EDA++: Estimation of Distribution Algorithms with Feasibility Conserving Mechanisms for Constrained Continuous Optimization

Handling non-linear constraints in continuous optimization is challenging, and finding a feasible solution is usually a difficult task. In the past few decades, various techniques have been developed to deal with linear and non-linear constraints. However, reaching feasible solutions has been a challenging task for most of these methods. In this paper, we adopt the framework of Estimation of Distribution Algorithms (EDAs) and propose a new algorithm (EDA++) equipped with some mechanisms to deal with non-linear constraints. These mechanisms are associated with different stages of the EDA, including seeding, learning and mapping. It is shown that, besides increasing the quality of the solutions in terms of objective values, the feasibility of the final solutions is guaranteed if an initial population of feasible solutions is seeded to the algorithm. The EDA with the proposed mechanisms is applied to two suites of benchmark problems for constrained continuous optimization and its performance is compared with some state-of-the-art algorithms and constraint handling methods. Conducted experiments confirm the speed, robustness and efficiency of the proposed algorithm in tackling various problems with linear and non-linear constraints.La Caixa Foundatio

Bayesian inference for algorithm ranking analysis

The statistical assessment of the empirical comparison of algorithms is an essential step in heuristic optimization. Classically, researchers have relied on the use of statistical tests. However, recently, concerns about their use have arisen and, in many fields, other (Bayesian) alternatives are being considered. For a proper analysis, different aspects should be considered. In this work we focus on the question: what is the probability of a given algorithm being the best? To tackle this question, we propose a Bayesian analysis based on the Plackett-Luce model over rankings that allows several algorithms to be considered at the same tim

Distance-based exponential probability models on constrained combinatorial optimization problems

Estimation of distribution algorithms have already demonstrated their utility when solving a broad range of combinatorial problems. However, there is still room for methodological improvements when approaching constrained type problems. The great majority of works in the literature implement external repairing or penalty schemes, or use ad-hoc sampling methods in order to avoid unfeasible solutions. In this work, we present a new way to develop EDAs for this type of problems by implementing distance-based exponential probability models defined exclusively on the set of feasible solutions. In order to illustrate this procedure, we take the 2-partition balanced Graph Partitioning Problem as a case of study, and design efficient learning and sampling methods in order to use these distance-based probability models in EDAs

Optimal multi-impulse space rendezvous considering limited impulse using a discretized Lambert problem combined with evolutionary algorithms

In this paper, a direct approach is presented to tackle the multi-impulse rendezvous problem considering the impulse limit. Particularly, the standard Lambert problem is extended toward several consequential orbit transfers for the rendezvous problem. A number of different evolutionary algorithms are taken into consideration. It is shown that the proposed approach can lead to the optimal multi-impulse transfer maneuver that has the minimum amount of fuel similar to the traditional two-impulse transfer without violating the impulse limitation. Results also indicate that the approach is efficient even when the number of stages increases due to lower impulse limitations

Are the artificially generated instances uniform in terms of difficulty?

In the field of evolutionary computation, it is usual to generate artificial benchmarks of instances that are used as a test-bed to determine the performance of the algorithms at hand. In this context, a recent work on permutation problems analyzed the implications of generating instances uniformly at random (u.a.r.) when building those benchmarks. Particularly, the authors analyzed instances as rankings of the solutions of the search space sorted according to their objective function value. Thus, two instances are considered equivalent when their objective functions induce the same ranking over the search space. Based on the analysis, they suggested that, when some restrictions hold, the probability to create easy rankings is higher than creating difficult ones. In this paper, we continue on that research line by adopting the framework of local search algorithms with the best improvement criterion. Particularly, we empirically analyze, in terms of difficulty, the instances (rankings) created u.a.r. of three popular problems: Linear Ordering Problem, Quadratic Assignment Problem and Flowshop Scheduling Problem. As the neighborhood system is critical for the performance of local search algorithms three different neighborhood systems have been considered: swap, interchange and insert. Conducted experiments reveal that (1) by sampling the parameters uniformly at random we obtain instances with a non-uniform distribution in terms of difficulty, (2) the distribution of the difficulty strongly depends on the pair problem-neighborhood considered, and (3) given a problem, the distribution of the difficulty seems to depend on the smoothness of the landscape induced by the neighborhood and on its size.Research Groups 2013-2018 (IT-609-13) TIN2016-78365-R(Spanish Ministry of Economy, Industry and Competitiveness

Spacecraft Trajectory Optimization: A review of Models, Objectives, Approaches and Solutions

This article is a survey paper on solving spacecraft trajectory optimization problems. The solving process is decomposed into four key steps of mathematical modeling of the problem, defining the objective functions, development of an approach and obtaining the solution of the problem. Several subcategories for each step have been identified and described. Subsequently, important classifications and their characteristics have been discussed for solving the problems. Finally, a discussion on how to choose an element of each step for a given problem is provided.La Caixa, TIN2016-78365-

On the symmetry of the Quadratic Assignment Problem through Elementary Landscape Decomposition

When designing meta-heuristic strategies to optimize the quadratic assignment problem (QAP), it is important to take into account the specific characteristics of the instance to be solved. One of the characteristics that has been pointed out as having the potential to affect the performance of optimization algorithms is the symmetry of the distance and flow matrices that form the QAP. In this paper, we further investigate the impact of the symmetry of the QAP on the performance of meta-heuristic algorithms, focusing on local search based methods. The analysis is carried out using the elementary landscape decomposition (ELD) of the problem under the swap neighborhood. First, we study the number of local optima and the relative contribution of the elementary components on a benchmark composed of different types of instances. Secondly, we propose a specific local search algorithm based on the ELD in order to experimentally validate the effects of the symmetry. The analysis carried out shows that the symmetry of the QAP is a relevant feature that influences both the characteristics of the elementary components and the performance of local search based algorithms.IT1244-19, PID2019-106453GA-I00/AEI/10.13039/501100011033, H202

Trajectory optimization of space vehicle in rendezvous proximity operation with evolutionary feasibility conserving techniques

In this paper, a direct approach is developed for discovering optimal transfer trajectories of close-range rendezvous of satellites considering disturbances in elliptical orbits. The control vector representing the inputs is parameterized via different interpolation methods, and an Estimation of Distribution Algorithm (EDA) that implements mixtures of probability models is presented. To satisfy the terminal conditions, which are represented as non-linear inequality constraints, several feasibility conserving mechanisms associated with learning and sampling methods of the EDAs are proposed, which guarantee the feasibility of the explored solutions. They include a particular implementation of a clustering algorithm, outlier detection, and several heuristic mapping methods. The combination of the proposed operators guides the optimization process in achieving the optimal solution by surfing the regions of the search domain associated with feasible solutions. Numerical simulations confirm that space transfer trajectories with minimum-fuel consumption for the chaser spacecraft can be obtained with terminal condition satisfaction in rendezvous proximity operation.KK-2021/00065 KK-2022/00106; PID2019-104933GB-10/AEI/10.13039/501100011033 PID2019-106453GAI00/AEI/10.13039/501100011033 IT1504-2

Hybrid Heuristics for the Linear Ordering Problem

The linear ordering problem (LOP) is one of the classical NP-Hard combinatorial optimization problems. Motivated by the difficulty of solving it up to optimality, in recent decades a great number of heuristic and meta-heuristic algorithms have been proposed. Despite the continuous work on this problem, there is still room nowadays for designing strategies that beat the state-of-the-art algorithms, and take a step forward in terms of the quality of the obtained solutions.In this paper, two novel schemes are presented. The first algorithm consists of an iterated local search algorithm that carries out an organized exploration of the search space. The second scheme is an extension of the previous algorithm that, based on the properties of the LOP, proposes an exact procedure that allows us to improve the quality of the solutions systematically. Conducted experiments on one of the hardest LOP benchmarks (xLOLIB) show that 77 new best results were found out of 78 instances. The described strategies also provide innovative ideas for developing more advanced algorithms for solving the LOP

Evolutionary algorithms to optimize low-thrust trajectory design in spacecraft orbital precession mission

In space environment, perturbations make the spacecraft lose its predefined orbit in space. One of these undesirable changes is the in-plane rotation of space orbit, denominated as orbital precession. To overcome this problem, one option is to correct the orbit direction by employing low-thrust trajectories. However, in addition to the orbital perturbation acting on the spacecraft, a number of parameters related to the spacecraft and its propulsion system must be optimized. This article lays out the trajectory optimization of orbital precession missions using Evolutionary Algorithms (EAs). In this research, the dynamics of spacecraft in the presence of orbital perturbation is modeled. The optimization approach is employed based on the parametrization of the problem according to the space mission. Numerous space mission cases have been studied in low and middle Earth orbits, where various types of orbital perturbations are acted on spacecraft. Consequently, several EAs are employed to solve the optimization problem. Results demonstrate the practicality of different EAs, along with comparing their convergence rates. With a unique trajectory model, EAs prove to be an efficient, reliable and versatile optimization solution, capable of being implemented in conceptual and preliminary design of spacecraft for orbital precession missions.IT-609-13 2013-2018, TIN2016-78365-