Adaptive Ranking Based Constraint Handling for Explicitly Constrained Black-Box Optimization

A novel explicit constraint handling technique for the covariance matrix adaptation evolution strategy (CMA-ES) is proposed. The proposed constraint handling exhibits two invariance properties. One is the invariance to arbitrary element-wise increasing transformation of the objective and constraint functions. The other is the invariance to arbitrary affine transformation of the search space. The proposed technique virtually transforms a constrained optimization problem into an unconstrained optimization problem by considering an adaptive weighted sum of the ranking of the objective function values and the ranking of the constraint violations that are measured by the Mahalanobis distance between each candidate solution to its projection onto the boundary of the constraints. Simulation results are presented and show that the CMA-ES with the proposed constraint handling exhibits the affine invariance and performs similarly to the CMA-ES on unconstrained counterparts.Comment: 9 page

Ortalama-varyans portföy optimizasyonunda genetik algoritma uygulamaları üzerine bir literatür araştırması

Mean-variance portfolio optimization model, introduced by Markowitz, provides a fundamental answer to the problem of portfolio management. This model seeks an efficient frontier with the best trade-offs between two conflicting objectives of maximizing return and minimizing risk. The problem of determining an efficient frontier is known to be NP-hard. Due to the complexity of the problem, genetic algorithms have been widely employed by a growing number of researchers to solve this problem. In this study, a literature review of genetic algorithms implementations on mean-variance portfolio optimization is examined from the recent published literature. Main specifications of the problems studied and the specifications of suggested genetic algorithms have been summarized

Solving the G-problems in less than 500 iterations: Improved efficient constrained optimization by surrogate modeling and adaptive parameter control

Constrained optimization of high-dimensional numerical problems plays an important role in many scientific and industrial applications. Function evaluations in many industrial applications are severely limited and no analytical information about objective function and constraint functions is available. For such expensive black-box optimization tasks, the constraint optimization algorithm COBRA was proposed, making use of RBF surrogate modeling for both the objective and the constraint functions. COBRA has shown remarkable success in solving reliably complex benchmark problems in less than 500 function evaluations. Unfortunately, COBRA requires careful adjustment of parameters in order to do so. In this work we present a new self-adjusting algorithm SACOBRA, which is based on COBRA and capable to achieve high-quality results with very few function evaluations and no parameter tuning. It is shown with the help of performance profiles on a set of benchmark problems (G-problems, MOPTA08) that SACOBRA consistently outperforms any COBRA algorithm with fixed parameter setting. We analyze the importance of the several new elements in SACOBRA and find that each element of SACOBRA plays a role to boost up the overall optimization performance. We discuss the reasons behind and get in this way a better understanding of high-quality RBF surrogate modeling

Evolutionary Synthesis of HVAC System Configurations: Algorithm Development.

This paper describes the development of an optimization procedure for the synthesis of novel heating, ventilating, and air-conditioning (HVAC) system configurations. Novel HVAC system designs can be synthesized using model-based optimization methods. The optimization problem can be considered as having three sub-optimization problems; the choice of a component set; the design of the topological connections between the components; and the design of a system operating strategy. In an attempt to limit the computational effort required to obtain a design solution, the approach adopted in this research is to solve all three sub-problems simultaneously. Further, the computational effort has been limited by implementing simplified component models and including the system performance evaluation as part of the optimization problem (there being no need in this respect to simulation the system performance). The optimization problem has been solved using a Genetic Algorithm (GA), with data structures and search operators that are specifically developed for the solution of HVAC system optimization problems (in some instances, certain of the novel operators may also be used in other topological optimization problems. The performance of the algorithm, and various search operators has been examined for a two-zone optimization problem (the objective of the optimization being to find a system design that minimizes the system energy use). In particular, the performance of the algorithm in finding feasible system designs has been examined. It was concluded that the search was unreliable when the component set was optimized, but if the component set was fixed as a boundary condition on the search, then the algorithm had an 81% probability of finding a feasible system design. The optimality of the solutions is not examined in this paper, but is described in an associated publication. It was concluded that, given a candidate set of system components, the algorithm described here provides an effective tool for exploring the novel design of HVAC systems. (c) HVAC & R journa

Searching the solution space in constructive geometric constraint solving with genetic algorithms

Geometric problems defined by constraints have an exponential number of solution instances in the number of geometric elements involved. Generally, the user is only interested in one instance such that besides fulfilling the geometric constraints, exhibits some additional properties. Selecting a solution instance amounts to selecting a given root every time the geometric constraint solver needs to compute the zeros of a multi valuated function. The problem of selecting a given root is known as the Root Identification Problem. In this paper we present a new technique to solve the root identification problem. The technique is based on an automatic search in the space of solutions performed by a genetic algorithm. The user specifies the solution of interest by defining a set of additional constraints on the geometric elements which drive the search of the genetic algorithm. The method is extended with a sequential niche technique to compute multiple solutions. A number of case studies illustrate the performance of the method.Postprint (published version