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

Learning Anytime Predictions in Neural Networks via Adaptive Loss Balancing

This work considers the trade-off between accuracy and test-time computational cost of deep neural networks (DNNs) via \emph{anytime} predictions from auxiliary predictions. Specifically, we optimize auxiliary losses jointly in an \emph{adaptive} weighted sum, where the weights are inversely proportional to average of each loss. Intuitively, this balances the losses to have the same scale. We demonstrate theoretical considerations that motivate this approach from multiple viewpoints, including connecting it to optimizing the geometric mean of the expectation of each loss, an objective that ignores the scale of losses. Experimentally, the adaptive weights induce more competitive anytime predictions on multiple recognition data-sets and models than non-adaptive approaches including weighing all losses equally. In particular, anytime neural networks (ANNs) can achieve the same accuracy faster using adaptive weights on a small network than using static constant weights on a large one. For problems with high performance saturation, we also show a sequence of exponentially deepening ANNscan achieve near-optimal anytime results at any budget, at the cost of a const fraction of extra computation

Adaptive Pareto Set Estimation for Stochastic Mixed Variable Design Problems

Many design problems require the optimization of competing objective functions that may be too complicated to solve analytically. These problems are often modeled in a simulation environment where static input may result in dynamic (stochastic) responses to the various objective functions. System reliability, alloy composition, algorithm parameter selection, and structural design optimization are classes of problems that often exhibit such complex and stochastic properties. Since the physical testing and experimentation of new designs can be prohibitively expensive, engineers need adequate predictions concerning the viability of various designs in order to minimize wasteful testing. Presumably, an appropriate stochastic multi-objective optimizer can be used to eliminate inefficient designs through the analysis of simulated responses. This research develops an adaptation of Walston’s [56] Stochastic Multi-Objective Mesh Adaptive Direct Search (SMOMADS) and Paciencia’s NMADS [45] based on Kim and de Weck’s [34] Adaptive Weighted Sum (AWS) procedure and standard distance to a reference point methods. This new technique is compared to standard heuristic based methods used to evaluate several real-world design problems. The main contribution of this paper is a new implementation of MADS for Mixed Variable and Stochastic design problems that drastically reduces dependence on subjective decision maker interaction

The Combinational Mutation Strategy of Differential Evolution Algorithm for Pricing Vanilla Options and Its Implementation on Data during Covid-19 Pandemic

Investors always want to know about the profit and the risk that they will be get before buying some assets. Our main focus is getting the profit and the probability of getting that profit using the differential evolution algorithm for vanilla option pricing on data before and during COVID-19 pandemic. Therefore, we model the pricing of an option using a bi-objective optimization problem using data before and during COVID-19 pandemic for one year expiration date. We change this problem into an optimization problem using adaptive weighted sum method. We use metaheuristics algorithm like Differential Evolution (DE) algorithm to solve this bi-objective optimization problems. In this paper, we also use modification of Differential Evolution for getting Pareto optimal solutions on vanilla option pricing for all contract. The algorithm is called Combinational Mutation Strategy of Differential Evolution (CmDE) algorithm. The results of our algorithm are satisfactory close to the real option price in the market data. Besides that, we also compare our result with the Black-Scholes results for validation. The results show that our results can approximate the real market options more accurate than Black-Scholes results. Hence, our bi-objective optimization using Combinational Mutation Strategy of Differential Evolution algorithm can be used to approximate the market real vanilla option pricing before and during COVID-19 pandemic

Joint optimization of power and data transfer in multiuser MIMO systems

We present an approach to solve the nonconvex optimization problem that arises when designing the transmit covariance matrices in multiuser multiple-input multiple-output (MIMO) broadcast networks implementing simultaneous wireless information and power transfer (SWIPT). The MIMO SWIPT problem is formulated as a general multiobjective optimization problem, in which data rates and harvested powers are optimized simultaneously. Two different approaches are applied to reformulate the (nonconvex) multiobjective problem. In the first approach, the transmitter can control the specific amount of power to be harvested by power transfer whereas in the second approach the transmitter can only control the proportion of power to be harvested among the different harvesting users. We solve the resulting formulations using the majorization-minimization (MM) approach. The solution obtained from the MM approach is compared to the classical block-diagonalization (BD) strategy, typically used to solve the nonconvex multiuser MIMO network by forcing no interference among users. Simulation results show that the proposed approach improves over the BD approach both the system sum rate and the power harvested by users. Additionally, the computational times needed for convergence of the proposed methods are much lower than the ones required for classical gradient-based approaches.Peer ReviewedPostprint (author's final draft

Petroleum Refinery Planning Under Uncertainty: A Multiobjective Optimization Approach with Economic and Operational Risk Management

In the current modernized globalization era, crude oil prices have reached a record high of USD 147 per barrel according to the NYMEX exchange on June 2008. It is forecast to spiral upwards (with the current graph trend) to a much higher price level. The current situation of fluctuating high petroleum crude oil prices is affecting the markets and industries worldwide by the uncertainty and volatility of the petroleum industry. As oil refining is the downstream of the petroleum industry, it is increasingly important for refineries to operate at an optimal level in the presence of volatility of crude oil prices. Downstream refineries must assess the potential impact that may affect its optimal profit margin by considering the costs of purchasing the raw material of crude oils and prices of saleable intermediates and products as well as production yields. With optimization, refinery will be able to operate at optimal condition. In this work, we have attempted to solve model formulation concerning the petroleum refinery planning under uncertainty. We use stochastic programming optimization incorporating the weighted sum method as well as the epsilon constraint method to solve the model formulation of the petroleum refinery planning under uncertainty. The objective of this research project is to formulate a deterministic model followed by a two stage stochastic programming model with recourse problem for a petroleum refinery planning. The two stage stochastic risk model is then reformulated using Mean Absolute Deviation as the risk measure. After formulating the stochastic model using Mean Absolute Deviation, the problem is then investigated using the Pareto front solution of efficient frontier of the resulting multiobjective optimization problem by using the Weighted Sum Method as well as the ε-constraint method in order to obtain the Pareto Optimal Curve which generates a wide selection of optimization solutions for our problem. The implementation of the multiobjective optimization problem is then automated to report the model solution by capturing the solution values using the GAMS looping system. Note that some of the major parameters used throughout the formulated stochastic programming model include prices of the raw material crude oil and saleable products, market demands for products, and production yields. The main contribution on this work in the first part is to conduct a further study/research on the implementation of the model formulation in Khor et al. (2008) where the model formulated by Khor et al. (2008) uses variance as the risk measure. The results obtain in the previous paper will be compared with the method in this paper that incorporates Mean Absolute Deviation as the risk measure. To further study the model formulated, the solution obtain is further enhanced using the Weighted Sum Method as well as the Epsilon constraint method to obtain the Pareto Optimal Curve generation. Hence, most of the exposition on the model formulation and solution algorithms are taken directly from the original paper so as to provide the readers with the most accurate information possible

An Improved NSGA-II and its Application for Reconfigurable Pixel Antenna Design

Based on the elitist non-dominated sorting genetic algorithm (NSGA-II) for multi-objective optimization problems, an improved scheme with self-adaptive crossover and mutation operators is proposed to obtain good optimization performance in this paper. The performance of the improved NSGA-II is demonstrated with a set of test functions and metrics taken from the standard literature on multi-objective optimization. Combined with the HFSS solver, one pixel antenna with reconfigurable radiation patterns, which can steer its beam into six different directions (θDOA = ± 15°, ± 30°, ± 50°) with a 5 % overlapping impedance bandwidth (S11 < − 10 dB) and a realized gain over 6 dB, is designed by the proposed self-adaptive NSGA-II

Optimization of electrical energy consumption and level reliability of water supply system

Generally, high operational cost is associated with all water supply system. This is as a result of the high amount of electric energy consumption ascribed to the system due to its components. The water supply system of the Mara-Japan Industrial Institute (MJII), Beranang, Selangor is one of such system that suffers this challenge of high operational cost. In this paper we have applied the use of an Adaptive Weighted Sum Genetic Algorithm to optimize the system operations such that it minimizes the high energy consumption as well as ensuring the overall reliability of the water level in the reservoir. The results obtained from the optimized model of the system show a promising and a significant reduction to the tune of 34.97% in the amount of energy consumed as compared with that of normal operations