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

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

Equity portfolio management with cardinality constraints and risk parity control using multi-objective particle swarm optimization

The financial crisis and the market uncertainty of the last years have pointed out the shortcomings of traditional portfolio theory to adequately manage the different sources of risk of the investment process. This paper addresses the issue by developing an alternative portfolio design, that integrates risk parity into the cardinality constrained portfolio optimization model. The resulting mixed integer programming problem is handled by an improved multi-objective particle swarm optimization algorithm. Three hybrid approaches, based on a repair mechanism and different versions of the constrained-domination principle, are proposed to handle constraints. The efficiency of the algorithm and the effectiveness of the solution approaches are assessed through a set of numerical examples. Moreover, the benefits of adopting the proposed strategy instead of the cardinality constrained mean-variance approach are validated in an out-of-sample experiment

Progress in AI Planning Research and Applications

Planning has made significant progress since its inception in the 1970s, in terms both of the efficiency and sophistication of its algorithms and representations and its potential for application to real problems. In this paper we sketch the foundations of planning as a sub-field of Artificial Intelligence and the history of its development over the past three decades. Then some of the recent achievements within the field are discussed and provided some experimental data demonstrating the progress that has been made in the application of general planners to realistic and complex problems. The paper concludes by identifying some of the open issues that remain as important challenges for future research in planning

Partial Evaluation Strategies for Expensive Evolutionary Constrained Optimization

Constrained optimization problems (COPs) are frequently encountered in real-world design applications. For some COPs, the evaluation of the objective(s) and/or constraint(s) may involve significant computational/temporal/financial cost. Such problems are referred to as expensive COPs (ECOPs). Surrogate modeling has been widely used in conjunction with optimization methods for such problems, wherein the search is partially driven by an approximate function instead of true expensive evaluations. However, for any true evaluation, nearly all existing methods compute all objective and constraint values together as one batch. Such full evaluation approaches may be inefficient for cases where the objective/constraint(s) can be evaluated independently of each other. In this article, we propose and study a constraint handling strategy for ECOPs using partial evaluations. The constraints are evaluated in a sequence determined based on their likelihood of being violated; and the evaluation is aborted if a constraint violation is encountered. Modified ranking strategies are introduced to effectively rank the solutions using the limited information thus obtained, while saving on significant function evaluations. The proposed algorithm is compared with a number of its variants to establish the utility of its key components systematically. Numerical experiments and benchmarking are conducted on a range of mathematical and engineering design problems to demonstrate the efficacy of the approach compared to state-of-The-Art evolutionary optimization approaches