## What is/are Decision Space?

Decision Space - Specifically, in decision space, the union population is partitioned into multiple clusters by using a density-based clustering method, aiming to assist the addition operator to strengthen the population diversity.^{[1]}In CA, the population update strategy adopts a fitness scheme, which is designed according to the change state of population during evolution, combining the convergence of the objective space with the diversity of the decision space.

^{[2]}One clustering is run in decision space to gather nearby solutions, which will classify solutions into multiple local clusters.

^{[3]}In addition, health managers, lacking institutional backing, resources and decision spaces, often must rely on soft power when dealing with health workers to ensure smooth collaboration in care.

^{[4]}This information has the potential to enrich the decision space of the decision maker and supports programmatic transparency, enhanced learning, and a broader level of accountability.

^{[5]}Moreover, we introduce a simple and effective CHT focusing on the exploration of the decision space, the Three Stage Penalty.

^{[6]}We leverage these predictions to provide assistance in two ways: (i) providing a label recommendation and (ii) reducing the labeler’s decision space by focusing their attention on only the most probable labels.

^{[7]}Background Decentralised and evidence-informed health systems rely on managers and practitioners at all levels having sufficient ‘decision space’ to make timely locally informed and locally relevant decisions.

^{[8]}This method dynamically clusters solutions in the decision space after solutions evaluations.

^{[9]}Moreover, a decision-making strategy is proposed to consider the user preference in the decision space.

^{[10]}Addressing such problems is not easy for existing evolutionary multi-objective algorithms (EMOAs) since they require finding solutions with good convergence and diversity in both objective and decision spaces.

^{[11]}In MMOPs, a solution in the objective space may have multiple inverse images in the decision space, which are termed as equivalent solutions.

^{[12]}Our purpose is to propose a new and effective methodology for solving (P) using a branch and bound based technique, in which, at each node of the search tree, new customized bounds are established to delete uninteresting areas from the decision space.

^{[13]}The approximator reduces the computational complexity of the adaptive control problem by parameterising the state and decision space.

^{[14]}Although some multimodal multiobjective evolutionary algorithms have been proposed to handle them, they can quickly converge to the easy-to-find equivalent Pareto optimal solutions, thereby losing their ability to improve solution diversity in decision space and performance in objective space.

^{[15]}Decision space is used to describe the decision-making power devolved to local government.

^{[16]}To further strengthen our understanding regarding CNN’s lack of robustness, a decision space visualisation process is proposed and presented in this work.

^{[17]}In order to get a better set of initial solutions, a population initialization method by mirror partitioning the decision space is given, in which we dynamically modify the sampling probability according to the performance of solutions contained in each sub-domain.

^{[18]}This article introduces a new algorithm for computing the set of supported non-dominated points in the objective space and all the corresponding efficient solutions in the decision space for the multi-objective spanning tree (MOST) problem.

^{[19]}Multimodal multiobjective optimization problems (MMOPs) widely exist in real-world applications, which have multiple equivalent Pareto-optimal solutions that are similar in the objective space but totally different in the decision space.

^{[20]}Considering that the decision space of such problems is usually sparse and has a block-like structure, we propose to use decomposition methods to accelerate the optimization process.

^{[21]}The approach can be applied to convolutional, fully-connected, and module-based deep network structures, in all cases leveraging the high decorrelation of neuron motifs found in the pre-decision space and cross-layer deconv dependency.

^{[22]}Although the zoning search (ZS) can improve the diversity in the decision space, assigning the same computational costs to each search subspace may be wasteful when computational resources are limited, especially on imbalanced problems.

^{[23]}First, through particle flying in the decision space, the problem space characteristic under deterministic environment is fully exploited to provide guidance for robust optimization.

^{[24]}Finally, taking advantage of the current obtained solutions, the new solutions in the decision space are updated via a linear interpolation method.

^{[25]}This control parameter adaptation and improved selection procedure results in controlling population diversity in decision space and identifying potential candidates in objective space, attaining true Pareto-optimal front with better convergence and diversity metrics.

^{[26]}To overcome this limitation, what is needed is a way to systemically explore the decision space of a historical case and then perturb the case by changing assumptions to assess the impact of those changes on the outcome space.

^{[27]}Each effect predominates in a different part of decision space: 1) a positive distractor effect predicts high-value distractors improve decision-making; 2) a negative distractor effect, of the type associated with divisive normalisation models entails decreased accuracy with increased distractor values.

^{[28]}We make the following key innovations in our design: (i) the use of relational features as inputs to the deep neural network approximating the decision space, which enables our algorithm to generalize to diverse network conditions, (ii) the use of packet-centric decisions to transform the routing problem into an episodic task by viewing packets, rather than wireless devices, as reinforcement learning agents, which provides a natural way to propagate and model rewards accurately during learning, and (iii) the use of extended-time actions to model the time spent by a packet waiting in a queue, which reduces the amount of training data needed and allows the learning algorithm to converge more quickly.

^{[29]}In this paper, a novel multimodal optimization evolutionary algorithm is proposed to optimize the decision space based on the minimum free energy to predict the secondary structure of RNA.

^{[30]}Using a lumped transmission circuit model for each anticipated topology and assuming synchrophasor availability at all generator terminals, a convex hull of potential load current perturbations is mapped into a decision space spanned by vectors of measurable current synchrophasors, where set convexity is preserved.

^{[31]}We analyze the concept of global convergence for multiobjective optimization algorithms and propose a convergence criterion based on the Hausdorff distance in the decision space.

^{[32]}ASMOGA uses the archive technique to save the history of the search procedure, so that the maintenance of the diversity in the decision space is satisfied adequately.

^{[33]}This paper explores the development of a simple set of heuristics using an inductive approach that seeks to reduce the decision space and add insight without being overly prescriptive or complicated.

^{[34]}In Phase II iterations, the function evaluation point is chosen from trial points that are predicted to be feasible and nondominated in the neighborhood of a current nondominated point using distance criteria in the objective and decision spaces.

^{[35]}Moreover, its prediction strategies not only predict Pareto-optimal set (PS) by quantile in the decision space but also predict the PF by quantile in objective space and then mapping back to decision space.

^{[36]}Aiming at the uncertainty of the carbon footprint caused by the unknown decision of product material solution, this paper proposes a low carbon design approach that uses the multigraph and colour marking to solve the problem of one edge assigned with multiple weights and the constraint problem of vertex combination in the decision space of product low carbon design.

^{[37]}In the first stage, a number of global searches will be conducted in sequence to explore different sub-spaces of the decision space, and the solution with the maximum uncertainty in the final generation of each global search will be evaluated using the exact expensive problems to improve the accuracy of the approximation on corresponding sub-space.

^{[38]}Simulation-based optimization models allow exploring the decision space and identify design options that best meet the design criteria.

^{[39]}Specifically, this mechanism takes advantage of the statistical differences between different solution sets in the decision space to guide the selection of some crucial decision variables.

^{[40]}Qualitative and quantitative evidence suggests that bureaucratic discretion exists, that is, administrative actions can be found on different ends of a decision space, and that its effects are potentially large.

^{[41]}Meta-heuristic algorithms are good optimization tools which look for decision space via simulating the behavior of animals and providing the possibility for presenting a set of points as a set of problem solutions.

^{[42]}The complexity measures with high variability across the subsamples are selected for posterior pool adaptation, where an evolutionary algorithm optimizes diversity in both complexity and decision spaces.

^{[43]}Although various “soft isolation” approaches, such as niching methods, have been proposed to promote the diversity and find multiple Pareto optimal solutions in the decision space, they may perform poorly on complex MMO problems (MMOPs) due to high environmental selection pressure and complex geometry of Pareto optimal sets (PSs).

^{[44]}The surrogate is used to propose a new sample of the decision vector for comparison with the current best candidate based on two possible criteria: minimize a combination of the surrogate and an inverse weighting distance function to balance between exploitation of the surrogate and exploration of the decision space, or maximize a function related to the probability that the new candidate will be preferred.

^{[45]}In the problem definition component, the user is prompted to define the areas of interest against which the performance metrics will be computed, define the sensor parameters and attach them to specific spacecraft, select which satellite orbital parameters will be added to the decision space of the GA, and specify the range of desired values for each optimization parameter.

^{[46]}In spite of many efforts made a complete model of machine spinning processes, due to its complexity, multidimensionality of the decision space and the present state of knowledge, is unachievable.

^{[47]}Our branch-and-bound is predominantly a decision space search method because the branching is performed on the decision variables, akin to single objective problems, although we also sometimes split gaps and branch in the objective space.

^{[48]}In terms of the inherent interactive mechanism between r-OAS and r-JRP, in which r-OAS generates a decision space for r-JRP and r-JRP then feeds the lowest operational costs back for use in r-OAS decision-making, a bilevel interactive optimization (BIO) is formulated to simultaneously address the two subproblems based on the Stackelberg game.

^{[49]}Then the feature information of decision space at the next time step is obtained using the interior point method.

^{[50]}

## multi objective optimization

Multimodal Multi-objective Optimization Problems (MMOPs) refer to the problems that have multiple Pareto-optimal solution sets in decision space corresponding to the same or similar Pareto-optimal front in objective space.^{[1]}Compared to the LPF design with 1-bit FTS, the 2-bit FTS design may use smaller decision space, take fewer iterations in multi-objective optimization searching, and yet achieve sharper roll-off rate, higher stopband suppression and a wider stopband.

^{[2]}In addition, an information-entropy model is proposed, using Value of Information (VOI) and Transinformation Entropy (TE), in a multi-objective optimization model to relax the computational burden and allow the entire decision space to be explored.

^{[3]}In the multimodal multi-objective optimization problems (MMOPs), at least two equivalent Pareto optimal solutions in decision space with an identical objective value are desired.

^{[4]}To search more Pareto optimal solution set in decision space, this paper uses the non-dominated sorting method in multi-objective optimization problem to perform the research of particle swarm optimization(PSO).

^{[5]}This paper presents a decision space scalability analysis of five PSO-based multi-objective optimization algorithms, namely optimized multi-objective particle swarm op-timization (OMOPSO), speed-constrained multi-objective particle swarm optimization (SMPSO), multi-objective particle swarm optimization with multiple search strategies (MMOPSO), multi-guide particle swarm optimization (MGPSO), and competitive mechanism-based multi-objective particle swarm optimization (CMOPSO) for 24, 50, 100, 500 and 1000 dimensions (decision variables) to see how well each one of the algorithms scales as the number of decision variables is increased.

^{[6]}Equivalent Pareto sets and local Pareto sets in decision space are involved in multimodal multi-objective optimization problems (MMOPs).

^{[7]}In this paper, we propose a surrogate-assisted expensive multi-objective optimization algorithm based on decision space compression.

^{[8]}Multimodal multi-objective optimization problems (MMOPs) involve locating equivalent Pareto optimal solutions in decision space with the same objective values.

^{[9]}In some studies, it is shown that the decision space discretization improves the performance of evolutionary multi-objective optimization (EMO) algorithms on continuous multi-objective test problems.

^{[10]}For the multi-objective optimization problems with complex decision space, the main challenge is how to choose the most suitable operator for the effective search in the complex decision space.

^{[11]}This paper proposes a directional search strategy in decision space by using the characteristics of continuous multi-objective optimization problem to optimize the high-dimensional multi-objective optimization.

^{[12]}The goal of multi-modal multi-objective optimization is to find all Pareto sets in the decision space.

^{[13]}First, in multi-objective optimization, besides the obtained global Pareto optimal solutions, all visited solutions in the evolutionary process are organized in both decision space and objective space.

^{[14]}Comparing to the multi-objective optimization, multimodal multi-objective optimization brings greater challenge since it involves both the decision space and objective space.

^{[15]}

## scale multiobjective optimization

Large-scale multiobjective optimization problems (LMOPs) bring significant challenges for traditional evolutionary operators, as their search capability cannot efficiently handle the huge decision space.^{[1]}Large-scale multiobjective optimization problems (LSMOPs) are challenging for existing approaches due to the complexity of objective functions and the massive volume of decision space.

^{[2]}At each generation, a set of individuals closer to the ideal point is chosen for performing a DS in the decision space, and those nondominated ones of the sampled solutions are used to assist the reproduction to improve the convergence in evolutionary large-scale multiobjective optimization.

^{[3]}

## multimodal multi objective

In the multimodal multi-objective optimization problems (MMOPs), there exists more than one Pareto optimal solutions in the decision space corresponding to the same location on the Pareto front in the objective space.^{[1]}In this article, we present two operators to use in multimodal multi-objective algorithms, namely a modified crowding distance operator and a neighbourhood Polynomial mutation, which take into account the distribution of solution in the decision space at run-time.

^{[2]}

## particle swarm optimization

, a particle swarm optimization (PSO) operator and differential evolution (DE) operator, is designed in iWOF, which aims to provide a robust search ability on finding optimal solutions in a huge decision space.^{[1]}

## Dimensional Decision Space

Signal parameters measured from the damaged ties are compared with those from undamaged/healthy ties to generate two- and four-dimensional decision spaces.^{[1]}Thanks to the powerful generative ability of the GANs, our proposed algorithm is capable of generating promising offspring solutions in high-dimensional decision space with limited training data.

^{[2]}However, the time and space complexity may preclude its use in high-dimensional decision space.

^{[3]}The resulting regret model accommodates preference cycles in a higher-dimensional decision space without violating transitivity.

^{[4]}Moreover, we extended these techniques to handle three-dimensional decision spaces and propose two solutions for visualizing the resulting volume of data points.

^{[5]}A function space-based method is developed to solve the proposed model, which converts the continuous-time problem into a mixed-integer linear programming problem with finite dimensional decision space.

^{[6]}A scalable and computationally efficient function space solution method is proposed that converts the continuous-time problems into mixed integer linear programming problems with finite-dimensional decision space.

^{[7]}In the proposed constraint DMPs, constraints are simply specified in the two-dimensional decision space.

^{[8]}However, the time and space complexity may preclude its use in high-dimensional decision space.

^{[9]},In the present study, some optimization models are built in the two-sided market type and the optimal solutions are found in a three-dimensional decision space.

^{[10]}

## Large Decision Space

OpenCSR is challenging due to a large decision space, and because many questions require implicit multi-hop reasoning.^{[1]}In order to handle complications resulting from a large decision space and complex environmental geometry, two key concepts are adopted: (a) a diffusion wavelet representation of the Markov chain for hierarchical abstraction of the state space; and (b) a desirability function-based representation of the Markov decision process (MDP) to efficiently calculate the optimal policy.

^{[2]}The Gaussian Process based Bayesian learning paradigm is central in the development of active learning approaches balancing exploration/exploitation in uncertain conditions towards effective generalization in large decision spaces.

^{[3]}After introducing implied challenges, a general workflow is proposed, and its components are described in detail, namely (a) an optimization model, which incorporates decisions on multiple domains and scales, taken by different actors of urban planning, (b) the graphical representation of multivariate data allowing to explore results and define new inputs, and (c) a methodology to efficiently capture the large decision space of planners.

^{[4]}These systems share characteristics with multi-agent systems in which a critical challenge is to manage a large decision space that exponentially increases with the number of actors.

^{[5]}In particular, we begin with a relatively large decision space by considering a theoretically continuous space that must be discretized.

^{[6]}

## Way Decision Space

There are two-way and three-way decision spaces that involve multiple information taxonomy.^{[1]}In this process, a major problem was addressed while existence of bipolar information in a three-way decision space.

^{[2]}In this process, a problem is addressed in measuring the bipolar attributes for each component of three–way decision space.

^{[3]}Finally, this paper discusses some applications of hesitant relations in the constructions of decision evaluation functions in three-way decision spaces.

^{[4]}

## Original Decision Space

CEMO-NR employs the community structure of networks to divide the original decision space into multiple small decision spaces, and then any multiobjective EA (MOEA) can be used to search for improved solutions in the reduced decision space.^{[1]}Inspired by the sparsity of multilayer networks, EM2MNR employs the restricted Boltzmann machine to extract low effective features from the original decision space and then decides whether to conduct knowledge transfer on these features.

^{[2]}The original decision space of the community structure is divided using the proposed work.

^{[3]}Different from existing DC-based algorithms that perform decomposition and optimization in the original decision space, EDC first establishes an eigenspace by conducting singular value decomposition on a set of high-quality solutions selected from recent generations.

^{[4]}

## Entire Decision Space

, TSEMO) searches the entire decision space and identifies an approximated Pareto front within a small number of simulations.^{[1]}In addition, an information-entropy model is proposed, using Value of Information (VOI) and Transinformation Entropy (TE), in a multi-objective optimization model to relax the computational burden and allow the entire decision space to be explored.

^{[2]}To conduct the fusion, the support function of “distance-based” classifier is redefined as a class-conditional probability density function, and the source competence of base classifier is estimated by the entropy-based method in validate space and extended to entire decision space using the normalized Gaussian potential function.

^{[3]}

## Complex Decision Space

Further medical applications reviewed include safety equipment, dental implants, and drug delivery systems, with findings suggesting a need for improved design methods to navigate the complex decision space enabled by 3D printing.^{[1]}The relative benefits of using 2D versus 3D techniques for data visualization is a complex decision space, with varying levels of uncertainty and disagreement in both the literature and in practice.

^{[2]}For the multi-objective optimization problems with complex decision space, the main challenge is how to choose the most suitable operator for the effective search in the complex decision space.

^{[3]}

## Huge Decision Space

, a particle swarm optimization (PSO) operator and differential evolution (DE) operator, is designed in iWOF, which aims to provide a robust search ability on finding optimal solutions in a huge decision space.^{[1]}Large-scale multiobjective optimization problems (LMOPs) bring significant challenges for traditional evolutionary operators, as their search capability cannot efficiently handle the huge decision space.

^{[2]}However, poor decision-making speed and robustness of decision-making algorithm lead to a non-optimal communication scheme in huge decision space.

^{[3]}

## Larger Decision Space

While previous adaptive bitrate algorithms (ABR) solely optimize bitrate for ensuring QoE of VOD, live video streaming has a larger decision space, making the optimization problem more difficult to solve.^{[1]}• Across all eight experimental levels, larger decision spaces (more target word choices) led to slower word identification.

^{[2]}

## Optimal Decision Space

The results show that when the funds for environmental governance technological innovation are insufficient, there is an optimal decision space to use green financial loans to implement technological innovation and upgrade, and then achieve the expected economic goals; Under a given level of environmental governance technology, environmental policies affect whether enterprises can make decisions on technological innovation and upgrading of environmental governance; Green financial mechanism will not.^{[1]}This process can be facilitated by the interactive exploration of the near-optimal decision space generated by an energy system optimisation model.

^{[2]}

## Limited Decision Space

While mid-size projects have limited decision space, there is value in better defining where systems strengthening contributions can actually be made.^{[1]}Since the surrogate models solely depend on the given historical data, the optimization algorithm is able to search only in a very limited decision space during offline data-driven optimization.

^{[2]}

## Model Decision Space

Given an adversarial image, firstly we map its reconstructed images during DIP optimization to the model decision space, where cross-boundary images can be detected and on-boundary images can be further localized.^{[1]}The hydro genomic mapping has the capability to locate specific hydro markers in model decision space that are responsible for certain hydro-meteorological responses, leading to both diagnostic and predictive descriptions of the model.

^{[2]}

## Whole Decision Space

CIE utilizes confident itemsets to discretize the whole decision space of a model to smaller subspaces.^{[1]}We propose a validation-based framework to balance the feasibility-optimality tradeoff more efficiently, by leveraging the typical low-dimensional structure of solution paths in these data-driven reformulations instead of estimates based on the whole decision space utilized by past approaches.

^{[2]}

## Called Decision Space

This paper proposes a run-time decision-making method, called Decision Space Explorer, for FPGA-based Systems-on-Chip (SoCs) to support changing workload requirements while simultaneously mitigating unpredictable variations in power budget, die temperature, and hardware resource constraints.^{[1]}This paper provides new Farkas-type results characterizing the inclusion of a given set, called contained set, into a second given set, called container set, both of them are subsets of some locally convex space, called decision space.

^{[2]}

## decision space corresponding

Multimodal Multi-objective Optimization Problems (MMOPs) refer to the problems that have multiple Pareto-optimal solution sets in decision space corresponding to the same or similar Pareto-optimal front in objective space.^{[1]}In multimodal multiobjective optimization problems (MMOOPs), there is more than one Pareto-optimal Set (PS) in the decision space corresponding to the same Pareto Front(PF).

^{[2]}Such featured problems may include multiple Pareto solutions in the decision space corresponding to the same objective value in the objective space, remarkably challenging the conventional solvers.

^{[3]}In the multimodal multi-objective optimization problems (MMOPs), there exists more than one Pareto optimal solutions in the decision space corresponding to the same location on the Pareto front in the objective space.

^{[4]}

## decision space dimension

This has the important advantage that the number of data points needed per iteration scales linearly with the decision space dimension.^{[1]}Unlike various multiobjective optimization algorithms, the performance of the proposed algorithm is greatly dependent on the decision space dimension instead of the number of objectives.

^{[2]}Our approach is evaluated on several synthetic game problems with varying number of players and decision space dimensions.

^{[3]}

## decision space search

Our branch-and-bound is predominantly a decision space search method because the branching is performed on the decision variables, akin to single objective problems, although we also sometimes split gaps and branch in the objective space.^{[1]}Specifically, since one of the proposed algorithms is a decision space search algorithm and the other one is a criterion space search algorithm, one can significantly outperform the other depending on the dimension of decision space and criterion space.

^{[2]}