The facility layout problem (FLP) is a configuration problem where the goal is to determine the most efficient arrangement of interacting departments in a facility so as to optimize the working time or material cost. The departments are usually represented as rectangle objects which location and dimensions that should be optimized. Since the problem is quite complex and very difficult to solve, approximate approaches for this problem have been popular in recent years.In this paper, our goal is to determine the positions and aspect ratios of a number of irregular rectangles so that the transportation cost is minimized. We propose a method using the evolutionary algorithm (EA) based on Levy Flights (LFs) for this problem. The proposed method uses LF to search a new solution on the search space. Recently, methods based on LF have also been shown to be more effective than the based on Random Walk. Since the main operation of EA is mutation, we expect an EA-LF combination to perform well. Experiments on the benchmark problems with the number of departments from 7 to 62 indicate that the proposed method is effective for large scale problems than conventional methods such as genetic algorithms and ant colony optimization.

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In this paper, we describe the IBP+EC which is a Reinforcement Learning (RL) method combining the Instance-Based Policy (IBP) and optimization by Evolution Computation (EC). The IBP+EC has attracted attention as a promising Direct Policy Search for severe problems that required foreseeing, and switching of control law according to a situation. However, the IBP has strong redundancy due to its policy expression, which makes optimization difficult. The main causes of the redundancy are "dependencies between instances" and "inactive instances". In particular, the "inactive instance" is a peculiar problem of the IBP and it is difficult to handle with a general-purpose optimization algorithm. Besides, the IBP needs to tune the number of instances, which is a parameter that significantly affects its performance. In a general control problem, since the optimal number of instances is rarely found out, its tuning is complicated. In this paper, we propose the IBP-CMA as an optimization method specialized for IBP-Optimization to cope with the above difficulties. The IBP-CMA algorithm is based on the (1+1)-CMA-ES which is a general evolutionary computation method for continuous optimization and is an elitist strategy. By the nature of (1+1)-CMA-ES, the IBP-CMA deals with the "dependencies between instances". Moreover, the IBP-CMA copes with the above-mentioned peculiar problem of the IBP by combining the (1+1)-CMA-ES with the mechanism that activates inactive instances and adapts the number of instances. The experiments in RL tasks show that the IBP-CMA performs well without parameter pre-adjustment.

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In this paper we focus on linearly constrained black-box optimization problems. We consider to use the covariance matrix adaptation evolution strategy (CMA-ES) to solve linearly constrained problems. A goodness of the CMA-ES is its invariant properties: invariance to increasing transformation of the objective function and invariance to affine transformation of the search space coordinate. These peroperties make the CMA-ES a state-of-the-art search algorithm for ill-conditioned and nonseparable unconstrained problems. When it is applied to a constrained problem, however, it is coupled with a constraint handling method that often breaks the invariance properties that the CMA-ES exhibits. To fully exploit the performance of the CMA-ES in constrained problems, a constraint handling method needs to have all the following invariance: invariance to arbitrary element-wise increasing transformation of the objective and constraint functions, invariance to affine transformation of the search space, and invariance to redundant constraints. In this paper, we propose a novel linear constraint handling technique with the above-mentioned invariance properties for the CMA-ES. The proposed method virtually transforms a constrained problem into an unconstrained one by adaptive penalization. The penalized fitness is defined as a weighted sum of the ranking on the objective and the ranking on the constraint violations measured by the Mahalanobis distance between each candidate solution to its projection onto the boundary of the constraints. Experimental results show that the CMA-ES with the proposed constraint handling exhibits the above-mentioned invariance properties and performs similarly both on constrained problems and their unconstrained counterpart.

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