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Abstract-In evolutionary multi-objective optimization, maintaining a good balance between convergence and diversity is particularly crucial to the performance of the evolutionary algorithms. In addition, it becomes increasingly important to incorporate user preferences because it will be less likely to achieve a representative subset of the Pareto optimal solutions using a limited population size as the number of objectives increases. This paper proposes a reference vector guided evolutionary algorithm for many-objective optimization. The reference vectors can not only be used to decompose the original multiobjective optimization problem into a number of single-objective sub-problems, but also to elucidate user preferences to target a preferred subset of the whole Pareto front. In the proposed algorithm, a scalarization approach, termed angle penalized distance, is adopted to balance convergence and diversity of the solutions in the high-dimensional objective space. An adaptation strategy is proposed to dynamically adjust the distribution of the reference vectors according to the scales of the objective functions. Our experimental results on a variety of benchmark test problems show that the proposed algorithm is highly competitive in comparison with five state-of-the-art evolutionary algorithms for many-objective optimization. In addition, we show that reference vectors are effective and cost-efficient for preference articulation, which is particularly desirable for many-objective optimization. Furthermore, a reference vector regeneration strategy is proposed for handling irregular Pareto fronts. Finally, the proposed algorithm is extended for solving constrained many-objective optimization problems.

We describe version 2 of RENCI PowerMon, a device that can be inserted between a computer power supply and the computer's main board to measure power usage at each of the DC power rails supplying the board. PowerMon 2 provides a capability to collect accurate, frequent, and time-correlated measurements. Since the measurements occur after the AC power supply, this approach eliminates power supply efficiency and time-domain filtering perturbations of the power measurements. PowerMon 2 provides detail about the power consumption of the hardware subsystems connected to each of its eight measurement channles. The device fits in an internal 3.5" hard disk drive bay, thus allowing it to be used in a 1U server chassis. It cost less than $150 per unit to fabricate our small quantity of prototypes.

Phenotypic plasticity and related processes (learning, developmental noise) have been proposed to both accelerate and slow down genetically based evolutionary change. While both views have been supported by various mathematical models and simulations, no general predictions have been offered as to when these alternative outcomes should occur. Here we propose a general framework to study the effects of plasticity on the rate of evolution under directional selection. It is formulated in terms of the fitness gain gradient, which measures the effect of a marginal change in the degree of plasticity on the slope of the relationship between the genotypic value of the focal trait and log fitness. If the gain gradient has the same sign as the direction of selection, an increase in plasticity will magnify the response to selection; if the two signs are opposite, greater plasticity will lead to slower response. We use this general result to derive conditions for the acceleration/deceleration under several simple forms of plasticity, including developmental noise. We also show that our approach explains the results of several specific models from the literature and thus provides a unifying framework.Keywords: Baldwin effect, genetic assimilation, learning, plasticity, developmental noise, fitness landscape.The relationship between the genotype and the phenotype is molded by broadly defined phenotypic plasticity. This includes phenomena such as random events during development (developmental noise) and direct effects of the * E-mail: ingo.paenke@aifb.uni-karlsruhe.de. † E-mail: bernhard.sendhoff@honda-ri.de. ‡ Corresponding author; e-mail: tadeusz.kawecki@unifr.ch. environment (such as poor nutrition resulting in small size). It also includes fortuitous interference of environmental factors, with development resulting in qualitatively new phenotypes (e.g., morphological phenocopies produced by heat shock in the classic experiments of Waddington [1952]). Another category consists of adaptive responses that evolved to maximize fitness in a heterogeneous environment, for example, induced defenses against predators or parasites. Finally, phenomena such as learning, intelligence, or the "memory" of vertebrate adaptive immune systems allow an individual to develop, within its lifetime, an adaptive response to a novel challenge, even one never encountered in the evolutionary past of the species. Much theoretical and empirical research in the past two decades has focused on the evolution of those various mechanisms of plasticity.Less attention has been paid to the consequences of those plastic processes for evolution. As plasticity changes the genotype-phenotype map, it will also usually change the relationship between genotype and fitness and thus affect the response to natural or artificial selection. In particular, adaptive plasticity or learning may allow genetically unfit individuals to compensate for the inadequacies of their genotypes and still attain high fitness. As a consequence, the genetic variation for fitness...

To approximate the Pareto front, most existing multiobjective evolutionary algorithms store the non-dominated solutions found so far in the population or in an external archive during the search. Such algorithms often require a high degree of diversity of the stored solutions and only a limited number of solutions can be achieved. By contrast, model-based algorithms can alleviate the requirement on solution diversity and in principle, as many solutions as needed can be generated. This paper proposes a new model-based method for representing and searching non-dominated solutions. The main idea is to construct Gaussian process based inverse models that map all found non-dominated solutions from the objective space to the decision space. These inverse models are then used to create offspring by sampling the objective space. To facilitate inverse modeling, the multivariate inverse function is decomposed into a group of univariate functions, where the number of inverse models is reduced using a random grouping technique. Extensive empirical simulations demonstrate that the proposed algorithm exhibits robust search performance on a variety of medium to high dimensional multiobjective optimization test problems. Additional non-dominated solutions are generated a posteriori using the constructed models to increase the density of solutions in the preferred regions at a low computational cost.