Performance Evaluation of Nature-Inspired Algorithms in constrained Optimization

In almost all scientific contributions to the field of Nature-Inspired Algorithms (NIAs), the researchers select some benchmark test suites, which makes possible to draw conclusions on the merit of the proposed algorithm. Hence, it is a vital task to compose comprehensive test suites with the aim of covering variety of different scenarios. Furthermore, while conducting comparative analysis of results obtained with NIAs, selection of the proper performance indicators are of paramount importance. This paper intends to address these two topics with a special stress on NIAs designed for constrained optimization

Gaussian Process Model Predictive Control of An Unmanned Quadrotor

The Model Predictive Control (MPC) trajectory tracking problem of an unmanned quadrotor with input and output constraints is addressed. In this article, the dynamic models of the quadrotor are obtained purely from operational data in the form of probabilistic Gaussian Process (GP) models. This is different from conventional models obtained through Newtonian analysis. A hierarchical control scheme is used to handle the trajectory tracking problem with the translational subsystem in the outer loop and the rotational subsystem in the inner loop. Constrained GP based MPC are formulated separately for both subsystems. The resulting MPC problems are typically nonlinear and non-convex. We derived 15 a GP based local dynamical model that allows these optimization problems to be relaxed to convex ones which can be efficiently solved with a simple active-set algorithm. The performance of the proposed approach is compared with an existing unconstrained Nonlinear Model Predictive Control (NMPC). Simulation results show that the two approaches exhibit similar trajectory tracking performance. However, our approach has the advantage of incorporating constraints on the control inputs. In addition, our approach only requires 20% of the computational time for NMPC.Comment: arXiv admin note: text overlap with arXiv:1612.0121

Deterministic and stochastic exploration of long asteroid fly-by sequences exploiting tree-graph and optimal substructure properties

In the past, space trajectory design was limited to the optimal design of transfers to single destinations. However, a somewhat more daring approach is today making the space community to consider missions that visit, with one single spacecraft, a multitude of celestial objects; such as asteroid tour mission proposals CASTAway or MANTIS, which both proposed to visit 10 or more asteroids in a quick succession of asteroid fly-bys. The design of these so-called asteroid tours is complicated by the fact that the sequence of asteroids is not known a priori, but is the objective of the optimisation itself. This leads to a complex mixed-integer non-linear programming (MINLP) problem, on which the decision variables assume both continuous and discrete values. Beyond the obvious complexity of such problem formulation, preliminary mission design requires not only to locate the global optimum solution but, also, to map the ensemble of solutions that leads to feasible transfers. This paper analyses the complexity of such search space, which can be efficiently modelled as a tree-graph of interconnected Lambert arc solutions between two consecutive asteroids. This allows to exploit the optimal substructure of the problem and enables complete tree traverse explorations for limited asteroid catalogues. Nevertheless, the search space quickly grows in complexity for larger catalogues, featuring a labyrinthine multi-modal structure and extreme non-linearities. This underlying complexity ultimately renders common stochastic heuristics, such as Ant Colony Optimization, rather inefficient. Mostly, due to the fact that the metaheuristic processes are not able to gather any real understanding, or knowledge, such that it can efficiently guide the search. Instead, an astrodynamics-lead heuristic based on the distance between spacecraft and asteroid at the asteroid’s MOID-point crossing epoch, enables an efficient pruning of the asteroid catalogue. Then, deterministic processes based on dynamic programming and beam search can be efficiently applied, providing solutions to both the global optimum and the constraint satisfaction problems

Efficiency of tree-search like heuristics to solve complex mixed-integer programming problems applied to the design of optimal space trajectories

In the past, space trajectory optimization was limited to optimal design of transfers to single destinations, where optimality refers to minimum propellant consumption or transfer time. New technologies, and a more daring approach to space, are today making the space community consider missions that target multiple destinations. In the present paper, we focus on missions that aim to visit multiple asteroids within a single launch. The trajectory design of these missions is complicated by the fact that the asteroid sequences are not known a priori but are the objective of the optimization itself. Usually, these problems are formulated as global optimization (GO) problems, under the formulation of mixed-integer non-linear programming (MINLP), on which the decision variables assume both continuous and discrete values. However, beyond the aim of finding the global optimum, mission designers are usually interested in providing a wide range of mission design options reflecting the multi-modality of the problems at hand. In this sense, a Constraint Satisfaction Problem (CSP) formulation is also relevant. In this manuscript, we focus on these two needs (i.e. tackling both the GO and the CSP) for the asteroid tour problem. First, a tree-search algorithm based upon the Bellman’s principle of optimality is described using dynamic programming approach to address the feasibility of solving the GO problem. This results in an efficient and scalable procedure to obtain global optimum solutions within large datasets of asteroids. Secondly, tree-search strategies like Beam Search and Ant Colony Optimization with back-tracking are tested over the CSP formulations. Results reveal that BS handles better the multi-modality of the search space when compared to ACO, as this latter solver has a bias towards elite solutions, which eventually hinders the diversity needed to efficiently cope with CSP over graphs

Gnowee: A Hybrid Metaheuristic Optimization Algorithm for Constrained, Black Box, Combinatorial Mixed-Integer Design

This paper introduces Gnowee, a modular, Python-based, open-source hybrid metaheuristic optimization algorithm (Available from https://github.com/SlaybaughLab/Gnowee). Gnowee is designed for rapid convergence to nearly globally optimum solutions for complex, constrained nuclear engineering problems with mixed-integer and combinatorial design vectors and high-cost, noisy, discontinuous, black box objective function evaluations. Gnowee's hybrid metaheuristic framework is a new combination of a set of diverse, robust heuristics that appropriately balance diversification and intensification strategies across a wide range of optimization problems. This novel algorithm was specifically developed to optimize complex nuclear design problems; the motivating research problem was the design of material stack-ups to modify neutron energy spectra to specific targeted spectra for applications in nuclear medicine, technical nuclear forensics, nuclear physics, etc. However, there are a wider range of potential applications for this algorithm both within the nuclear community and beyond. To demonstrate Gnowee's behavior for a variety of problem types, comparisons between Gnowee and several well-established metaheuristic algorithms are made for a set of eighteen continuous, mixed-integer, and combinatorial benchmarks. These results demonstrate Gnoweee to have superior flexibility and convergence characteristics over a wide range of design spaces. We anticipate this wide range of applicability will make this algorithm desirable for many complex engineering applications.Comment: 43 pages, 7 tables, 6 figure

Hybrid evolutionary techniques for constrained optimisation design

This thesis a research program in which novel and generic optimisation methods were developed so that can be applied to a multitude of mathematically modelled business problems which the standard optimisation techniques often fail to deal with. The continuous and mixed discrete optimisation methods have been investigated by designing new approaches that allow users to more effectively tackle difficult optimisation problems with a mix of integer and real valued variables. The focus of this thesis presents practical suggestions towards the implementation of hybrid evolutionary approaches for solving optimisation problems with highly structured constraints. This work also introduces a derivation of the different optimisation methods that have been reported in the literature. Major theoretical properties of the new methods have been presented and implemented. Here we present detailed description of the most essential steps of the implementation. The performance of the developed methods is evaluated against real-world benchmark problems, and the numerical results of the test problems are found to be competitive compared to existing methods

Stochastic Optimisation for Complex Mixed-Integer Programming Problems in Asteroid Tour Missions

Deep space exploration is key to understand the origin of our Solar System and address the Earth impact risk. Space Trajectory Design (STD) has evolved and incremented in complexity due to the interest within the space community to explore multiple celestial bodies in a single mission. This thesis focuses on an Asteroid Tour Trajectory in the context of the CASTAway mission. CASTAway is a mission proposal for European Space Agency’s 5th call of medium-size missions to explore the Asteroid Main Belt. The objective is not to find the global optima but find feasible sequences of asteroid fly-bys, as per feasible tours of 12 asteroids of a total Δv of less than 9 km/s is meant. The complexity of the problem is given by the large number of possible permutations of 12-asteroid tour solutions – even with a reduced catalogue of 158 asteroids – and because of being a Mixed-Integer Non-Linear Programming (MINLP) problem. Because of this, metaheuristics are used to tackle the problem. A novel problem modelling that achieves uniqueness on the cost paths of the Search Space and a novel ACO solver is presented, with the general objective for the whole CASTPath project of finding a robust low computational heuristic. Due to the scientific interest on having diversity in the sequences, a similarity measurement tool is also developed. Several test cases with different ACO tuning parameters are run on a High Performance Computer. Results show that this algorithm outperforms the previous heuristics on CASTPath obtaining the lowest Δv (7.27 km/s) achieved by an heuristic and finding multiple feasible sequences (97 in 1 h). Moreover, the new problem modelling has allowed within the research group, to find the global optima (6.98 km/s) for this asteroid catalogue by Dynamic Programming

Developing Statistical Models to Assess Productivity in the Automotive Manufacturing Sector

The purpose of this study is to identify the most important activity in a value chain, effective factors, their impact, and to find estimation models of the most well-known productivity measurement, Hours per Vehicle (HPV), in the automotive industry in North American manufacturing plants. HPV is a widely recognized production performance indicator that is used by a significant percentage of worldwide automakers. During a comprehensive literature review, 13 important factors that affect HPV were defined as launching a new vehicle, ownership, car segment, model types, year, annual available working days, vehicle variety, flexibility, annual production volume, car assembly and capacity (CAC) utilization, outsourcing, platform strategy, and hourly employee\u27s percentage.;Data used in this study was from North American plants that participated in the Harbour\u27s survey from 1999 to 2007. Data are synthesized using a uniform methodology from information supplied by the plants and supplemented with plant visits by Harbour Consulting auditors. Overall, there are 682 manufacturing plants in the statistical sample from 10 different multinational automakers.;Several robust and advanced statistical methods were used to analyze the data and derive the best possible HPV regression equations. The final statistical models were validated through exhaustive cross-validation procedures. Mixed integer distributed ant colony optimization (MIDACO) algorithm, a nonlinear programming algorithm, that can robustly solve problems with critical function properties like high non-convexity, non-differentiability, flat spots, and even stochastic noise was used to achieve HPV target value.;During the study period, the HPV was reduced 48 minutes on the average each year. Annual production volume, flexible manufacturing, outsourcing, and platform strategy improve HPV. However, vehicle variety, model types, available annual working days, CAC, percentage of the hourly employees, and launching a new model penalize HPV. Japanese plants are the benchmark regarding the HPV followed by joint ventures and Americans. On average, the HPV is lower for Japanese and joint ventures in comparison to American automakers by about 1.83 and 1.28 hours, respectively. Launching a new model and adding a new variety in body styles or chassis configurations raises the HPV, depending on the car class; however, manufacturing plants compensate for this issue by using platform sharing and flexible manufacturing strategies. While launching a new vehicle common platform sharing, flexible manufacturing, and more salaried employees (lower hourly) strategies will help carmakers to overcome the effect of launching new vehicles productivity penalization to some extent.;The research investigates current strategies that help automakers to enhance their production performance and reduce their productivity gap. The HPV regression equations that are developed in this research may be used effectively to help carmakers to set guidelines to improve their productivity with respect to internal and external constraints, strengths, weaknesses, opportunities, and threats

Nonlinear mixed integer based optimization technique for space applications

In this thesis a new algorithm for mixed integer nonlinear programming (MINLP) is developed and applied to several real world applications with special focus on space applications. The algorithm is based on two main components, which are an extension of the Ant Colony Optimization metaheuristic and the Oracle Penalty Method for constraint handling. A sophisticated implementation (named MIDACO) of the algorithm is used to numerically demonstrate the usefulness and performance capabilities of the here developed novel approach on MINLP. An extensive amount of numerical results on both, comprehensive sets of benchmark problems (with up to 100 test instances) and several real world applications, are presented and compared to results obtained by concurrent methods. It can be shown, that the here developed approach is not only fully competitive with established MINLP algorithms, but is even able to outperform those regarding global optimization capabilities and cpu runtime performance. Furthermore, the algorithm is able to solve challenging space applications, that are considered here as mixed integer problems for the very first time