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Simultaneous optimization of several physiochemical properties is an important task in the drug design process. Molecule optimization formulated as optimization problems usually provide several conflicting objectives. The number of molecular properties as well as the cost-intensive methods of molecule property prediction are stringent requirements...
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... recombination and mutation rate corresponds to the findings in [10] and is motivated by a suitable bal- ance of exploration and exploitation. Figures 3 and 4 depict the ACV results of the non-dominated solutions (NDS) in each generation identified by COSEA-MO and NSGA-II. The ACV-values are scaled for a better visualization. ...
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... One of the examples is the maximizing performance while minimizing fuel consumption and emission of pollutants of a vehicle (Chang, 2015). Another example is the searching for new remedial drugs in the medical field: maximizing strength of the drug while minimizing synthesis costs and unwanted side effects (Emmerich Michael T. M., 2018;Rosenthal and Borschbach, 2017;van der Horst et al., 2012). There are many other examples that brought the attention of the research community: the minimization of different types of error rates in machine learning (false positives, false negatives) (Wang et al., 2015;Yevseyeva et al., 2013), the optimization of delivery costs and inventory costs in logistics (Geiger and Sevaux, 2011), the optimization of building designs with respect to health, energy efficiency, and cost criteria (Hopfe et al., 2012). ...
Decision trees play a very important role in knowledge representation because of its simplicity and self-explanatory nature. We study the optimization of the parameters of the decision trees to find a shorter as well as more accurate decision tree. Since these two criteria are in conflict, we need to find a decision tree with suitable parameters that can be a trade off between two criteria. Hence, we design two algorithms to build a decision tree with a given threshold of the number of vertices based on the bi-criteria optimization technique. Then, we calculate the local and global misclassification rates for these trees. Our goal is to study the effect of changing the threshold for the bi-criteria optimization of the decision trees. We apply our algorithms to 13 decision tables from UCI Machine Learning Repository and recommend the suitable threshold that can give us more accurate decision trees with a reasonable number of vertices.
... The multi-objective optimization problem (MOP) is to optimize several objectives simultaneously over a common feasible set. MOPs have broad applications in economics [14], finance [5], medical science [50,52], and machine learning [53]. In this paper, we consider the MOP in the form min f (x) := (f 1 (x), . . . ...
The multi-objective optimization is to optimize several objective functions over a common feasible set. Since the objectives usually do not share a common optimizer, people often consider (weakly) Pareto points. This paper studies multi-objective optimization problems that are given by polynomial functions. First, we study the convex geometry for (weakly) Pareto values and give a convex representation for them. Linear scalarization problems (LSPs) and Chebyshev scalarization problems (CSPs) are typical approaches for getting (weakly) Pareto points. For LSPs, we show how to use tight relaxations to solve them, how to detect existence or nonexistence of proper weights. For CSPs, we show how to solve them by moment relaxations. Moreover, we show how to check if a given point is a (weakly) Pareto point or not and how to detect existence or nonexistence of (weakly) Pareto points. We also study how to detect unboundedness of polynomial optimization, which is used to detect nonexistence of proper weights or (weakly) Pareto points.
... Other applications can be found in medicine. For example, when looking for new therapeutic drugs, we maximize a drug's potency while minimizing the cost of synthesis and undesirable side effects [23]. ...
Many different decision problems require taking a compromise between the various goals we want to achieve into account. A specific group of features often decides the state of a given object. An example of such a task is the feature selection that allows increasing the decision’s quality while minimizing the cost of features or the total budget. The work’s main purpose is to compare feature selection methods such as the classical approach, the one-objective optimization, and the multi-objective optimization. The article proposes a feature selection algorithm using the Genetic Algorithm with various criteria, i.e., the cost and accuracy. In this way, the optimal Pareto points for the nonlinear problem of multi-criteria optimization were obtained. These points constitute a compromise between two conflicting objectives. By carrying out various experiments on various base classifiers, it has been shown that the proposed approach can be used in the task of optimizing difficult data.
... When searching for new therapeutic drugs, obviously the potency of the drug is to be maximized. But also the minimization of synthesis costs and the minimization of unwanted side effects are much-needed objectives (van der Horst et al. 2012;Rosenthal and Borschbach 2017). ...
In almost no other field of computer science, the idea of using bio-inspired search paradigms has been so useful as in solving multiobjective optimization problems. The idea of using a population of search agents that collectively approximate the Pareto front resonates well with processes in natural evolution, immune systems, and swarm intelligence. Methods such as NSGA-II, SPEA2, SMS-EMOA, MOPSO, and MOEA/D became standard solvers when it comes to solving multiobjective optimization problems. This tutorial will review some of the most important fundamentals in multiobjective optimization and then introduce representative algorithms, illustrate their working principles, and discuss their application scope. In addition, the tutorial will discuss statistical performance assessment. Finally, it highlights recent important trends and closely related research fields. The tutorial is intended for readers, who want to acquire basic knowledge on the mathematical foundations of multiobjective optimization and state-of-the-art methods in evolutionary multiobjective optimization. The aim is to provide a starting point for researching in this active area, and it should also help the advanced reader to identify open research topics.
de novo Drug Design (dnDD) aims to create new molecules that satisfy multiple conflicting objectives. Since several desired properties can be considered in the optimization process, dnDD is naturally categorized as a many-objective optimization problem (ManyOOP), where more than three objectives must be simultaneously optimized. However, a large number of objectives typically pose several challenges that affect the choice and the design of optimization methodologies. Herein, we cover the application of multi- and many-objective optimization methods, particularly those based on Evolutionary Computation and Machine Learning techniques, to enlighten their potential application in dnDD. Additionally, we comprehensively analyze how molecular properties used in the optimization process are applied as either objectives or constraints to the problem. Finally, we discuss future research in many-objective optimization for dnDD, highlighting two important possible impacts: i) its integration with the development of multi-target approaches to accelerate the discovery of innovative and more efficacious drug therapies and ii) its role as a catalyst for new developments in more fundamental and general methodological frameworks in the field.
The first step in drug design is the identification and optimization of lead molecules for therapeutic and diagnostic interventions. The analysis of molecular properties requires high laboratory evaluation costs. Computer-aided drug design provides effective approaches to optimize molecules with two general aims: firstly, the identification of candidate targets with several optimized physiochemical properties. Secondly, lead libraries have to be build with a broad range of compounds revealing a high genetic diversity among themselves with an at most similar behavior in bioactivity. MOEAs are nowadays established in vitro processes for molecular optimization problems with a continuous complexity increase. Therefore, MOEAs solving multi- and many-objective optimization problems with a suitable balance of convergence and genetic dissimilarity are challenging. For this purpose, a MOEA especially evolved for molecular optimization is enhanced by optionally two balancing survival selection strategies: a Pareto-based strategy is applied on a two-dimensional indicator problem consisting of a convergence and genetic diversity measure. The second strategy uses truncation selection based on a ranking measure referring to the convergence and genetic diversity measure. These configurations are compared to the recently proposed ad-MOEA with a specific environmental survival selection for multi- and many-objective optimization on four molecular optimization problems from 3 up to 6 objectives.
Many interesting search problems can be formulated as bi-objective search problems, that is, search problems where two kinds of costs have to be minimized, for example, travel distance and time for transportation problems. Instead of looking for a single optimal path, we compute a Pareto-optimal frontier in bi-objective search, which is a set of paths in which no two paths dominate each other. Bi-objective search algorithms perform dominance checks each time a new path is discovered. Thus, the efficiency of these checks is key to performance. In this article, we propose algorithms for two kinds of bi-objective search problems. First, we consider the problem of computing the Pareto-optimal frontier of the paths that connect a given start state with a given goal state. We propose Bi-Objective A* (BOA*), a heuristic search algorithm based on A*, for this problem. Second, we consider the problem of computing one Pareto-optimal frontier for each state s of the search graph, which contains the paths that connect a given start state with s. We propose Bi-Objective Dijkstra (BOD), which is based on BOA*, for this problem. A common feature of BOA* and BOD is that all dominance checks are performed in constant time, unlike the dominance checks of previous algorithms. We show in our experimental evaluation that both BOA* and BOD are substantially faster than state-of-the-art bi-objective search algorithms.
The design of a new therapeutic agent is a time-consuming and expensive process. The rise of machine intelligence provides a grand opportunity of expeditiously discovering novel drug candidates through smart search in the vast molecular structural space. In this paper, we propose a new approach called adversarial deep evolutionary learning (ADEL) to search for novel molecules in the latent space of an adversarial generative model and keep improving the latent representation space. In ADEL, a custom-made adversarial autoencoder (AAE) model is developed and trained under a deep evolutionary learning (DEL) process. This involves an initial training of the AAE model, followed by an integration of multi-objective evolutionary optimization in the continuous latent representation space of the AAE rather than the discrete structural space of molecules. By using the AAE, an arbitrary distribution can be provided to the training of AAE such that the latent representation space is set to that distribution. This allows for a starting latent space from which new samples can be produced. Throughout the process of learning, new samples of high quality are generated after each iteration of training and then added back into the full dataset, therefore, allowing for a more comprehensive procedure of understanding the data structure. This combination of evolving data and continuous learning not only enables improvement in the generative model, but the data as well. By comparing ADEL to the previous work in DEL, we see that ADEL can obtain better property distributions. We show that ADEL is able to design high-quality molecular structures which can be further used for virtual and experimental screenings.
Computer-aided drug design is an approach to effectively identify and analyse molecules for therapeutic and diagnostic interventions. Generally, libraries with a broad range of compounds revealing a high genetic diversity with an at most similar behavior in bioactivity have to be created. For this purpose, an evolutionary process for multi- and many-objective Molecular Optimization (MO) has been designed and improved during the past decade. Diversity plays a central role in Evolutionary Algorithms (EAs) to prevent premature convergence to suboptimal solutions and several methods to promote diversity on different levels of an EA have been proposed. The aspect of genetic diversity in MO is a further challenge that has to be controlled and promoted by different strategies on various stages of a problem-specific EA. This work presents an application-specific re-interpretation of different diversity aspects on various stages of an EA for MO. A sophisticated survival selection strategy combining a specific ranking method with application-specific diversity promoting technologies is introduced and benchmarked to the recently proposed many-objective evolutionary algorithm AnD on four molecular optimization problems with 3 up to 6 objectives.
The identification of qualified peptides as ligands for diagnostic and therapeutic interventions requires the solution of multi- and many-objective biochemical optimization problems. A MOEA has been designed for molecular optimization with a combined indicator- and Pareto-based selection strategy that encounters common classification problems of the solutions’ quality with the rise of the problem dimension. Therefore, a sophisticated selection strategy is presented in this work that selects the individuals for the succeeding generation related to two general aspects in biochemical optimization: the first aspect reflects the peptide quality and the second one the genetic dissimilarity among the peptides in a population. The search behavior of this aspect-based selection is compared to the traditional selection on generic 3- to 6-dimensional physiochemical optimization problems and the impact of the reference point in the aspect-based selection is investigated.
