Solving Constraint Optimization Problems Research Articles

Self-Adaptive Forensic-Based Investigation Algorithm with Dynamic Population for Solving Constraint Optimization Problems

The Forensic-Based Investigation (FBI) algorithm is a novel metaheuristic algorithm. Many researches have shown that FBI is a promising algorithm due to two specific population types. However, there is no sufficient information exchange between these two population types in the original FBI algorithm. Therefore, FBI suffers from many problems. This paper incorporates a novel self-adaptive population control strategy into FBI algorithm to adjust parameters based on the fitness transformation from the previous iteration, named SaFBI. In addition to the self-adaptive mechanism, our proposed SaFBI refers to a novel updating operator to further improve the robustness and effectiveness of the algorithm. To prove the availability of the proposed algorithm, we select 51 CEC benchmark functions and two well-known engineering problems to verify the performance of SaFBI. Experimental and statistical results manifest that the proposed SaFBI algorithm performs superiorly compared to some state-of-the-art algorithms.

Study on reservoir optimal operation based on coupled adaptive ε constraint and multi strategy improved Pelican algorithm

The optimal operation of reservoir groups is a strongly constrained, multi-stage, and high-dimensional optimization problem. In response to this issue, this article couples the standard Pelican optimization algorithm with adaptive ε constraint methods, and further improves the optimization performance of the algorithm by initializing the population with a good point set, reverse differential evolution, and optimal individual t-distribution perturbation strategy. Based on this, an improved Pelican algorithm coupled with adaptive ε constraint method is proposed (ε-IPOA). The performance of the algorithm was tested through 24 constraint testing functions to find the optimal ability and solve constraint optimization problems. The results showed that the algorithm has strong optimization ability and stable performance. In this paper, we select Sanmenxia and Xiaolangdi reservoirs as the research objects, establish the maximum peak-cutting model of terrace reservoirs, apply the ε-IPOA algorithm to solve the model, and compare it with the ε-POA (Pelican algorithm coupled with adaptive ε constraint method) and ε-DE (Differential Evolution Algorithm) algorithms, the results indicate that ε. The peak flow rate of the Huayuankou control point solved by the IPOA algorithm is 12,319 m3/s, which is much lower than the safe overflow flow rate of 22,000 m3/s at the Huayuankou control point, with a peak shaving rate of 44%, and other algorithms do not find effective solutions meeting the constraint conditions. This paper provides a new idea for solving the problem of flood control optimal operation of cascade reservoirs.

Separate but Equal: Equality in Belief Propagation for Single Cycle Graphs

Belief propagation is a widely used incomplete optimization algorithm, whose main theoretical properties hold only under the assumptions that beliefs are not equal. Nevertheless, there is much evidence that equality between beliefs does occur. A method to overcome belief equality by using unary function-nodes is assumed to resolve the problem. We focus on Min-sum, the belief propagation version for solving constraint optimization problems. We prove that on a single cycle graph, belief equality can be avoided only when the algorithm converges to the optimal solution. In any other case, the unary function methods will not prevent equality, rendering some existing results in need of reassessment. We differentiate between belief equality, which includes equal beliefs in a single message, and assignment equality, that prevents a coherent selection of assignments to variables. We show the necessary and satisfying conditions for both.

Finding Good Partial Assignments during Restart-Based Branch and Bound Search

Restart-based Branch-and-Bound Search (BBS) is a standard algorithm for solving Constraint Optimization Problems (COPs). In this paper, we propose an approach to find good partial assignments to jumpstart search at each restart for general COPs, which are identified by comparing different best solutions found in different restart runs. We consider information extracted from historical solutions to evaluate the quality of the partial assignments. Thus the good partial assignments are dynamically updated as the current best solution evolves. Our approach makes restart-based BBS explore different promising sub-search-spaces to find high-quality solutions. Experiments on the MiniZinc benchmark suite show how our approach brings significant improvements to a black-box COP solver equipped with the state of the art search techniques. Our method finds better solutions and proves optimality for more instances.

Coordinate descent method for solving constraint optimization problems

The study generally aims to find line search technique with exact line search without relying on update or invertible Hessian matrix at every iteration, and theoretical improvement for if H be a symmetric matrix then has n mutually orthogonal eigenvectors.

Predictive Machine Learning of Objective Boundaries for Solving COPs

Solving Constraint Optimization Problems (COPs) can be dramatically simplified by boundary estimation, that is providing tight boundaries of cost functions. By feeding a supervised Machine Learning (ML) model with data composed of the known boundaries and extracted features of COPs, it is possible to train the model to estimate the boundaries of a new COP instance. In this paper, we first give an overview of the existing body of knowledge on ML for Constraint Programming (CP), which learns from problem instances. Second, we introduce a boundary estimation framework that is applied as a tool to support a CP solver. Within this framework, different ML models are discussed and evaluated regarding their suitability for boundary estimation, and countermeasures to avoid unfeasible estimations that avoid the solver finding an optimal solution are shown. Third, we present an experimental study with distinct CP solvers on seven COPs. Our results show that near-optimal boundaries can be learned for these COPs with only little overhead. These estimated boundaries reduce the objective domain size by 60-88% and can help the solver find near-optimal solutions early during the search.

Lightning search algorithm: a comprehensive survey.

The lightning search algorithm (LSA) is a novel meta-heuristic optimization method, which is proposed in 2015 to solve constraint optimization problems. This paper presents a comprehensive survey of the applications, variants, and results of the so-called LSA. In LSA, the best-obtained solution is defined to improve the effectiveness of the fitness function through the optimization process by finding the minimum or maximum costs to solve a specific problem. Meta-heuristics have grown the focus of researches in the optimization domain, because of the foundation of decision-making and assessment in addressing various optimization problems. A review of LSA variants is displayed in this paper, such as the basic, binary, modification, hybridization, improved, and others. Moreover, the classes of the LSA’s applications include the benchmark functions, machine learning applications, network applications, engineering applications, and others. Finally, the results of the LSA is compared with other optimization algorithms published in the literature. Presenting a survey and reviewing the LSA applications is the chief aim of this survey paper.

A Novel Nature-Inspired Technique Based on Mushroom Reproduction for Constraint Solving and Optimization

Constraint optimization consists of looking for an optimal solution maximizing a given objective function while meeting a set of constraints. In this study, we propose a new algorithm based on mushroom reproduction for solving constraint optimization problems. Our algorithm, that we call Mushroom Reproduction Optimization (MRO), is inspired by the natural reproduction and growth mechanisms of mushrooms. This process includes the discovery of rich areas with good living conditions allowing spores to grow and develop their own colonies. Given that constraint optimization problems often suffer from a high-time computation cost, we thoroughly assess MRO performance on well-known constrained engineering and real-world problems. The experimental results confirm the high performance of MRO, comparing to other known metaheursitcs, in dealing with complex optimization problems.

Finding Good Subtrees for Constraint Optimization Problems Using Frequent Pattern Mining

Making good decisions at the top of a search tree is important for finding good solutions early in constraint optimization. In this paper, we propose a method employing frequent pattern mining (FPM), a classic datamining technique, to find good subtrees for solving constraint optimization problems. We demonstrate that applying FPM in a small number of random high-quality feasible solutions enables us to identify subtrees containing optimal solutions in more than 55% of problem instances for four real world benchmark problems. The method works as a plugin that can be combined with any search strategy for branch-and-bound search. Exploring the identified subtrees first, the method brings substantial improvements for four efficient search strategies in both total runtime and runtime of finding optimal solutions.

Differential Evolution Algorithm Based on Ensemble of Constraint Handling Techniques and Multi-Population Framework

Aimed at improving the insufficient search ability of constraint differential evolution with single constraint handling technique when solving complex optimization problem, this paper proposes a constraint differential evolution algorithm based on ensemble of constraint handling techniques and multi-population framework, called ECMPDE. First, handling three improved variants of differential evolution algorithms are dynamically matched with two constraint handling techniques through the constraint allocation mechanism. Each combination includes three variants with corresponding constraint handling technique and these combinations are in the set. Second, the population is divided into three smaller subpopulations and one larger reward subpopulation. Then a combination with three constraint algorithms is randomly selected from the set, and the three constraint algorithms are run in three sub-populations respectively. According to the improvement of fitness value, the optimal constraint algorithm is selected to run on the reward sub-population, which can share information and close cooperation among populations. In order to verify the effectiveness of the proposed algorithm, 12 standard constraint optimization problems and 10 engineering constraint optimization problems are tested. The experimental results show that ECMPDE is an effective algorithm for solving constraint optimization problems.

A regularization method for the reconstruction of adsorption isotherms in liquid chromatography

Determining competitive adsorption isotherms is an open problem in liquid chromatography. Since traditional experimental trial-and-error approaches are too complex and expensive, a modern technique of obtaining adsorption isotherms is to solve the inverse problem so that the simulated batch separation coincides with actual experimental results. This is a typical ill-posed problem. Moreover, in almost all cases the observed concentration at the outlet is the total response of all components, which makes the problem more difficult. In this work, we tackle the ill-posedness with a new regularization method, which is based on the fact that the adsorption isotherms do not depend on the injection profile. The proposed method transfers the original problem to an optimization problem with a time-dependent convection–diffusion equation constraint. Iterative algorithms for solving constraint optimization problems for both the equilibrium-dispersive and the transport-dispersive models are developed. The mass transfer resistance is also estimated by the proposed inverse method. A regularization parameter selection method and the convergence property of the proposed algorithm are discussed. Finally, numerical tests for both synthetic problems and real-world problems are given to show the efficiency and feasibility of the proposed regularization method.

Lightning search algorithm

This paper introduces a novel metaheuristic optimization method called the lightning search algorithm (LSA) to solve constraint optimization problems. It is based on the natural phenomenon of lightning and the mechanism of step leader propagation using the concept of fast particles known as projectiles. Three projectile types are developed to represent the transition projectiles that create the first step leader population, the space projectiles that attempt to become the leader, and the lead projectile that represent the projectile fired from best positioned step leader. In contrast to that of the counterparts of the LSA, the major exploration feature of the proposed algorithm is modeled using the exponential random behavior of space projectile and the concurrent formation of two leader tips at fork points using opposition theory. To evaluate the reliability and efficiency of the proposed algorithm, the LSA is tested using a well-utilized set of 24 benchmark functions with various characteristics necessary to evaluate a new algorithm. An extensive comparative study with four other well-known methods is conducted to validate and compare the performance of the LSA. The result demonstrates that the LSA generally provides better results compared with the other tested methods with a high convergence rate.

Heat transfer search (HTS): a novel optimization algorithm

In this paper, a new metaheuristic optimization algorithm based on the law of thermodynamics and heat transfer is introduced. In the proposed algorithm, the search agents are molecules of the system that interact with each other as well as with the surrounding to attain thermal equilibrium state. The interactions of molecules are through various modes of heat transfer (i.e. conduction, convection and radiation). The performance of the proposed algorithm is investigated by implementing it for the parameter optimization of 24 well defined constrained optimization problems of Congress on Evolutionary Computation 2006 (CEC 2006). The results obtained using the proposed algorithm are compared with the results of some well-known metaheuristic search algorithms available in the literature. The statistical analysis of the experimental work has been carried out by conducting Friedman's rank test and Holm post hoc procedure. The comparative results validate the competitive and efficient performance of the proposed algorithm for solving constraint optimization problems.

A hierarchical parallel genetic approach for the graph coloring problem

Graph Coloring Problems (GCPs) are constraint optimization problems with various applications including time tabling and frequency allocation. The GCP consists in finding the minimum number of colors for coloring the graph vertices such that adjacent vertices have distinct colors. We propose a hierarchical approach based on Parallel Genetic Algorithms (PGAs) to solve the GCP. We call this new approach Hierarchical PGAs (HPGAs). In addition, we have developed a new operator designed to improve PGAs when solving constraint optimization problems in general and GCPs in particular. We call this new operator Genetic Modification (GM). Using the properties of variables and their relations, GM generates good individuals at each iteration and inserts them into the PGA population in the hope of reaching the optimal solution sooner. In the case of the GCP, the GM operator is based on a novel Variable Ordering Algorithm (VOA) that we propose. Together with the new crossover and the estimator of the initial solution we have developed, GM allows our solving approach to converge towards the optimal solution sooner than the well known methods for solving the GCP, even for hard instances. This was indeed clearly demonstrated by the experiments we conducted on the GCP instances taken from the well known DIMACS website.

DESIGN AND OPTIMIZATION OF MULTILAYERED ELECTROMAGNETIC SHIELD USING A REAL-CODED GENETIC ALGORITHM

We report optimized design of multilayered electromag- netic shield using real coded genetic algorithm. It is observed that the shielding efiectiveness in multilayer design is higher than single layered counterpart of equal thickness. An efiort has been made to develop an alternative approach to achieve speciflc objective of identifying the design characteristics of each layer in the multilayered shielding con- flguration. The proposed approach incorporates interrelated factors, such as absorption and re∞ection in the design optimization as per speciflc shielding requirements. The design problem has been solved using shielding efiectiveness theory based on transmission line (TL) modeling and real-coded genetic algorithm (GA) with simulated bi- nary crossover (SBX) and parameter-based mutation. The advantage of real-coded GA lies in e-cient solution for electromagnetic interfer- ence (EMI) shielding design due to its strength in solving constraint optimization problems of continuous variables with many parameters without any gradient information. Additionally, the role of material parameters, such as permittivity and permeability on re∞ection char- acteristics and shielding efiectiveness, has also been investigated and optimized using the proposed models and real-coded GA. Theoretical optimization of electromagnetic parameters has been carried out for SE » 40dB for many industrial/commercial applications and SE » 80dB for military applications.

A relative feasibility degree based approach for constrained optimization problems

Based on the ratio of the size of the feasible region of constraints to the size of the feasible region of a constrained optimization problem, we propose a new constraint handling approach to improve the efficiency of heuristic search methods in solving the constrained optimization problems. In the traditional classification of a solution candidate, it is either a feasible or an infeasible solution. To refine this classification, a new concept about the relative feasibility degree of a solution candidate is proposed to represent the amount by which the ‘feasibility’ of the solution candidate exceeds that of another candidate. Relative feasibility degree based selection rules are also proposed to enable evolutionary computation techniques to accelerate the search process of reaching a feasible region. In addition, a relative feasibility degree based differential evolution algorithm is derived to solve constraint optimization problems. The proposed approach is tested with nine benchmark problems. Results indicate that our approach is very competitive compared with four existing state-of-the-art techniques, though still sensitive to the intervals of control parameters of the differential evolution.

Advanced generic neighborhood heuristics for VNS

Weighted CSP (Constraint Satisfaction Problems) are used to model and to solve constraint optimization problems. As most WCSP are solved by local search methods that use large neighborhoods, selecting the neighborhood to explore is crucial. However, designing efficient neighborhoods is difficult and problem dependent. The very few generic heuristics defined for CSP , as ConflictVar or H-PGLNS, are not well suited for WCSP . In this paper, we propose new generic neighborhood heuristics dedicated to WCSP . Our heuristics take advantage of both conflicted variables and the topology of the constraints graph. We define the concept of freedom degree of a variable to make a compromise between these two criteria, and introduce a diversification criterion by choosing non-conflicted variables connected to conflicted ones. Then we extend, in a systematic way, each proposed heuristic in order to take into account violation costs of constraints. Experiments have been performed on real life instances (RLFAP) as well as random instances (GRAPH and Kbtree) using VNS/LDS+CP (a particular instance of VNS we developed). Experiments show that our generic heuristics clearly outperform ConflictVar and H-PGLNS. Among all topological heuristics we proposed, ConflictVar-MaxDeg appears to be the best one.

Low Discrepancy Initialized Particle Swarm Optimization for Solving Constrained Optimization Problems

Population based metaheuristics are commonly used for global optimization problems. These techniques depend largely on the generation of initial population. A good initial population may not only result in a better fitness function value but may also help in faster convergence. Although these techniques have been popular since more than three decades very little research has been done on the initialization of the population. In this paper, we propose a modified Particle Swarm Optimization (PSO) called Improved Constraint Particle Swarm Optimization (ICPSO) algorithm for solving constrained optimization. The proposed ICPSO algorithm is initialized using quasi random Vander Corput sequence and differs from unconstrained PSO algorithm in the phase of updating the position vectors and sorting every generation solutions. The performance of ICPSO algorithm is validated on eighteen constrained benchmark problems. The numerical results show that the proposed algorithm is a quite promising for solving constraint optimization problems.

Real time identification and control of dynamic systems using recurrent neural networks

Recently, several recurrent neural networks for solving constraint optimization problems were developed. In this paper, we propose a novel approach to the use of a projection neural network for solving real time identification and control of time varying systems. In addition to low complexity and simple structure, the proposed neural network can solve wider classes of time varying systems compare with other neural networks that are used for optimization such as Hopfield neural networks. Simulation results demonstrate the effectiveness and characteristics of the proposed neural network compared with a Hopfield neural network.

Solving constraint optimization problems from CLP-style specifications using heuristic search techniques

Presents a framework for efficiently solving logic formulations of combinatorial optimization problems using heuristic search techniques. In order to integrate cost, lower-bound and upper-bound specifications with conventional logic programming languages, we augment a constraint logic programming (CLP) language with embedded constructs for specifying the cost function and with a few higher-order predicates for specifying the lower and upper bound functions. We illustrate how this simple extension vastly enhances the ease with which optimization problems involving combinations of Min and Max can be specified in the extended language CLP* and we show that CSLDNF (Constraint SLD resolution with Negation as Failure) resolution schemes are not efficient for solving optimization problems specified in this language. Therefore, we describe how any problem specified using CLP* can be converted into an implicit AND/OR graph, and present an algorithm called GenSolve which can branch-and-bound using upper and lower bound estimates, thus exploiting the full pruning power of heuristic search techniques. A technical analysis of GenSolve is provided. We also provide experimental results comparing various control strategies for solving CLP* programs.