Analysis of Solution Quality of a Multiobjective Optimization-based Evolutionary Algorithm for Knapsack Problem

Multi-objective optimisation is regarded as one of the most promising ways for dealing with constrained optimisation problems in evolutionary optimisation. This paper presents a theoretical investigation of a multi-objective optimisation evolutionary algorithm for solving the 0-1 knapsack problem. Two initialisation methods are considered in the algorithm: local search initialisation and greedy search initialisation. Then the solution quality of the algorithm is analysed in terms of the approximation ratio

CIXL2: A Crossover Operator for Evolutionary Algorithms Based on Population Features

In this paper we propose a crossover operator for evolutionary algorithms with real values that is based on the statistical theory of population distributions. The operator is based on the theoretical distribution of the values of the genes of the best individuals in the population. The proposed operator takes into account the localization and dispersion features of the best individuals of the population with the objective that these features would be inherited by the offspring. Our aim is the optimization of the balance between exploration and exploitation in the search process. In order to test the efficiency and robustness of this crossover, we have used a set of functions to be optimized with regard to different criteria, such as, multimodality, separability, regularity and epistasis. With this set of functions we can extract conclusions in function of the problem at hand. We analyze the results using ANOVA and multiple comparison statistical tests. As an example of how our crossover can be used to solve artificial intelligence problems, we have applied the proposed model to the problem of obtaining the weight of each network in a ensemble of neural networks. The results obtained are above the performance of standard methods

Evaluating MAP-Elites on Constrained Optimization Problems

Constrained optimization problems are often characterized by multiple constraints that, in the practice, must be satisfied with different tolerance levels. While some constraints are hard and as such must be satisfied with zero-tolerance, others may be soft, such that non-zero violations are acceptable. Here, we evaluate the applicability of MAP-Elites to "illuminate" constrained search spaces by mapping them into feature spaces where each feature corresponds to a different constraint. On the one hand, MAP-Elites implicitly preserves diversity, thus allowing a good exploration of the search space. On the other hand, it provides an effective visualization that facilitates a better understanding of how constraint violations correlate with the objective function. We demonstrate the feasibility of this approach on a large set of benchmark problems, in various dimensionalities, and with different algorithmic configurations. As expected, numerical results show that a basic version of MAP-Elites cannot compete on all problems (especially those with equality constraints) with state-of-the-art algorithms that use gradient information or advanced constraint handling techniques. Nevertheless, it has a higher potential at finding constraint violations vs. objectives trade-offs and providing new problem information. As such, it could be used in the future as an effective building-block for designing new constrained optimization algorithms

Decomposition-Based Multiobjective Optimization for Constrained Evolutionary Optimization

Pareto dominance-based multiobjective optimization has been successfully applied to constrained evolutionary optimization during the last two decades. However, as another famous multiobjective optimization framework, decomposition-based multiobjective optimization has not received sufficient attention from constrained evolutionary optimization. In this paper, we make use of decomposition-based multiobjective optimization to solve constrained optimization problems (COPs). In our method, first of all, a COP is transformed into a biobjective optimization problem (BOP). Afterward, the transformed BOP is decomposed into a number of scalar optimization subproblems. After generating an offspring for each subproblem by differential evolution, the weighted sum method is utilized for selection. In addition, to make decomposition-based multiobjective optimization suit the characteristics of constrained evolutionary optimization, weight vectors are elaborately adjusted. Moreover, for some extremely complicated COPs, a restart strategy is introduced to help the population jump out of a local optimum in the infeasible region. Extensive experiments on three sets of benchmark test functions, namely, 24 test functions from IEEE CEC2006, 36 test functions from IEEE CEC2010, and 56 test functions from IEEE CEC2017, have demonstrated that the proposed method shows better or at least competitive performance against other state-of-the-art methods

Bi-Level Optimization Considering Uncertainties of Wind Power and Demand Response

Recently, world-wide power systems have been undergone a paradigm change with increasing penetration of renewable energy. The renewable energy is clean with low operation cost while subject to significant variability and uncertainty. Therefore, integration of renewables presents various challenges in power systems. Meanwhile, to offset the uncertainty from renewables, demand response (DR) has gained considerable research interests because of DR’s flexibility to mitigate the uncertainty from renewables. In this dissertation, various power system problems using bi-level optimization are investigated considering the uncertainties from wind power and demand response. In power system planning, reactive power planning (RPP) under high-penetration wind power is studied in this dissertation. To properly model wind power uncertainty, a multi-scenario framework based on alternating current optimal power flow (ACOPF) considering the voltage stability constraint under the worst wind scenario and transmission N-1 contingency is developed. The objective of RPP in this work is to minimize the VAR investment and the expected generation cost. Benders decomposition is used to solve this model with an upper level problem for VAR allocation optimization and generation cost minimization as a lower problem. Then, several problems related wind power and demand response uncertainties under power market operation are investigated. These include: an efficient and effective method to calculate the LMP intervals under wind uncertainty is proposed; the load serving entities’ strategic bidding through a coupon-based demand response (CBDR) with which a load serving entity (LSE) may participate in the electricity market as strategic bidders by offering CBDR programs to customers; the impact of financial transmission right (FTR) with CBDR programs is also studied from the perspective of LSEs; and the stragegic scheduling of energy storages owned by LSEs considering the impact of charging and discharging on the bus LMP. In these problems, a bi-level optimization framework is presented with various objective functions representing different problems as the upper level problems and the ISO’s economic dispatch (ED) as the lower level problem. The bi-level model is addressed with mathematic program with equilibrium constraints (MPEC) model and mixed-integer linear programming (MILP), which can be easily solved with the available optimization software tool

Towards a comprehensive modeling framework for studying glucose repression in yeast

The yeast Saccharomyces cerevisiae is an important model organism for human health and for industry applications as a cell factory. For both purposes, it has been an important organism for studying glucose repression. Glucose sensing and signaling is a complex biological system, where the SNF1 pathway is the main pathway responsible for glucose repression. However, it is highly interconnected with the cAMP-PKA, Snf3-Rgt2 and TOR pathways. To handle the complexity, mathematical modeling has successfully aided in elucidating the structure, mechanism, and dynamics of the pathway. In this thesis, I aim to elucidate what the effect of the interconnection of glucose repression with sensory and metabolic pathways in yeast is, specifically, how crosstalk influences the signaling cascade; what the main effects of nutrient signaling on the metabolism are and how those are affected by intrinsic stress, such as damage accumulation. Here, I have addressed these questions by developing new frameworks for mathematical modeling. A vector based method for Boolean representation of complex signaling events is presented. The method reduces the amount of necessary nodes and eases the interpretation of the Boolean states by separating different events that could alter the activity of a protein. This method was used to study how crosstalk influences the signaling cascade.To be able to represent a diverse biological network using methods suitable for respective pathways, we also developed two hybrid models. The first is demonstrating a framework to connect signaling pathways with metabolic networks, enabling the study of long-term signaling effects on the metabolism. The second hybrid model is demonstrating a framework to connect models of signaling and metabolism to growth and damage accumulation, enabling the study of how the long-term signaling effects on the metabolism influence the lifespan. This thesis represents a step towards comprehensive models of glucose repression. In addition, the methods and frameworks in this thesis can be applied and extended to other signaling pathways