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We study how to efficiently allocate the infinitesimal divisible resource under auction mechanism in a dynamic way. We propose a Vickrey–Clarke–Groves-type auction mechanism with a 2-D bid which specifies a per unit price and a maximum of the demand. Due to the absence of enough information related to the infinite dimensional valuations of individual players in a single-bid strategy, it is challenging to implement the efficient Nash equilibrium (NE) in a dynamic way. In this paper, we introduce a pair of parameters related to players’ valuations, and design a decentralized dynamic process assisted with this pair of values, such that at each iteration, a single player updates its best bid under a constrained set of demand. Under the proposed auction mechanism, we show the incentive compatibility, efficiency, and uniqueness of the NE. Furthermore, our method is guaranteed to converge to the efficient NE, and it presents the enhanced convergence performance compared with those methods proposed in the literature. Case studies are given to demonstrate the results developed in this paper. [ABSTRACT FROM PUBLISHER]

When solving constrained optimization problems (COPs) by evolutionary algorithms, the search algorithm plays a crucial role. In general, we expect that the search algorithm has the capability to balance not only diversity and convergence but also constraints and objective function during the evolution. For this purpose, this paper proposes a composite differential evolution (DE) for constrained optimization, which includes three different trial vector generation strategies with distinct advantages. In order to strike a balance between diversity and convergence, one of these three trial vector generation strategies is able to increase diversity, and the other two exhibit the property of convergence. In addition, to accomplish the tradeoff between constraints and objective function, one of the two trial vector generation strategies for convergence is guided by the individual with the least degree of constraint violation in the population, and the other is guided by the individual with the best objective function value in the population. After producing offspring by the proposed composite DE, the feasibility rule and the $\boldsymbol {\varepsilon }$ constrained method are combined elaborately for selection in this paper. Moreover, a restart scheme is proposed to help the population jump out of a local optimum in the infeasible region for some extremely complicated COPs. By assembling the above techniques together, a constrained composite DE is proposed. The experiments on two sets of benchmark test functions with various features, i.e., 24 test functions from IEEE CEC2006 and 18 test functions with 10 dimensions and 30 dimensions from IEEE CEC2010, have demonstrated that the proposed method shows better or at least competitive performance against other state-of-the-art methods. [ABSTRACT FROM AUTHOR]

This paper proposes a united-based imperialist competitive algorithm (UICA) for compensatory neural fuzzy systems. The original imperialist competitive algorithm (ICA) comprises numerous empires in the population, and each empire comprises one imperialist and some colonies. Each country represents a feasible solution in the empire, and the more favorable solutions become imperialists, taking over less favorable solutions (i.e., colonies). In the ICA, each colony moves toward its relevant imperialist according to an assimilation policy. This paper proposes a UICA that focuses on this assimilation policy to explore the characteristics of the colonies. The assimilation policy consists of three major parts in this paper. In the first part, a colony searches for the best previous position of the colony. In the second part, the colony faces the best-so-far imperialist. In the third part, the colony moves toward the corresponding imperialist of the colony. The proposed UICA was applied to nonlinear system problems, and the experimental results indicated that the proposed UICA is effective. [ABSTRACT FROM PUBLISHER]

In this paper, we introduce a novel method for the discovery of value functions for Markov decision processes (MDPs). This method, which we call value function discovery (VFD), is based on ideas from the evolutionary algorithm field. VFDs key feature is that it discovers descriptions of value functions that are algebraic in nature. This feature is unique, because the descriptions include the model parameters of the MDP. The algebraic expression of the value function discovered by VFD can be used in several scenarios, e.g., conversion to a policy (with one-step policy improvement) or control of systems with time-varying parameters. The work in this paper is a first step toward exploring potential usage scenarios of discovered value functions. We give a detailed description of VFD and illustrate its application on an example MDP. For this MDP, we let VFD discover an algebraic description of a value function that closely resembles the optimal value function. The discovered value function is then used to obtain a policy, which we compare numerically to the optimal policy of the MDP. The resulting policy shows near-optimal performance on a wide range of model parameters. Finally, we identify and discuss future application scenarios of discovered value functions. [ABSTRACT FROM PUBLISHER]

Multiobjective evolutionary algorithms (MOEAs) have proven their effectiveness and efficiency in solving problems with two or three objectives. However, recent studies show that MOEAs face many difficulties when tackling problems involving a larger number of objectives as their behavior becomes similar to a random walk in the search space since most individuals are nondominated with respect to each other. Motivated by the interesting results of decomposition-based approaches and preference-based ones, we propose in this paper a new decomposition-based dominance relation to deal with many-objective optimization problems and a new diversity factor based on the penalty-based boundary intersection method. Our reference point-based dominance (RP-dominance), has the ability to create a strict partial order on the set of nondominated solutions using a set of well-distributed reference points. The RP-dominance is subsequently used to substitute the Pareto dominance in nondominated sorting genetic algorithm-II (NSGA-II). The augmented MOEA, labeled as RP-dominance-based NSGA-II, has been statistically demonstrated to provide competitive and oftentimes better results when compared against four recently proposed decomposition-based MOEAs on commonly-used benchmark problems involving up to 20 objectives. In addition, the efficacy of the algorithm on a realistic water management problem is showcased. [ABSTRACT FROM AUTHOR]

With the increase in the number of optimization objectives, balancing the convergence and diversity in evolutionary multiobjective optimization becomes more intractable. So far, a variety of evolutionary algorithms have been proposed to solve many-objective optimization problems (MaOPs) with more than three objectives. Most of the existing algorithms, however, find difficulties in simultaneously counterpoising convergence and diversity during the whole evolutionary process. To address the issue, this paper proposes to solve MaOPs via multistage evolutionary search. To be specific, a two-stage evolutionary algorithm is developed, where the convergence and diversity are highlighted during different search stages to avoid the interferences between them. The first stage pushes multiple subpopulations with different weight vectors to converge to different areas of the Pareto front. After that, the nondominated solutions coming from each subpopulation are selected for generating a new population for the second stage. Moreover, a new environmental selection strategy is designed for the second stage to balance the convergence and diversity close to the Pareto front. This selection strategy evenly divides each objective dimension into a number of intervals, and then one solution having the best convergence in each interval will be retained. To assess the performance of the proposed algorithm, 48 benchmark functions with 7, 10, and 15 objectives are used to make comparisons with five representative many-objective optimization algorithms. [ABSTRACT FROM AUTHOR]

Differential evolution is one of the most powerful evolutionary algorithms for single objective optimization problems in the literature. Its application in the multiobjective optimization problems is also very successful, and many kinds of promising multiobjective differential evolution (MODE) algorithms have been proposed in the literature. This paper develops a new variant of MODE with two features. First, a set of personal archives are maintained to evolve the search process instead of a population with a fixed size, and a truncation procedure is used to enhance selection pressure. Second, multiple biased mutation operators incorporating the target solution quality are proposed, and an adaptive selection method is adopted to allocate the mutation operators to solutions. The proposed MODE is referred to as the MODE with personal archive and biased self-adaptive mutation selection (BiasMOSaDE). A set of 31 benchmark multiobjective problems selected from the literature are adopted to evaluate its performance. Computational results illustrate that the proposed BiasMOSaDE is competitive or even superior to several state-of-the-art MODEs in the literature. [ABSTRACT FROM AUTHOR]

In evolutionary computation, balancing the diversity and convergence of the population for multiobjective evolutionary algorithms (MOEAs) is one of the most challenging topics. Decomposition-based MOEAs are efficient for population diversity, especially when the branch partitions the objective space of multiobjective optimization problem (MOP) into a series of subspaces, and each subspace retains a set of solutions. However, a persisting challenge is how to strengthen the population convergence while maintaining diversity for decomposition-based MOEAs. To address this issue, we first define a novel metric to measure the contributions of subspaces to the population convergence. Then, we develop an adaptive strategy that allocates computational resources to each subspace according to their contributions to the population. Based on the above two strategies, we design an objective space partition-based adaptive MOEA, called OPE-MOEA, to improve population convergence, while maintaining population diversity. Finally, 41 widely used MOP benchmarks are used to compare the performance of the proposed OPE-MOEA with other five representative algorithms. For the 41 MOP benchmarks, the OPE-MOEA significantly outperforms the five algorithms on 28 MOP benchmarks in terms of the metric hypervolume. [ABSTRACT FROM AUTHOR]

Nonlinear equation systems (NESs) are ubiquitous, and solving them is an important yet challenging task in numerical computation. Most of the NESs usually contain multiple roots. To locate multiple roots, the use of evolutionary algorithms attracts more attention recently. For the purpose of finding different roots within a limited computational budget in a single run simultaneously, in this article, a hybrid niching-based differential evolution with two archives, referred to as HNDE/2A, is proposed. It can be featured as: 1) two niching techniques, i.e., crowding and speciation, are combined to balance the diversity and convergence; 2) a root archive is used to save the found roots during the run. Additionally, if a root is saved into the root archive, it will be reinitialized immediately to further promote the population diversity; and 3) an inferior offspring archive is presented to utilize the useful information of the inferior offspring. To evaluate the performance of our proposal, 30 problems are chosen as the test suite. Moreover, HNDE/2A is also used to solve two real-world problems. Compared with other algorithms, HNDE/2A yields better results in terms of the root ratio and the success rate with a less computational budget. [ABSTRACT FROM AUTHOR]

Convergence, diversity and feasibility are three important issues when solving constrained multiobjective optimization problems (CMOPs). To deal with the balance among convergence, diversity and feasibility well, this article proposes a cooperative multiobjective evolutionary algorithm with propulsive population (CMOEA-PP) for solving CMOPs. CMOEA-PP has two populations, including propulsive population and normal population, and these two populations work cooperatively. Specifically, propulsive population focuses on convergence. Normal population gives priority to feasibility and is obligated to maintain diversity. To cross through the infeasible region and reach the Pareto front (PF), propulsive population does not consider constraints in the early stage and only considers constraints in the later stage. To further accelerate the speed of convergence, propulsive population only searches for corner solutions and center solutions, while normal population searches for the whole PF. As a result, propulsive population can cross through the infeasible region because of the lack of attention to feasibility. In addition, propulsive population also can guide and accelerate the convergence of the evolutionary process. Comprehensive experiment results on several sets of benchmark problems demonstrate that CMOEA-PP is better than existing state-of-the-art competitors. [ABSTRACT FROM AUTHOR]

Solving constrained multiobjective optimization problems brings great challenges to an evolutionary algorithm, since it simultaneously requires the optimization among several conflicting objective functions and the satisfaction of various constraints. Hence, how to adjust the tradeoff between objective functions and constraints is crucial. In this article, we propose a dynamic selection preference-assisted constrained multiobjective differential evolutionary (DE) algorithm. In our approach, the selection preference of each individual is suitably switching from the objective functions to constraints as the evolutionary process. To be specific, the information of objective function, without considering any constraints, is extracted based on Pareto dominance to maintain the convergence and diversity by exploring the feasible and infeasible regions; while the information of constraint is used based on constrained dominance principle to promote the feasibility. Then, the tradeoff in these two kinds of information is adjusted dynamically, by emphasizing the utilization of objective functions at the early stage and focusing on constraints at the latter stage. Furthermore, to generate the promising offspring, two DE operators with distinct characteristics are selected as components of the search algorithm. Experiments on four test suites including 56 benchmark problems indicate that the proposed method exhibits superior or at least competitive performance, in comparison with other well-established methods. [ABSTRACT FROM AUTHOR]

Quantum-inspired differential evolution (QDE) is an evolutionary algorithm, which can effectively solve complex optimization problems. However, sometimes, it easily leads to premature convergence and low search ability and falls to local optima. To overcome these problems, based on the MSIQDE (improved QDE with multistrategies) algorithm, an enhanced MSIQDE algorithm based on mixing multiple strategies, namely, EMMSIQDE is proposed in this article. In the EMMSIQDE, a new differential mutation strategy of a difference vector is proposed to enhance the search ability and descent ability. Then, a new multipopulation mutation evolution mechanism is designed to ensure the relative independence of each subpopulation and the population diversity. The feasible solution space transformation strategy is used to achieve the optimal solution by mapping the quantum chromosome from a unit space to solution space. Finally, some multidimensional unimodal and multimodal functions are selected to demonstrate the optimization performance of EMMSIQDE. The results demonstrate that the EMMSIQDE is significantly better than the DE, QDE, QGA, and MSIQDE, and has better optimization ability, scalability, efficiency, and stability. [ABSTRACT FROM AUTHOR]

Offspring generation plays an important role in evolutionary multiobjective optimization. However, generating promising candidate solutions effectively in high-dimensional spaces is particularly challenging. To address this issue, we propose an adaptive offspring generation method for large-scale multiobjective optimization. First, a preselection strategy is proposed to select a balanced parent population, and then these parent solutions are used to construct direction vectors in the decision spaces for reproducing promising offspring solutions. Specifically, two kinds of direction vectors are adaptively used to generate offspring solutions. The first kind takes advantage of the dominated solutions to generate offspring solutions toward the Pareto optimal set (PS) for convergence enhancement, while the other kind uses those nondominated solutions to spread the solutions over the PS for diversity maintenance. The proposed offspring generation method can be embedded in many existing multiobjective evolutionary algorithms (EAs) for large-scale multiobjective optimization. Experiments are conducted to reveal the mechanism of our proposed adaptive reproduction strategy and validate its effectiveness. Experimental results on some large-scale multiobjective optimization problems have demonstrated the competitive performance of our proposed algorithm in comparison with five state-of-the-art large-scale EAs. [ABSTRACT FROM AUTHOR]

JADE is a differential evolution (DE) algorithm and has been shown to be very competitive in comparison with other evolutionary optimization algorithms. However, it suffers from the premature convergence problem and is easily trapped into local optima. This article presents a novel JADE variant by incorporating chaotic local search (CLS) mechanisms into JADE to alleviate this problem. Taking advantages of the ergodicity and nonrepetitious nature of chaos, it can diversify the population and thus has a chance to explore a huge search space. Because of the inherent local exploitation ability, its embedded CLS can exploit a small region to refine solutions obtained by JADE. Hence, it can well balance the exploration and exploitation in a search process and further improve its performance. Four kinds of its CLS incorporation schemes are studied. Multiple chaotic maps are individually, randomly, parallelly, and memory-selectively incorporated into CLS. Experimental and statistical analyses are performed on a set of 53 benchmark functions and four real-world optimization problems. Results show that it has a superior performance in comparison with JADE and some other state-of-the-art optimization algorithms. [ABSTRACT FROM AUTHOR]