A Steady-State and Generational Evolutionary Algorithm for Dynamic Multiobjective Optimization

This paper presents a new algorithm, called steady-state and generational evolutionary algorithm, which combines the fast and steadily tracking ability of steady-state algorithms and good diversity preservation of generational algorithms, for handling dynamic multiobjective optimization. Unlike most existing approaches for dynamic multiobjective optimization, the proposed algorithm detects environmental changes and responds to them in a steady-state manner. If a change is detected, it reuses a portion of outdated solutions with good distribution and relocates a number of solutions close to the new Pareto front based on the information collected from previous environments and the new environment. This way, the algorithm can quickly adapt to changing environments and thus is expected to provide a good tracking ability. The proposed algorithm is tested on a number of bi- and three-objective benchmark problems with different dynamic characteristics and difficulties. Experimental results show that the proposed algorithm is very competitive for dynamic multiobjective optimization in comparison with state-of-the-art methods.

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The Effect of Information Utilization: Introducing a Novel Guiding Spark in the Fireworks Algorithm

The fireworks algorithm (FWA) is a competitive swarm intelligence algorithm which has been shown to be very useful in many applications. In this paper, a novel guiding spark (GS) is introduced to further improve its performance by enhancing the information utilization in the FWA. The idea is to use the objective function’s information acquired by explosion sparks to construct a guiding vector (GV) with promising direction and adaptive length, and to generate an elite solution called a GS by adding the GV to the position of the firework. The FWA with GS is called the guided FWA (GFWA). Experimental results show that the GS contributes greatly to both exploration and exploitation of the GFWA. The GFWA outperforms previous versions of the FWA and other swarm and evolutionary algorithms on a large variety of test functions and it is also a useful method for large scale optimization. The principle of the GS is very simple but efficient, which can be easily transplanted to other population-based algorithms.

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Efficient Use of Partially Converged Simulations in Evolutionary Optimization

For many real-world optimization problems, evaluating a solution involves running a computationally expensive simulation model. This makes it challenging to use evolutionary algorithms that usually have to evaluate thousands of solutions before converging. On the other hand, in many cases, even a prematurely stopped run of the simulation may serve as a cheaper, albeit less accurate (low fidelity), estimate of the true fitness value. For evolutionary optimization, this opens up the opportunity to decide about the simulation run length for each individual. In this paper, we propose a mechanism that is capable of learning the appropriate simulation run length for each solution. To test our approach, we propose two new benchmark problems, one simple artificial benchmark function and one benchmark based on a computational fluid dynamics (CFDs) simulation scenario to design a toy submarine. As we demonstrate, our proposed algorithm finds good solutions much more quickly than always using the full CFDs simulation and provides much better solution quality than a strategy of progressively increasing the fidelity level over the course of optimization.

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Artificial Immune System With Local Feature Selection for Short-Term Load Forecasting

In this paper, a new forecasting model based on artificial immune system (AIS) is proposed. The model is used for short-term electrical load forecasting as an example of forecasting time series with multiple seasonal cycles. Artificial immune system learns to recognize antigens (AGs) representing two fragments of the time series: 1) fragment preceding the forecast (input vector) and 2) forecasted fragment (output vector). Antibodies as recognition units recognize AGs by selected features of input vectors and learn output vectors. In the test procedure, new AG with only input vector is recognized by some antibodies (ABs). Its output vector is reconstructed from activated ABs. The unique feature of the proposed AIS is the embedded property of local feature selection. Each AB learns in the clonal selection process its optimal subset of features (a paratope) to improve its recognition and prediction abilities. In the simulation studies the proposed model was tested on real power system data and compared with other AIS-based forecasting models as well as neural networks, autoregressive integrated moving average, and exponential smoothing. The obtained results confirm good performance of the proposed model.

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Ranking Vectors by Means of the Dominance Degree Matrix

In multi-/many-objective evolutionary algorithms (MOEAs), there are varieties of vector ranking schemes, including nondominated sorting, dominance counting, and so on. Usually, these vector ranking schemes in the classical MOEAs are of high computational complexity. Thus, in recent years, many researchers put emphasis on the further improvement of the computational complexity of the vector ranking schemes. In this paper, we propose the dominance degree matrix for a set of vectors and design a fast method to construct this new data structure, which requires ${O}$ (mNlog ${N}$ ) comparisons on average. The dominance degree matrix is constructed based on the properties of Pareto domination, and it can convert the dominance comparison into counting the number of special element pairs. Based on the dominance degree matrix, we develop a new and efficient implementation of nondominated sorting called dominance degree approach for nondominated sorting (DDA-NS), which has an average time complexity of ${O}$ (mN $^{2}$ ) but only requires ${O}$ (mNlog ${N}$ ) objective function value comparisons on average. Empirical results demonstrate that DDA-NS clearly outperforms six other representative approaches for nondominated sorting in most cases and DDA-NS performs well when dealing with large-size and many-objective populations. In addition, we also use the dominance degree matrix to form a new method for calculating the dominance strength for Strength Pareto Evolutionary Algorithm (SPEA)2, which greatly –
mproves the efficiency of the naive calculation method in SPEA2. Experiments on benchmark problems show that the Nondominated Sorting Genetic Algorithm (NSGA)-II and NSGA-III framework embedding DDA-NS and the SPEA2 framework embedding the new method of calculating the dominance strength indeed achieve the improvement of the runtime.

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Table of contents

Presents the table of contents for this issue of the publication.

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Continuous Dynamic Constrained Optimization With Ensemble of Locating and Tracking Feasible Regions Strategies

Dynamic constrained optimization problems (DCOPs) are difficult to solve because both objective function and constraints can vary with time. Although DCOPs have drawn attention in recent years, little work has been performed to solve DCOPs with multiple dynamic feasible regions from the perspective of locating and tracking multiple feasible regions in parallel. Moreover, few benchmarks have been proposed to simulate the dynamics of multiple disconnected feasible regions. In this paper, first, the idea of tracking multiple feasible regions, originally proposed by Nguyen and Yao, is enhanced by specifically adopting multiple subpopulations. To this end, the dynamic species-based particle swam optimization (DSPSO), a representative multipopulation algorithm, is adopted. Second, an ensemble of locating and tracking feasible regions strategies is proposed to handle different types of dynamics in constraints. Third, two benchmarks are designed to simulate the DCOPs with dynamic constraints. The first benchmark, including two variants of G24 (called G24v and G24w), could control the size of feasible regions. The second benchmark, named moving feasible regions benchmark (MFRB), is highly configurable. The global optimum of MFRB is calculated mathematically for experimental comparisons. Experimental results on G24, G24v, G24w, and MFRB show that the DSPSO with the ensemble of strategies performs significantly better than the original DSPSO and other typical algorithms.

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Member Get-A-Member (MGM) Program

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Necessary and Sufficient Conditions for Surrogate Functions of Pareto Frontiers and Their Synthesis Using Gaussian Processes

This paper introduces necessary and sufficient conditions that surrogate functions must satisfy to properly define frontiers of nondominated solutions in multiobjective optimization (MOO) problems. These new conditions work directly on the objective space, and thus are agnostic about how the solutions are evaluated. Therefore, real objectives or user-designed objectives’ surrogates are allowed, opening the possibility of linking independent objective surrogates. To illustrate the practical consequences of adopting the proposed conditions, we use Gaussian processes (GPs) as surrogates endowed with monotonicity soft constraints and with an adjustable degree of flexibility, and compare them to regular GPs and to a frontier surrogate method in the literature that is the closest to the method proposed in this paper. Results show that the necessary and sufficient conditions proposed here are finely managed by the constrained GP, guiding to high-quality surrogates capable of suitably synthesizing an approximation to the Pareto frontier in challenging instances of MOO, while an existing approach that does not take the theory proposed in consideration defines surrogates which greatly violate the conditions to describe a valid frontier.

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Structured Memetic Automation for Online Human-Like Social Behavior Learning

Meme automaton is an adaptive entity that autonomously acquires an increasing level of capability and intelligence through embedded memes evolving independently or via social interactions. This paper begins a study on memetic multiagent system (MeMAS) toward human-like social agents with memetic automaton. We introduce a potentially rich meme-inspired design and operational model, with Darwin’s theory of natural selection and Dawkins’ notion of a meme as the principal driving forces behind interactions among agents, whereby memes form the fundamental building blocks of the agents’ mind universe. To improve the efficiency and scalability of MeMAS, we propose memetic agents with structured memes in this paper. Particularly, we focus on meme selection design where the commonly used elitist strategy is further improved by assimilating the notion of like-attracts-like in the human learning. We conduct experimental study on multiple problem domains and show the performance of the proposed MeMAS on human-like social behavior.

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