Characterization of the optimization problem is a crucial task in many recent optimization research topics (e.g., explainable algorithm performance assessment, and automated algorithm selection and ...configuration). The state-of-the-art approaches use exploratory landscape analysis to represent the optimization problem, where for each one, a set of features is extracted using a set of candidate solutions sampled by a sampling strategy over the whole decision space. This paper proposes a novel representation of continuous optimization problems by encoding the information found in the interaction between an algorithm and an optimization problem. The new problem representation is learned using the information from the states/positions in the optimization run trajectory (i.e., the candidate solutions visited by the algorithm). With the novel representation, the problem can be characterized dynamically during the optimization run, instead of using a set of candidate solutions from the whole decision space that have never been observed by the algorithm. The novel optimization problem representation is called Opt2Vec and uses an autoencoder type of neural network to encode the information found in the interaction between an optimization algorithm and optimization problem into an embedded subspace. The Opt2Vec representation efficiency is shown by enabling different optimization problems to be successfully identified using only the information obtained from the optimization run trajectory.
•Representation learning is applied on each individual population of optimization process trajectory.•The Opt2Vec representations are captured through the algorithm's behavior (its populations).•The Opt2Vec representations are suitable for dynamic problem characterization.•The Opt2Vec representations are invariant to simple transformations (shifting/scaling).•The Opt2Vec representations are scalable over different problem dimensions.
Optimization in dynamic environments is a challenging but important task since many real-world optimization problems are changing over time. Evolutionary computation and swarm intelligence are good ...tools to address optimization problems in dynamic environments due to their inspiration from natural self-organized systems and biological evolution, which have always been subject to changing environments. Evolutionary optimization in dynamic environments, or evolutionary dynamic optimization (EDO), has attracted a lot of research effort during the last 20 years, and has become one of the most active research areas in the field of evolutionary computation. In this paper we carry out an in-depth survey of the state-of-the-art of academic research in the field of EDO and other meta-heuristics in four areas: benchmark problems/generators, performance measures, algorithmic approaches, and theoretical studies. The purpose is to for the first time (i) provide detailed explanations of how current approaches work; (ii) review the strengths and weaknesses of each approach; (iii) discuss the current assumptions and coverage of existing EDO research; and (iv) identify current gaps, challenges and opportunities in EDO.
•An information-sharing strategy is introduced for multi-model prediction methods.•This strategy lets each solution exploit information from the adjacent solutions.•A similarity metric is proposed to ...determine corresponding solutions.•Weighted pointwise prediction method (WPPM) is developed for dynamic optimization.•The superiority of WPPM over existing prediction methods is demonstrated.
Prediction methods are useful tools for dynamic multiobjective optimization (DMO), especially if the changes roughly follow some patterns. Multi-model prediction methods, in particular, may capture different types of change patterns; however, they should address two issues. First, they should define a similarity measure that can correctly find the corresponding Pareto-optimal solutions in two successive time steps. Second, they should be reasonably robust to input errors. This study introduces a new information-sharing strategy to improve the robustness of multi-model prediction methods in which each prediction model utilizes some information from the individual models of adjacent solutions. An adaptive scheme based on the relative distribution of population members is also proposed to utilize this information properly. The efficacy of this strategy in improving the robustness of the multi-model prediction method is demonstrated. Furthermore, this study introduces a similarity metric and thoroughly analyzes it alongside some of the commonly used similarity metrics for DMO. A weighted pointwise prediction method (WPPM) for DMO is then developed using the formulated information-sharing strategy and the proposed variable-based similarity metric. WPPM is compared with other well-known prediction methods on the CEC2018 test suite for DMO, with the numerical results revealing the superiority of WPPM.
In this paper, the problem of finite horizon inverse optimal control (IOC) is investigated, where the quadratic cost function of a dynamic process is required to be recovered based on the observation ...of optimal control sequences. We propose the first complete result of the necessary and sufficient condition for the existence of corresponding standard linear quadratic (LQ) cost functions. Under feasible cases, the analytic expression of the whole solution space is derived and the equivalence of weighting matrices in LQ problems is discussed. For infeasible problems, an infinite dimensional convex problem is formulated to obtain a best-fit approximate solution with minimal control residual. And the optimality condition is solved under a static quadratic programming framework to facilitate the computation. Finally, numerical simulations are used to demonstrate the effectiveness and feasibility of the proposed methods.
This study examined how students' interest, self-efficacy, and perceived difficulty change during a task, how those changes relate to each other, and how they predict performance. Sixth-graders ...(N = 1024) rated their interest, self-efficacy, and perceived difficulty repeatedly during a dynamic problem-solving task. Results from the estimated non-linear and piecewise latent growth curve models showed interest and self-efficacy to decrease, and perceived difficulty first to increase, and then to decrease, over time. The levels of and changes in interest and self-efficacy correlated positively with each other, but negatively with perceived difficulty. Task performance was positively predicted by initial interest and less negative change in self-efficacy, and negatively by initial perceived difficulty and steeper increase in it. The results suggest perceived difficulty to have a distinctive role in the dynamics of task-specific motivation, and on-task changes to be relatively independent of more general motivation and competence.
•Changes in on-task motivation during a dynamic problem-solving task examined•Interest and self-efficacy decreased, perceived difficulty increased during the task•Levels and changes in interest, self-efficacy, and perceived difficulty correlated•Changes in on-task motivation independent of intrinsic value and achievement•Changes in interest and perceived difficulty predicted task performance
In this paper we propose to study wave propagation, transmission and reflection in band-gap mechanical metamaterials via the relaxed micromorphic model. To do so, guided by a suitable variational ...procedure, we start deriving the jump duality conditions to be imposed at surfaces of discontinuity of the material properties in non-dissipative, linear-elastic, isotropic, relaxed micromorphic media. Jump conditions to be imposed at surfaces of discontinuity embedded in Cauchy and Mindlin continua are also presented as a result of the application of a similar variational procedure. The introduced theoretical framework subsequently allows the transparent set-up of different types of micro-macro connections granting the description of both (i) internal connexions at material discontinuity surfaces embedded in the considered continua and, as a particular case, (ii) possible connections between different (Cauchy, Mindlin or relaxed micromorphic) continua. The established theoretical framework is general enough to be used for the description of a wealth of different physical situations and can be used as reference for further studies involving the need of suitably connecting different continua in view of (meta-)structural design. In the second part of the paper, we focus our attention on the case of an interface between a classical Cauchy continuum on one side and a relaxed micromorphic one on the other side in order to perform explicit numerical simulations of wave reflection and transmission. This particular choice is descriptive of a specific physical situation in which a classical material is connected to a phononic crystal. The reflective properties of this particular interface are numerically investigated for different types of possible micro-macro connections, so explicitly showing the effect of different boundary conditions on the phenomena of reflection and transmission. Finally, the case of the connection between a Cauchy continuum and a Mindlin one is presented as a numerical study, so showing that band-gap description is not possible for such continua, in strong contrast with the relaxed micromorphic case.
•The algorithm ranked second at the second international nurse rostering competition.•The approach combines online optimization and the sample average approximation.•The rostering problem is solved ...with a branch-and-price algorithm.•The code of the implementation is open source and available in a public repository.
In this paper, we focus on the problem studied in the second international nurse rostering competition: a personalized nurse scheduling problem under uncertainty. The schedules must be computed week by week over a planning horizon of up to eight weeks. We present the work that the authors submitted to this competition and which was awarded the second prize.
At each stage, the dynamic algorithm is fed with the staffing demand and nurses preferences for the current week and computes an irrevocable schedule for all nurses without knowledge of future inputs. The challenge is to obtain a feasible and near-optimal schedule at the end of the horizon.
The online stochastic algorithm described in this paper draws inspiration from the primal-dual algorithm for online optimization and the sample average approximation, and is built upon an existing static nurse scheduling software. The procedure generates a small set of candidate schedules, rank them according to their performance over a set of test scenarios, and keeps the best one. Numerical results show that this algorithm is very robust, since it has been able to produce feasible and near optimal solutions on most of the proposed instances ranging from 30 to 120 nurses over a horizon of 4 or 8 weeks. Finally, the code of our implementation is open source and available in a public repository.
The cement grinding process requires monitoring of unit power consumption and specific surface area indicators to improve production efficiency and product quality. The strong coupling between ...operational variables necessitates careful adjustment of these variables to prevent production from becoming instability. Furthermore, the continuous and time-dependent nature of the process makes this adjustment particularly challenging. To address this dual dynamic problem, we have developed a multi-objective optimization model, with global optimization as the desired outcome, to optimize unit power consumption and specific surface area. Our optimization algorithm, termed “Optimization Algorithm - Dynamic Search Space and Rolling Time Domain” (OA-DSTR), considers the problem of dynamic production process. First, the algorithm uses a dynamic search space strategy, allowing for changes in the constraint range of the operational variables and introducing a fluctuation coefficient (FC) to measure solution rationality. Second, to deal with the time-dependent problem, we have added a rolling time domain strategy, enabling real-time monitoring of the cement grinding process. The experimental results show that OA-DSTR not only ensures global optimization, but also realizes the tracking of dynamic conditions, improving the stability of the cement grinding process and achieving a lower FC value.
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•A prediction model of energy consumption in cement calcination system is proposed.•An improved prediction algorithm is proposed to predict f-cao.•The multi-objective optimization model of cement calcination system is designed.•A multi-objective optimization algorithm considering dual dynamic problems is proposed.•Achieved the goal of energy saving, quality improvement and system stability.
A reinitialization approach is an effective way of generalizing a static multi-objective optimization method to a dynamic one. It is usually comprised of a prediction operator for predicting the ...approximate location(s) of the optimal solution(s) and a variation operator for enhancing the diversity of the reinitialized solution(s) after a change. While many recent studies have focused on prediction methods, the importance of the variation operator has usually been overlooked. This study systematically explores the effects of the accuracy of the prediction method employed as well as the frequency and severity of the change on the optimal strength of the variation used for reinitialization. Subsequently, it introduces an adaptive variation operator for dynamic multi-objective optimization which can learn the optimal variation strength on-the-fly. To develop this method, firstly, a heredity measure for evolutionary algorithms is formulated to quantify the contribution of each reinitialized solution to the optimization process by measuring the presence of its traits in the final population. Some carefully designed descriptive simulations are performed to explore the capability of the proposed method to learn the optimal variation strength and its sensitivity to the change severity, initial variation strength, and accuracy of the employed prediction method. Finally, the performance of this variation operator on 42 dynamic multi-objective test problems is compared with those of five other popular ones, with numerical comparisons revealing its superior learning capability.
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•Factors impacting the optimal variation strength for reinitialization are analyzed.•A new measure to quantify the contributions of initial solutions is introduced.•A novel method (HBAV) is proposed for adaption of the random variation strength.•The capability of HBAV in learning the optimal variation strength is demonstrated.•HBAV outperforms existing operators for adjusting the random variation strength.
We formulate a relaxed linear elastic micromorphic continuum model with symmetric Cauchy force stresses and curvature contribution depending only on the micro-dislocation tensor. Our relaxed model is ...still able to fully describe rotation of the microstructure and to predict nonpolar size effects. It is intended for the homogenized description of highly heterogeneous, but nonpolar materials with microstructure liable to slip and fracture. In contrast to classical linear micromorphic models, our free energy is not uniformly pointwise positive definite in the control of the independent constitutive variables. The new relaxed micromorphic model supports well-posedness results for the dynamic and static case. There, decisive use is made of new coercive inequalities recently proved by Neff, Pauly and Witsch and by Bauer, Neff, Pauly and Starke. The new relaxed micromorphic formulation can be related to dislocation dynamics, gradient plasticity and seismic processes of earthquakes. It unifies and simplifies the understanding of the linear micromorphic models.
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