531 research outputs found
Optimal Net-Load Balancing in Smart Grids with High PV Penetration
Mitigating Supply-Demand mismatch is critical for smooth power grid
operation. Traditionally, load curtailment techniques such as Demand Response
(DR) have been used for this purpose. However, these cannot be the only
component of a net-load balancing framework for Smart Grids with high PV
penetration. These grids can sometimes exhibit supply surplus causing
over-voltages. Supply curtailment techniques such as Volt-Var Optimizations are
complex and computationally expensive. This increases the complexity of
net-load balancing systems used by the grid operator and limits their
scalability. Recently new technologies have been developed that enable the
rapid and selective connection of PV modules of an installation to the grid.
Taking advantage of these advancements, we develop a unified optimal net-load
balancing framework which performs both load and solar curtailment. We show
that when the available curtailment values are discrete, this problem is
NP-hard and develop bounded approximation algorithms for minimizing the
curtailment cost. Our algorithms produce fast solutions, given the tight timing
constraints required for grid operation. We also incorporate the notion of
fairness to ensure that curtailment is evenly distributed among all the nodes.
Finally, we develop an online algorithm which performs net-load balancing using
only data available for the current interval. Using both theoretical analysis
and practical evaluations, we show that our net-load balancing algorithms
provide solutions which are close to optimal in a small amount of time.Comment: 11 pages. To be published in the 4th ACM International Conference on
Systems for Energy-Efficient Built Environments (BuildSys 17) Changes from
previous version: Fixed a bug in Algorithm 1 which was causing some min cost
solutions to be misse
Meta-raps: Parameter Setting And New Applications
Recently meta-heuristics have become a popular solution methodology, in terms of both research and application, for solving combinatorial optimization problems. Meta-heuristic methods guide simple heuristics or priority rules designed to solve a particular problem. Meta-heuristics enhance these simple heuristics by using a higher level strategy. The advantage of using meta-heuristics over conventional optimization methods is meta-heuristics are able to find good (near optimal) solutions within a reasonable computation time. Investigating this line of research is justified because in most practical cases with medium to large scale problems, the use of meta-heuristics is necessary to be able to find a solution in a reasonable time. The specific meta-heuristic studied in this research is, Meta-RaPS; Meta-heuristic for Randomized Priority Search which is developed by DePuy and Whitehouse in 2001. Meta-RaPS is a generic, high level strategy used to modify greedy algorithms based on the insertion of a random element (Moraga, 2002). To date, Meta-RaPS had been applied to different types of combinatorial optimization problems and achieved comparable solution performance to other meta-heuristic techniques. The specific problem studied in this dissertation is parameter setting of Meta-RaPS. The topic of parameter setting for meta-heuristics has not been extensively studied in the literature. Although the parameter setting method devised in this dissertation is used primarily on Meta-RaPS, it is applicable to any meta-heuristic\u27s parameter setting problem. This dissertation not only enhances the power of Meta-RaPS by parameter tuning but also it introduces a robust parameter selection technique with wide-spread utility for many meta-heuristics. Because the distribution of solution values generated by meta-heuristics for combinatorial optimization problems is not normal, the current parameter setting techniques which employ a parametric approach based on the assumption of normality may not be appropriate. The proposed method is Non-parametric Based Genetic Algorithms. Based on statistical tests, the Non-parametric Based Genetic Algorithms (NPGA) is able to enhance the solution quality of Meta-RaPS more than any other parameter setting procedures benchmarked in this research. NPGA sets the best parameter settings, of all the methods studied, for 38 of the 41 Early/Tardy Single Machine Scheduling with Common Due Date and Sequence-Dependent Setup Time (ETP) problems and 50 of the 54 0-1 Multidimensional Knapsack Problems (0-1 MKP). In addition to the parameter setting procedure discussed, this dissertation provides two Meta-RaPS combinatorial optimization problem applications, the 0-1 MKP, and the ETP. For the ETP problem, the Meta-RaPS application in this dissertation currently gives the best meta-heuristic solution performance so far in the literature for common ETP test sets. For the large ETP test set, Meta-RaPS provided better solution performance than Simulated Annealing (SA) for 55 of the 60 problems. For the small test set, in all four different small problem sets, the Meta-RaPS solution performance outperformed exiting algorithms in terms of average percent deviation from the optimal solution value. For the 0-1 MKP, the present Meta-RaPS application performs better than the earlier Meta-RaPS applications by other researchers on this problem. The Meta-RaPS 0-1 MKP application presented here has better solution quality than the existing Meta-RaPS application (Moraga, 2005) found in the literature. Meta-RaPS gives 0.75% average percent deviation, from the best known solutions, for the 270 0-1 MKP test problems
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Combinatorial optimization and metaheuristics
Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (âefficientâ) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find âquicklyâ (reasonable run-times), with âhighâ probability, provable âgoodâ solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods
A Heuristic Algorithm for Resource Allocation/Reallocation Problem
This paper presents a 1-opt heuristic approach to solve resource allocation/reallocation problem which is known as 0/1 multichoice multidimensional knapsack problem (MMKP). The intercept matrix of the constraints is employed to find optimal or near-optimal solution of the MMKP. This heuristic approach is tested for 33 benchmark problems taken from OR library of sizes upto 7000, and the results have been compared with optimum solutions. Computational complexity is proved to be (2) of solving heuristically MMKP using this approach. The performance of our heuristic is compared with the best state-of-art heuristic algorithms with respect to the quality of the solutions found. The encouraging results especially for relatively large-size test problems indicate that this heuristic approach can successfully be used for finding good solutions for highly constrained NP-hard problems
Incorporating Memory and Learning Mechanisms Into Meta-RaPS
Due to the rapid increase of dimensions and complexity of real life problems, it has become more difficult to find optimal solutions using only exact mathematical methods. The need to find near-optimal solutions in an acceptable amount of time is a challenge when developing more sophisticated approaches. A proper answer to this challenge can be through the implementation of metaheuristic approaches. However, a more powerful answer might be reached by incorporating intelligence into metaheuristics.
Meta-RaPS (Metaheuristic for Randomized Priority Search) is a metaheuristic that creates high quality solutions for discrete optimization problems. It is proposed that incorporating memory and learning mechanisms into Meta-RaPS, which is currently classified as a memoryless metaheuristic, can help the algorithm produce higher quality results.
The proposed Meta-RaPS versions were created by taking different perspectives of learning. The first approach taken is Estimation of Distribution Algorithms (EDA), a stochastic learning technique that creates a probability distribution for each decision variable to generate new solutions. The second Meta-RaPS version was developed by utilizing a machine learning algorithm, Q Learning, which has been successfully applied to optimization problems whose output is a sequence of actions. In the third Meta-RaPS version, Path Relinking (PR) was implemented as a post-optimization method in which the new algorithm learns the good attributes by memorizing best solutions, and follows them to reach better solutions. The fourth proposed version of Meta-RaPS presented another form of learning with its ability to adaptively tune parameters. The efficiency of these approaches motivated us to redesign Meta-RaPS by removing the improvement phase and adding a more sophisticated Path Relinking method. The new Meta-RaPS could solve even the largest problems in much less time while keeping up the quality of its solutions.
To evaluate their performance, all introduced versions were tested using the 0-1 Multidimensional Knapsack Problem (MKP). After comparing the proposed algorithms, Meta-RaPS PR and Meta-RaPS Q Learning appeared to be the algorithms with the best and worst performance, respectively. On the other hand, they could all show superior performance than other approaches to the 0-1 MKP in the literature
Simulated annealing and Tabu search in the long run: A comparison on QAP tasksâ
AbstractSimulated Annealing (SA) and Tabu Search (TS) are compared on the Quadratic Assignment Problem. A recent work on the same benchmark suite argued that SA could achieve a reasonable solution quality with fewer function evaluations than TS. The discussion is extended by showing that the conclusions must be changed if the task is hard or a very good approximation of the optimal solution is desired, or if CPU time is the relevant parameter. In addition, a recently proposed version of TS (the Reactive Tabu Search) solves the problem of finding the proper list size with an automatic memory-based reaction mechanism
A Survey of League Championship Algorithm: Prospects and Challenges
The League Championship Algorithm (LCA) is sport-inspired optimization
algorithm that was introduced by Ali Husseinzadeh Kashan in the year 2009. It
has since drawn enormous interest among the researchers because of its
potential efficiency in solving many optimization problems and real-world
applications. The LCA has also shown great potentials in solving
non-deterministic polynomial time (NP-complete) problems. This survey presents
a brief synopsis of the LCA literatures in peer-reviewed journals, conferences
and book chapters. These research articles are then categorized according to
indexing in the major academic databases (Web of Science, Scopus, IEEE Xplore
and the Google Scholar). The analysis was also done to explore the prospects
and the challenges of the algorithm and its acceptability among researchers.
This systematic categorization can be used as a basis for future studies.Comment: 10 pages, 2 figures, 2 tables, Indian Journal of Science and
Technology, 201
BQ-NCO: Bisimulation Quotienting for Efficient Neural Combinatorial Optimization
Despite the success of neural-based combinatorial optimization methods for
end-to-end heuristic learning, out-of-distribution generalization remains a
challenge. In this paper, we present a novel formulation of Combinatorial
Optimization Problems (COPs) as Markov Decision Processes (MDPs) that
effectively leverages common symmetries of COPs to improve out-of-distribution
robustness. Starting from a direct MDP formulation of a constructive method, we
introduce a generic way to reduce the state space, based on Bisimulation
Quotienting (BQ) in MDPs. Then, for COPs with a recursive nature, we specialize
the bisimulation and show how the reduced state exploits the symmetries of
these problems and facilitates MDP solving. Our approach is principled and we
prove that an optimal policy for the proposed BQ-MDP actually solves the
associated COPs. We illustrate our approach on five classical problems: the
Euclidean and Asymmetric Traveling Salesman, Capacitated Vehicle Routing,
Orienteering and Knapsack Problems. Furthermore, for each problem, we introduce
a simple attention-based policy network for the BQ-MDPs, which we train by
imitation of (near) optimal solutions of small instances from a single
distribution. We obtain new state-of-the-art results for the five COPs on both
synthetic and realistic benchmarks. Notably, in contrast to most existing
neural approaches, our learned policies show excellent generalization
performance to much larger instances than seen during training, without any
additional search procedure
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