Tornado: An Autonomous Chaotic Algorithm for Large Scale Global Optimization

In this paper we propose an autonomous chaotic optimization algorithm, called Tornado, for large scale global optimization problems. The algorithm introduces advanced symmetrization, levelling and fine search strategies for an efficient and effective exploration of the search space and exploitation of the best found solutions. To our knowledge, this is the first accurate and fast autonomous chaotic algorithm solving large scale optimization problems. A panel of various benchmark problems with different properties were used to assess the performance of the proposed chaotic algorithm. The obtained results has shown the scalability of the algorithm in contrast to chaotic optimization algorithms encountered in the literature. Moreover, in comparison with some state-of-the-art meta-heuristics (e.g. evolutionary algorithms, swarm intelligence), the computational results revealed that the proposed Tornado algorithm is an effective and efficient optimization algorithm

Multilevel Design Optimization Under Uncertainty with Application to Product-Material Systems

The main objective of this research is to develop a computational design tool for multilevel optimization of product-material systems under uncertainty. To accomplish this goal, an exponential penalty function (EPF) formulation based on method of multipliers is developed for solving multilevel optimization problems within the framework of Analytical Target Cascading (ATC). The original all-at-once constrained optimization problem is decomposed into a hierarchical system with consistency constraints enforcing the target-response coupling in the connected elements. The objective function is combined with the consistency constraints in each element to formulate an augmented Lagrangian with EPF. The EPF formulation is implemented using double-loop (EPF I) and single-loop (EPF II) coordination strategies and two penalty-parameter-updating schemes. The computational characteristics of the proposed approaches are investigated using different nonlinear convex and non-convex optimization problems. An efficient reliability-based design optimization method, Single Loop Single Vector (SLSV), is integrated with Augmented Lagrangian (AL) formulation of ATC for solution of hierarchical multilevel optimization problems under uncertainty. In the proposed SLSV+AL approach, the uncertainties are propagated by matching the required moments of connecting responses/targets and linking variables present in the decomposed system. The accuracy and computational efficiency of SLSV+AL are demonstrated through the solution of different benchmark problems and comparison of results with those from other optimization methods. Finally, the developed computational design optimization tool is used for design optimization of hybrid multiscale composite sandwich plates with/without uncertainty. Both carbon nanofiber (CNF) waviness and CNF-matrix interphase properties are included in the model. By decomposing the sandwich plate, structural and material designs are combined and treated as a multilevel optimization problem. The application problem considers the minimum-weight design of an in-plane loaded sandwich plate with a honeycomb core and laminated composite face sheets that are reinforced by both conventional continuous fibers and CNF-enhanced polymer matrix. Besides global buckling, shear crimping, intracell buckling, and face sheet wrinkling are also treated as design constraints

Multilevel Design Optimization Under Uncertainty with Application to Product-Material Systems

The main objective of this research is to develop a computational design tool for multilevel optimization of product-material systems under uncertainty. To accomplish this goal, an exponential penalty function (EPF) formulation based on method of multipliers is developed for solving multilevel optimization problems within the framework of Analytical Target Cascading (ATC). The original all-at-once constrained optimization problem is decomposed into a hierarchical system with consistency constraints enforcing the target-response coupling in the connected elements. The objective function is combined with the consistency constraints in each element to formulate an augmented Lagrangian with EPF. The EPF formulation is implemented using double-loop (EPF I) and single-loop (EPF II) coordination strategies and two penalty-parameter-updating schemes. The computational characteristics of the proposed approaches are investigated using different nonlinear convex and non-convex optimization problems. An efficient reliability-based design optimization method, Single Loop Single Vector (SLSV), is integrated with Augmented Lagrangian (AL) formulation of ATC for solution of hierarchical multilevel optimization problems under uncertainty. In the proposed SLSV+AL approach, the uncertainties are propagated by matching the required moments of connecting responses/targets and linking variables present in the decomposed system. The accuracy and computational efficiency of SLSV+AL are demonstrated through the solution of different benchmark problems and comparison of results with those from other optimization methods. Finally, the developed computational design optimization tool is used for design optimization of hybrid multiscale composite sandwich plates with/without uncertainty. Both carbon nanofiber (CNF) waviness and CNF-matrix interphase properties are included in the model. By decomposing the sandwich plate, structural and material designs are combined and treated as a multilevel optimization problem. The application problem considers the minimum-weight design of an in-plane loaded sandwich plate with a honeycomb core and laminated composite face sheets that are reinforced by both conventional continuous fibers and CNF-enhanced polymer matrix. Besides global buckling, shear crimping, intracell buckling, and face sheet wrinkling are also treated as design constraints

Power Load Management as a Computational Market

Power load management enables energy utilities to reduce peak loads and thereby save money. Due to the large number of different loads, power load management is a complicated optimization problem. We present a new decentralized approach to this problem by modeling direct load management as a computational market. Our simulation results demonstrate that our approach is very efficient with a superlinear rate of convergence to equilibrium and an excellent scalability, requiring few iterations even when the number of agents is in the order of one thousand. Aframework for analysis of this and similar problems is given which shows how nonlinear optimization and numerical mathematics can be exploited to characterize, compare, and tailor problem-solving strategies in market-oriented programming

Bat Algorithm: Literature Review and Applications

Bat algorithm (BA) is a bio-inspired algorithm developed by Yang in 2010 and BA has been found to be very efficient. As a result, the literature has expanded significantly in the last 3 years. This paper provides a timely review of the bat algorithm and its new variants. A wide range of diverse applications and case studies are also reviewed and summarized briefly here. Further research topics are also discussed.Comment: 10 page

Algorithm Portfolio for Individual-based Surrogate-Assisted Evolutionary Algorithms

Surrogate-assisted evolutionary algorithms (SAEAs) are powerful optimisation tools for computationally expensive problems (CEPs). However, a randomly selected algorithm may fail in solving unknown problems due to no free lunch theorems, and it will cause more computational resource if we re-run the algorithm or try other algorithms to get a much solution, which is more serious in CEPs. In this paper, we consider an algorithm portfolio for SAEAs to reduce the risk of choosing an inappropriate algorithm for CEPs. We propose two portfolio frameworks for very expensive problems in which the maximal number of fitness evaluations is only 5 times of the problem's dimension. One framework named Par-IBSAEA runs all algorithm candidates in parallel and a more sophisticated framework named UCB-IBSAEA employs the Upper Confidence Bound (UCB) policy from reinforcement learning to help select the most appropriate algorithm at each iteration. An effective reward definition is proposed for the UCB policy. We consider three state-of-the-art individual-based SAEAs on different problems and compare them to the portfolios built from their instances on several benchmark problems given limited computation budgets. Our experimental studies demonstrate that our proposed portfolio frameworks significantly outperform any single algorithm on the set of benchmark problems

Robust Monotonic Optimization Framework for Multicell MISO Systems

The performance of multiuser systems is both difficult to measure fairly and to optimize. Most resource allocation problems are non-convex and NP-hard, even under simplifying assumptions such as perfect channel knowledge, homogeneous channel properties among users, and simple power constraints. We establish a general optimization framework that systematically solves these problems to global optimality. The proposed branch-reduce-and-bound (BRB) algorithm handles general multicell downlink systems with single-antenna users, multiantenna transmitters, arbitrary quadratic power constraints, and robustness to channel uncertainty. A robust fairness-profile optimization (RFO) problem is solved at each iteration, which is a quasi-convex problem and a novel generalization of max-min fairness. The BRB algorithm is computationally costly, but it shows better convergence than the previously proposed outer polyblock approximation algorithm. Our framework is suitable for computing benchmarks in general multicell systems with or without channel uncertainty. We illustrate this by deriving and evaluating a zero-forcing solution to the general problem.Comment: Published in IEEE Transactions on Signal Processing, 16 pages, 9 figures, 2 table

A Constraint-directed Local Search Approach to Nurse Rostering Problems

In this paper, we investigate the hybridization of constraint programming and local search techniques within a large neighbourhood search scheme for solving highly constrained nurse rostering problems. As identified by the research, a crucial part of the large neighbourhood search is the selection of the fragment (neighbourhood, i.e. the set of variables), to be relaxed and re-optimized iteratively. The success of the large neighbourhood search depends on the adequacy of this identified neighbourhood with regard to the problematic part of the solution assignment and the choice of the neighbourhood size. We investigate three strategies to choose the fragment of different sizes within the large neighbourhood search scheme. The first two strategies are tailored concerning the problem properties. The third strategy is more general, using the information of the cost from the soft constraint violations and their propagation as the indicator to choose the variables added into the fragment. The three strategies are analyzed and compared upon a benchmark nurse rostering problem. Promising results demonstrate the possibility of future work in the hybrid approach