Set Of Candidate Solutions Research Articles

Stochastic global optimization algorithms: A systematic formal approach

Up to now, different algorithmic methods have been developed to find ’good’ solutions (near to the optimal solution) for global optimization problems that cannot be solved using analytical methods. In particular, algorithmic methods such as differential evolution, evolutionary algorithms, and hill climbing belong to the class of Stochastic Global Optimization Algorithms (SGoals). In general, an SGoal iteratively applies stochastic operations to a set of candidate solutions (population), following, in some cases, a heuristic/metaheuristic. Although some research works have tried to formalize SGoals using Markov kernels, such formalization is not general and sometimes is blurred. In this paper, we propose a comprehensive, systematic and formal approach for studying SGoals. First, we present concepts of probability theory that are required to perform such formalization and we demonstrate that the swapping, sorting, and permutation functions, among others, can be represented by Markov kernels. Then, we introduce the joint Markov kernel as a way of characterizing the combination of stochastic methods. Next, we define the optimization space, a σ-algebra that contains ϵ-optimal states, and develop Markov kernels for stochastic methods like swapping, sorting and permutation. Finally, we introduce sufficient convergence conditions for SGoals and present some popular SGoals in terms of the developed theory.

Likelihood-based offline map matching of GPS recordings using global trace information

In batch map matching the objective is to derive from a time series of position data the sequence of road segments visited by the traveler for posterior analysis. Taking into account the limited accuracy of both the map and the measurement devices several different movements over network links may have generated the observed measurements. The set of candidate solutions can be reduced by adding assumptions about the traveller’s behavior (e.g. respecting speed limits, using shortest paths, etc.). The set of feasible assumptions however, is constrained by the intended posterior analysis of the link sequences produced by map matching. This paper proposes a method that only uses the spatio-temporal information contained in the input data (GPS recordings) not reduced by any additional assumption.The method partitions the trace of GPS recordings so that all recordings in a part are chronologically consecutive and match the same set of road segments. Each such trace part leads to a collection of partial routes that can be qualified by their likelihood to have generated the trace part. Since the trace parts are chronologically ordered, an acyclic directed graph can be used to find the best chain of partial routes. It is used to enumerate candidate solutions to the map matching problem.Qualification based on behavioral assumptions is added in a separate later stage. Separating the stages helps to make the underlying assumptions explicit and adaptable to the purpose of the map matched results. The proposed technique is a multi-hypothesis technique (MHT) that does not discard any hypothesized path until the second stage.A road network extracted from OpenStreetMap (OSM) is used. In order to validate the method, synthetic realistic GPS traces were generated from randomly generated routes for different combinations of device accuracy and recording period. Comparing the base truth to the map matched link sequences shows that the proposed technique achieves a state of the art accuracy level.

Stochastic decision optimisation based on deterministic approximations of processes described as closed-form arithmetic simulation

We propose an efficient one-stage stochastic optimisation algorithm for the problem of finding process controls that minimise the expectation of cost while satisfying multiple deterministic and stochastic feasibility constraints with a given high probability. The proposed algorithm is based on a series of deterministic approximations to produce a candidate solution set and on a refinement step using stochastic simulations with optimal simulation budget allocation. We conduct an experimental study for a real-world manufacturing service network, which shows that the proposed algorithm significantly outperforms four popular simulation-based stochastic optimisation algorithms.

An adjustable sample average approximation algorithm for the stochastic production‐inventory‐routing problem

We consider a stochastic single item production‐inventory‐routing problem with a single producer, multiple clients, and multiple vehicles. At the clients, demand is allowed to be backlogged incurring a penalty cost. Demands are considered uncertain. A recourse model is presented, and valid inequalities are introduced to enhance the model. A new general approach that explores the sample average approximation (SAA) method is introduced. In the sample average approximation method, several sample sets are generated and solved independently in order to obtain a set of candidate solutions. Then, the candidate solutions are tested on a larger sample, and the best solution is selected among the candidates. In contrast to this approach, called static, we propose an adjustable approach that explores the candidate solutions in order to identify common structures. Using that information, part of the first‐stage decision variables is fixed, and the resulting restricted problem is solved for a larger size sample. Several heuristic algorithms based on the mathematical model are considered within each approach. Computational tests based on randomly generated instances are conducted to test several variants of the two approaches. The results show that the new adjustable SAA heuristic performs better than the static one for most of the instances.

A Flocking-Based Approach for Distributed Stochastic Optimization

In recent years, the paradigm of cloud computing has emerged as an architecture for computing that makes use of distributed (networked) computing resources. In this paper, we consider a distributed computing algorithmic scheme for stochastic optimization, which relies on modest communication requirements among processors and most importantly, does not require synchronization. Specifically, we analyze a scheme with N > 1 independent threads each implementing a stochastic gradient algorithm. The threads are coupled via a perturbation of the gradient (with attractive and repulsive forces) in a similar manner to mathematical models of flocking, swarming, and other group formations found in nature with mild communication requirements. When the objective function is convex, we show that a flocking-like approach for distributed stochastic optimization provides a noise reduction effect similar to that of a centralized stochastic gradient algorithm based upon the average of N gradient samples at each step. The distributed nature of flocking makes it an appealing computational alternative. We show that when the overhead related to the time needed to gather N samples and synchronization is not negligible, the flocking implementation outperforms a centralized stochastic gradient algorithm based upon the average of N gradient samples at each step. When the objective function is not convex, the flocking-based approach seems better suited to escape locally optimal solutions due to the repulsive force that enforces a certain level of diversity in the set of candidate solutions. Here again, we show that the noise reduction effect is similar to that associated to the centralized stochastic gradient algorithm based upon the average of N gradient samples at each step.

Complexity of min–max–min robustness for combinatorial optimization under discrete uncertainty

We consider combinatorial optimization problems with uncertain linear objective functions. In the min–max–min robust optimization approach, a fixed number k of feasible solutions is computed such that the respective best of them is optimal in the worst case. The idea is to calculate the set of candidate solutions in a potentially expensive preprocessing phase and then select the best solution out of this set in real-time, once the actual scenario is known. In this paper, we investigate the complexity of the resulting min–max–min problem in the case of discrete uncertainty, as well as its connection to the classical min–max robust counterpart, for many classical combinatorial optimization problems. Essentially, it turns out that the min–max–min problem is not harder to solve than the min–max problem, while producing much better solutions in general for larger k. In particular, this approach may mitigate the so-called price of robustness, making it an attractive alternative to the classical robust optimization approach in many practical applications.

A novel volumetric criterion for optimal shape matching of surfaces for protein-protein docking

AbstractThe problem of molecular docking is to predict whether two given molecules bind together to interact. A shape-based algorithm is proposed for predictive docking by noting that shape complementarity between their outer surfaces is necessary for two molecules to bind. A methodology with five stages has been developed to find the pose in which the shape complementarity is maximum. It involves surface generation, segmentation, parameterization, shape matching, and filtering and scoring. The most significant contribution of this paper is the novel scoring function called ‘Normalized Volume Mismatch’ which evaluates the matching between a pair of surface patches efficiently by measuring the gap or solid volume entrapped between two patches of a pair of proteins when they are placed one against the other at a contact point. After the evaluation, it is found that, with local shape complementarity as the only criterion, the algorithm is able to predict a conformation close to the exact one, in case of known docking conformations, and also rank the same among the top 40 solutions. This is remarkable considering the fact that many existing docking methods fail to rank a near-native conformation among top 50 solutions. The shape-based approaches are used for the initial stage of docking to identify a small set of candidate solutions to be investigated further with exhaustive energy studies etc. The ability of capturing the correct conformation as highly ranked among top few candidate solutions is the most valuable facet of this new predictive docking algorithm.Highlights A new rigid-body docking algorithm is proposed for protein–protein docking. An approach using techniques of cad/cam for a problem in biology is presented. Unlike many existing ones, a volume based scoring criterion is proposed. The new criteria can capture even multiple possible docking conformation. Entire automatic docking procedures is based on shape complementarity only.

An improved Opposition-Based Sine Cosine Algorithm for global optimization

A new method to solve global optimization and engineering problems called OBSCA.The proposed method improves the SCA by using opposite-based learning.We apply the OBSCA over mathematical benchmark functions.We test OBSCA in engineering optimization problems.Comparisons support the improvement on the performance of OBCSA. Real life optimization problems require techniques that properly explore the search spaces to obtain the best solutions. In this sense, it is common that traditional optimization algorithms fail in local optimal values. The Sine Cosine Algorithms (SCA) has been recently proposed; it is a global optimization approach based on two trigonometric functions. SCA uses the sine and cosine functions to modify a set of candidate solutions; such operators create a balance between exploration and exploitation of the search space. However, like other similar approaches, SCA tends to be stuck into sub-optimal regions that it is reflected in the computational effort required to find the best values. This situation occurs due that the operators used for exploration do not work well to analyze the search space. This paper presents an improved version of SCA that considers the opposition based learning (OBL) as a mechanism for a better exploration of the search space generating more accurate solutions. OBL is a machine learning strategy commonly used to increase the performance of metaheuristic algorithms. OBL considers the opposite position of a solution in the search space. Based on the objective function value, the OBL selects the best element between the original solution and its opposite position; this task increases the accuracy of the optimization process. The hybridization of concepts from different fields is crucial in intelligent and expert systems; it helps to combine the advantages of algorithms to generate more efficient approaches. The proposed method is an example of this combination; it has been tested over several benchmark functions and engineering problems. Such results support the efficacy of the proposed approach to find the optimal solutions in complex search spaces.

Predictive Control with On-Off actuators of Partially Fading Memory Systems

This paper presents a new algorithm for the predictive control of systems with on-off actuators that it is tailored for systems in which part of the state vector depends only slightly on past values of the control signal beyond a certain t — L time instant. An example of this is a system with both slow and fast stable dynamics, where the fast ones vanishes after a certain time while the slow dynamics are still influencing the transient state. The algorithm is based on an iterative procedure that constructs a set of candidate solutions to the predictive control problem. The size of the candidate solutions set is reduced from 2N to a user specified value M that can be set accordingly to the computing capabilities of the machine in which the algorithm is to be implemented. The algorithm considers nonlinear systems and although the solution is suboptimal, the approximation error is small in practice and reduces with higher M values. The results are illustrated with a simulated example.

A multiobjective robust controller synthesis approach aided by multicriteria decision analysis

This paper proposes a methodology for robust dynamic output-feedback control synthesis of uncertain linear systems represented by polytopic models. This control problem results in a semi-infinite optimization problem. The proposed synthesis procedure improves a previous two-step procedure, composed of synthesis and analysis, by employing both a multiobjective evolutionary algorithm (MOEA) and a multiple criteria decision making (MCDM) strategy in the synthesis step. The analysis stage is performed via a Branch and Bound (B&B) algorithm, enabling the validation of the former step. In the proposed multiobjective approach, the project aim is to meet the specifications of (i) reference signal tracking response, (ii) disturbance rejection and (iii) measurement noise attenuation. The project specifications are quantified in terms of H∞ and H2 norms of closed-loop transfer functions. Essentially, this technique combines the flexibility of a dedicated MOEA together with the minimax semi-infinite programming problem. Since a MOEA evolves a set of candidate solutions in parallel, the suggested strategy provides a diverse set of controller designs, which is very useful for an a posteriori decision-making process. A proposed multicriteria decision-aid strategy is employed, in addition, as a controller design tool, aiming to incorporate the decision-maker preferences throughout the process, which (i) enables a guided evolutionary search to a trade-off region (of solutions) of practical interest and (ii) assists the definition of an adequate final controller, characterized by a reasonable practical trade-off concerning the criteria. The application of the suggested framework is illustrated on three case studies in order to demonstrate the effectiveness of the method presented.

Identifying a Set of Key Members in Social Networks Using SDP-Based Stochastic Search and Integer Programming Algorithms

This paper presents two semi-definite programming (SDP) based methods to solve the Key Player Problem (KPP). The KPP is to identify a set of [Formula: see text] nodes (i.e., key players) from a social network of size [Formula: see text] such that the number of nodes connected to these [Formula: see text] nodes is maximized. The KPP has applications in social diffusion and products adoption as it helps maximizing information diffusion and impact. We first formulate the KPP as an integer program (IP) and then convert it into an SDP formulation, which can be solved efficiently and produce a set of high quality candidate solutions. We develop an IP-based algorithm and a stochastic search (greedy) algorithm to find the final solution for the KPP. We compare our algorithms with existing methods in small and large networks with different network structures, including random graph, scale-free network, and community-based scale-free network (CSN). Computational results show that our algorithms are more efficient in solving the KPP in all networks. In addition, we examine how the network structure influences the nodes coverage. It is found that CSNs allow the highest nodes coverage due to their community and scale-free structure.

Early-stage decision making approach for the selection of optimally integrated biorefinery processes

Lignocellulosic biorefineries are the best non-petroleum alternatives for a sustainable development. In the biorefinery process design, it is important to implement an algorithm that allows systematic generation, evaluation of energy conversion chains and making comparison of different pathways, ranking them according to different performance criteria. To achieve these goals, a methodology has been proposed to systematically define an ordered set of solutions using mixed integer linear programming models with integer cut constraints. In this study, we apply a systematic approach which adopts thermo-environomic optimization together with heat integration to assess the economic performance, environmental impact and energy requirement of several process options. Both sugars and syngas platforms are compared considering multiple products (energy services, valuable chemicals, fuels). A superstructure of different processes is developed and heat recovery potentials in the systems are analyzed using pinch analysis. Different pathways are evaluated and ranked according to different objective functions to understand the best combination of products and the synergies between them. Our results provide a set of candidate solutions according to minimum total cost and environmental impact as objective functions, considering benefit of heat integration between different pathways to obtain energy efficient biorefinery systems with improved process economics and reduced environmental impacts.

Genetic scatter search algorithm to solve the one-commodity pickup and delivery vehicle routing problem

PurposeIn this paper, the author introduces a new variant of the pickup and delivery transportation problem, where one commodity is collected from many pickup locations to be delivered to many delivery locations within pre-specified time windows (one–to many–to many). The author denotes to this new variant as the 1-commodity pickup-and-delivery vehicle routing problem with soft time windows (1-PDVRPTW).Design/methodology/approachThe author proposes a hybrid genetic algorithm and a scatter search to solve the 1-PDVRPTW. It proposes a new constructive heuristic to generate the initial population solution and a scatter search (SS) after the crossover and mutation operators as a local search. The hybrid genetic scatter search replaces two steps in SS with crossover and mutation, respectively.FindingsSo, the author proposes a greedy local search algorithm as a metaheuristic to solve the 1-PDVRPTW. Then, the author proposes to hybridize the metaheuristic to solve this variant and to make a good comparison with solutions presented in the literature.Originality/valueThe author considers that this is the first application in one commodity. The solution methodology based on scatter search method combines a set of diverse and high-quality candidate solutions by considering the weights and constraints of each solution.

A Leukocyte Detection Technique in Blood Smear Images Using Plant Growth Simulation Algorithm

For quite some time, the analysis of leukocyte images has drawn significant attention from the fields of medicine and computer vision alike where various techniques have been used to automate the manual analysis and classification of such images. Analysing such samples manually for detecting leukocytes is time-consuming and prone to error as the cells have different morphological features. Therefore, in order to automate and optimize the process, the nature-inspired Plant Growth Simulation Algorithm (PGSA) has been applied in this paper. An automated detection technique of white blood cells embedded in obscured, stained and smeared images of blood samples has been presented in this paper which is based on a random bionic algorithm and makes use of a fitness function that measures the similarity of the generated candidate solution to an actual leukocyte. As the proposed algorithm proceeds the set of candidate solutions evolves, guaranteeing their fit with the actual leukocytes outlined in the edge map of the image. The experimental results of the stained images and the empirical results reported validate the higher precision and sensitivity of the proposed method than the existing methods. Further, the proposed method reduces the feasible sets of candidate points in each iteration, thereby decreasing the required run time of load flow, objective function evaluation, thus reaching the goal state in minimum time and within the desired constraints.

A multi-objective evolutionary algorithm for multi-period dynamic emergency resource scheduling problems

The resource distribution in post-disaster is an important part of emergency resource scheduling. In this paper, we first design a multi-objective optimization model for multi-period dynamic emergency resource scheduling (ERS) problems. Then, using the framework of multi-objective evolutionary algorithm based on decomposition (MOEA/D), an MOEA is proposed to solve this model. In the proposed algorithm, new evolutionary operators are designed with the intrinsic properties of multi-period dynamic ERS problems in mind. The experimental results show that the proposed algorithm can get a set of better candidate solutions than the non-dominated sorting genetic algorithm II (NSGA-II).

Fixed-time traffic signal optimization using a multi-objective evolutionary algorithm and microsimulation of urban networks

Large cities have been facing serious problems in the management of traffic, owing to the increasing number of vehicles and pedestrians. Traffic engineering is essential in managing traffic and improving urban mobility. This paper deals with the problem of fixed-time signal programming on traffic networks. A new bi-objective optimization model is proposed to maximize the average and minimize the variance of the vehicle speeds in the network. Although the first function is commonly discussed in the literature, the second one is novel, and its aim is to provide flow balance along the network. This combination of functions is optimized by the Memory-Based Variable-Length Nondominated Sorting Genetic Algorithm 2 (MBVL-NSGA2), which avoids the revaluation of candidate solutions. This approach was validated through experiments using the microscopic simulator GISSIM, in a multi-intersection real network, using measured data from Belo Horizonte traffic engineering company (BHTRANS). The practical results of MBVL-NSGA2 were compared with four approaches: (1) current BHTRANS solutions; (2) a genetic algorithm optimizing the first function; (3) a genetic algorithm optimizing the second function, and; (4) the traditional NSGA2. Analysis showed that this proposal is able to generate better traffic signal plans, at the same time that it generates a diversified set of efficient candidate solutions.

An object localization optimization technique in medical images using plant growth simulation algorithm.

The analysis of leukocyte images has drawn interest from fields of both medicine and computer vision for quite some time where different techniques have been applied to automate the process of manual analysis and classification of such images. Manual analysis of blood samples to identify leukocytes is time-consuming and susceptible to error due to the different morphological features of the cells. In this article, the nature-inspired plant growth simulation algorithm has been applied to optimize the image processing technique of object localization of medical images of leukocytes. This paper presents a random bionic algorithm for the automated detection of white blood cells embedded in cluttered smear and stained images of blood samples that uses a fitness function that matches the resemblances of the generated candidate solution to an actual leukocyte. The set of candidate solutions evolves via successive iterations as the proposed algorithm proceeds, guaranteeing their fit with the actual leukocytes outlined in the edge map of the image. The higher precision and sensitivity of the proposed scheme from the existing methods is validated with the experimental results of blood cell images. The proposed method reduces the feasible sets of growth points in each iteration, thereby reducing the required run time of load flow, objective function evaluation, thus reaching the goal state in minimum time and within the desired constraints.

Identification of a Set of Candidate Solutions for Optimal Positioning of Damping Layers

One method to lower noise in a cabin is to position damping layers on vibrating panels, thereby reducing their radiated power. To assess the damping effect, criteria like the ERP (equivalent radiated power) are widely employed, which estimate the radiated sound power of a panel without taking into account the actual complex system. Advantageously only a part of the structure has to be modeled, but the optimal solution found on the simplified model then often fails for the complete, coupled system, especially if several variants of a cabin have to be considered. Hence, it is proposed to use the structure-only optimization for identification of a set of candidate solutions for optimal positioning of damping layers. These candidate solutions used as initial designs for the coupled investigations should be well distributed in the design space to avoid being wrongly stuck in an optimum with inferior coupled performance. Evolutionary optimization strategies are especially suited for such a multi-modal optimization to derive a candidate set of local optima. They perform better with a small number of design variables, which is achieved by a special parametrization approach for shape and position of damping layers suggested here. This enables the use of a multi-modal optimization method for the positioning of damping layers, which identifies not only one optimal position, but a set of good candidate solutions (set of local minima) on the coarse structure-only model, which are applied to several cabin variants and may be used as initialization and acceleration of coupled optimization.

An integrated cognitive computing approach for systematic conceptual design

Conceptual design plays an important role in product life cycle, which requires engineers to use sound design theory, cross-disciplinary knowledge, and complex technical support to acquire design concepts. However, the lack of sufficient computational tools makes it difficult for designers to fully explore in the wide design solution spaces. Therefore, this paper proposes an integrated cognitive computing approach to formalize the cognitive activities of conceptual design. A cognitive computing model composed of concept associative memory, concept generation, and decision-making process is established based on the integration of cognitive psychology and engineering design. First of all, the Hopfield neural network is used to acquire similar concept solutions for specific subfunctions from a knowledge base. Then, morphological matrix and genetic algorithm are introduced to produce a set of feasible candidate solutions in the concept generation process. Furthermore, a technique for order preference by similarity to an ideal solution is applied to evaluate the generated concept solutions and obtain the optimal solution automatically. Finally, a case study is given to demonstrate the effectiveness and efficiency of the proposed approach.

A Multi-Stage Krill Herd Algorithm for Global Numerical Optimization

A multi-stage krill herd (MSKH) algorithm is presented to fully exploit the global and local search abilities of the standard krill herd (KH) optimization method. The proposed method involves exploration and exploitation stages. The exploration stage uses the basic KH algorithm to select a good candidate solution set. This phase is followed by fine-tuning a good candidate solution in the exploitation stage with a focused local mutation and crossover (LMC) operator in order to enhance the reliability of the method for solving global numerical optimization problems. Moreover, the elitism scheme is introduced into the MSKH method to guarantee the best solution. The performance of MSKH is verified using twenty-five standard and rotated and shifted benchmark problems. The results show the superiority of the proposed algorithm to the standard KH and other well-known optimization methods.