variation operator that is designed to extensively exploit linkage models by effectively combining partial solutions. Here, we bring the strengths of GOMEA to Genetic Programming (GP), introducing GP-GOMEA. Under the hypothesis of having little problem-specific knowledge, and in an effort to design easy-to-use EAs, GP-GOMEA requires no parameter specification. On a set of well-known benchmark problems we find that GP-GOMEA outperforms standard GP while being on par with more recently introduced, state-of-the-art EAs. We furthermore introduce Input-space Entropy-based Building-block Learning (IEBL), a novel approach to identifying and encapsulating relevant building blocks (subroutines) into new terminals and functions. On problems with an inherent degree of modularity, IEBL can contribute to compact solution representations, providing a large potential for knock-on effects in performance. On the difficult, but highly modular Even Parity problem, GP-GOMEA+IEBL obtains excellent scalability, solving the 14-bit instance in less than 1 hour.

We generalise a recently proposed concurrent flexibility metric to overcome some of its shortcomings. We show that these shortcomings can be removed if one selects an optimal subset of variables for which the concurrent flexibility is determined. The flexibility of the remaining variables does not play a role in the determination of the flexibility of the system. We present a preliminary experimental evaluation of the improvement in concurrent flexibility that can be obtained by comparing some (approximation) algorithms. Their performance on several benchmark sets is evaluated. As a result, in some cases the concurrent flexibility of an STN can be enhanced by 20 - 50%.

Decomposition is a technique to obtain complete solutions by assembling independently obtained partial solutions. In particular, constraint decomposition plays an important role in distributed databases, distributed scheduling and violation detection: It enables conflict-free local decision making, while avoiding communication overloading. One of the main issues in decomposition is the loss of flexibility due to decomposition. Here, flexibility roughly refers to the freedom in choosing suitable values for the variables in order to satisfy the constraints. In this paper, we concentrate on linear constraint systems and efficient decomposition techniques for them. Using a generalization of a flexibility metric developed for Simple Temporal Networks, we show how an efficient decomposition technique for linear constraint systems can be derived that minimizes the loss of flexibility. As a by-product of this decomposition technique, we propose an intuitively attractive flexibility metric for linear constraint systems where decomposition does not incur any loss of flexibility.

Multi-agent Pathfinding is a relevant problem in a wide range of domains, for example in robotics and video games research. Formally, the problem considers a graph consisting of vertices and edges, and a set of agents occupying vertices. An agent can only move to an unoccupied, neighbouring vertex, and the problem of finding the minimal sequence of moves to transfer each agent from its start location to its destination is an NP-hard problem. We present Push and Rotate, a new algorithm that is complete for Multi-agent Pathfinding problems in which there are at least two empty vertices. Push and Rotate first divides the graph into subgraphs within which it is possible for agents to reach any position of the subgraph, and then uses the simple push, swap, and rotate operations to find a solution; a post-processing algorithm is also presented that eliminates redundant moves. Push and Rotate can be seen as extending Luna and Bekris's Push and Swap algorithm, which we showed to be incomplete in a previous publication. In our experiments we compare our approach with the Push and Swap, MAPP, and Bibox algorithms. The latter algorithm is restricted to a smaller class of instances as it requires biconnected graphs, but can nevertheless be considered state of the art due to its strong performance. Our experiments show that Push and Swap suffers from incompleteness, MAPP is generally not competitive with Push and Rotate, and Bibox is better than Push and Rotate on randomly generated biconnected instances, while Push and Rotate performs better on grids.

In case of a plan failure, plan-repair is a more promising solution than replanning from scratch. The effectiveness of plan-repair depends on knowledge of which plan action failed and why. Therefore, in this paper, we propose an Extended Spectrum Based Diagnosis approach that efficiently pinpoints failed actions. Unlike Model Based Diagnosis (MBD), it does not require the fault models and behavioral descriptions of actions. Our approach first computes the likelihood of an action being faulty and subsequently proposes optimal probe locations to refine the diagnosis. We also exploit knowledge of plan steps that are instances of the same plan operator to optimize the selection of the most informative diagnostic probes. In this paper, we only focus on diagnostic aspect of plan-repair process.

We develop a novel learning algorithm RTI for identifying a deterministic real-time automaton (DRTA) from labeled time-stamped event sequences. The RTI algorithm is based on the current state of the art in deterministic finite-state automaton (DFA) identification, called evidence-driven state-merging (EDSM). In addition to having a DFA structure, a DRTA contains time constraints between occurrences of consecutive events. Although this seems a small difference, we show that the problem of identifying a DRTA is much more difficult than the problem of identifying a DFA: identifying only the time constraints of a DRTA given its DFA structure is already NP-complete. In spite of this additional complexity, we show that RTI is a correct and complete algorithm that converges efficiently (from polynomial time and data) to the correct DRTA in the limit. To the best of our knowledge, this is the first algorithm that can identify a timed automaton model from time-stamped event sequences.A straightforward alternative to identifying DRTAs is to identify a DFA that models time implicitly, i.e., a DFA that uses different states for different points in time. Such a DFA can be identified by first sampling the timed sequences using a fixed frequency, and subsequently applying EDSM to the resulting non-timed event sequences. We evaluate the performance of both RTI and this sampling approach experimentally on artificially generated data. In these experiments RTI outperforms the sampling approach significantly. Thus, we show that if we obtain data from a real-time system, it is easier to identify a DRTA from this data than to identify an equivalent DFA.

We advocate the use of an explicit time representation in syntactic pattern recognition because it can result in more succinct models and easier learning problems. We apply this approach to the real-world problem of learning models for the driving behavior of truck drivers. We discretize the values of onboard sensors into simple events. Instead of the common syntactic pattern recognition approach of sampling the signal values at a fixed rate, we model the time constraints using timed models. We learn these models using the RTI+ algorithm from grammatical inference, and show how to use computational mechanics and a form of semi-supervised classification to construct a real-time automaton classifier for driving behavior. Promising results are shown using this new approach.

We consider a multi-agent planning problem as a set of activities that has to be planned by several autonomous agents. In general, due to the possible dependencies between the agents’ activities or interactions during execution of those activities, allowing agents to plan individually may lead to a very inefficient or even infeasible solution to the multi-agent planning problem. This is exactly where plan coordination methods come into play. In this paper, we aim at the development of coordination by design techniques that (i) let each agent construct its plan completely independent of the others while (ii) guaranteeing that the joint combination of their plans always is coordinated. The contribution of this paper is twofold. Firstly, instead of focusing only on the feasibility of the resulting plans, we will investigate the additional costs incurred by the coordination by design method, that means, we propose to take into account the price of autonomy : the ratio of the costs of a solution obtained by coordinating selfish agents versus the costs of an optimal solution. Secondly, we will point out that in general there exist at least two ways to achieve coordination by design: one called concurrent decomposition and the other sequential decomposition . We will briefly discuss the applicability of these two methods, and then illustrate them with two specific coordination problems: coordinating tasks and coordinating resource usage. We also investigate some aspects of the price of autonomy of these two coordination methods.

Diagnosis of plan failures is an important subject in both single- and multi-agent planning. Plan diagnosis can be used to deal with plan failures in three ways: (i) to provide information necessary for the adjustment of the current plan or for the development of a new plan, (ii) to point out which equipment and/or agents should be repaired or adjusted to avoid further violation of the plan execution, and (iii) to identify the agents responsible for plan-execution failures. We introduce two general types of plan diagnosis: primary plan diagnosis identifying the incorrect or failed execution of actions, and secondary plan diagnosis that identifies the underlying causes of the faulty actions. Furthermore, three special cases of secondary plan diagnosis are distinguished, namely agent diagnosis , equipment diagnosis and environment diagnosis .

We consider a model-based diagnosis approach to the diagnosis of plans. Here, a plan performed by some agent(s) is considered as a system to be diagnosed. We introduce a simple formal model of plans and plan execution where it is assumed that the execution of a plan can be monitored by making partial observations of plan states. These observed states are used to compare them with states predicted based on (normal) plan execution. Deviations between observed and predicted states can be explained by qualifying some plan steps in the plan as behaving abnormally. A diagnosis is a subset of plan steps qualified as abnormal that can be used to restore the compatibility between the predicted and the observed partial state. Besides minimum and subset minimal diagnoses, we argue that in plan-based diagnosis maximum informative diagnoses should be considered as preferred diagnoses, too. The latter ones are diagnoses that make the strongest predictions with respect to partial states to be observed in the future. We show that in contrast to minimum diagnoses, finding a (subset minimal) maximum informative diagnosis can be achieved in polynomial time. Finally, we show how these diagnoses can be found efficiently if the plan is distributed over a number of agents.

In a multi-agent routing problem, agents must find the shortest-time path from source to destination while avoiding deadlocks and collisions with other agents. Agents travel over an infrastructure of resources (such as intersections and road segments between intersections), and each resource r has (i) a capacity C(r), which is the maximum number of agents that may occupy the resource at the same time, and (ii) a minimum travel time D(r). Example 1 illustrates this multi-agent routing problem.

In many domains successful execution of plans requires careful monitoring and repair. Diagnosis of plan execution supports this process by identifying causes of plan failure.