Encoding transformation-based differential evolution algorithm for solving knapsack problem with single continuous variable

The Capacitated Facility Location Problem (CFLP) is to locate a set of facilities with capacity constraints, to satisfy at the minimum cost the order-demands of a set of clients. A multi-source version of the problem is considered in which each client can be served by more than one facility. In this paper we present a reformulation of the CFLP based on Mixed Dicut Inequalities, a family of minimum knapsack inequalities of a mixed type, containing both binary and continuous (flow) variables. By aggregating flow variables, any Mixed Dicut Inequality turns into a binary minimum knapsack inequality with a single continuous variable. We will refer to the convex hull of the feasible solutions of this minimum knapsack problem as the Mixed Dicut polytope. We observe that the Mixed Dicut polytope is a rich source of valid inequalities for the CFLP: basic families of valid CFLP inequalities, like Variable Upper Bounds, Cover, Flow Cover and Effective Capacity Inequalities, are valid for the Mixed Dicut polytope. Furthermore we observe that new families of valid inequalities for the CFLP can be derived by the lifting procedures studied for the minimum knapsack problem with a single continuous variable. To deal with large-scale instances, we have developed a Branch-and-Cut-and-Price algorithm, where the separation algorithm consists of the complete enumeration of the facets of the Mixed Dicut polytope for a set of candidate Mixed Dicut Inequalities. We observe that our procedure returns inequalities that dominate most of the known classes of inequalities presented in the literature. We report on computational experience with instances up to 1000 facilities and 1000 clients to validate the approach.

We present a separation procedure for a class of valid inequalities (mixed lifted cover inequalities) for the mixed binary knapsack set with a single continuous variable. It consists of the following steps: (i) the continuous variable is fixed to a given value, (ii) a valid inequality for the corresponding binary knapsack set is computed, (iii) the inequality is lifted using an iterative procedure to become valid for the mixed integer knapsack set. Computational experience on a wide set of mixed integer programming instances from MIPLIB and Mittleman sets is carried out, showing that our cutting plane algorithm leads to significant improvement in lower bounds, with negligible additional computational effort.

The area of parameterized approximation seeks to combine approximation and parameterized algorithms to obtain, e.g., (1+epsilon)-approximations in f(k,epsilon)n^O(1) time where k is some parameter of the input. The goal is to overcome lower bounds from either of the areas. We obtain the following results on parameterized approximability: - In the maximum independent set of rectangles problem (MISR) we are given a collection of n axis parallel rectangles in the plane. Our goal is to select a maximum-cardinality subset of pairwise non-overlapping rectangles. This problem is NP-hard and also W[1]-hard [Marx, ESA'05]. The best-known polynomial-time approximation factor is O(log log n) [Chalermsook and Chuzhoy, SODA'09] and it admits a QPTAS [Adamaszek and Wiese, FOCS'13; Chuzhoy and Ene, FOCS'16]. Here we present a parameterized approximation scheme (PAS) for MISR, i.e. an algorithm that, for any given constant epsilon>0 and integer k>0, in time f(k,epsilon)n^g(epsilon), either outputs a solution of size at least k/(1+epsilon), or declares that the optimum solution has size less than k. - In the (2-dimensional) geometric knapsack problem (2DK) we are given an axis-aligned square knapsack and a collection of axis-aligned rectangles in the plane (items). Our goal is to translate a maximum cardinality subset of items into the knapsack so that the selected items do not overlap. In the version of 2DK with rotations (2DKR), we are allowed to rotate items by 90 degrees. Both variants are NP-hard, and the best-known polynomial-time approximation factor is 2+epsilon [Jansen and Zhang, SODA'04]. These problems admit a QPTAS for polynomially bounded item sizes [Adamaszek and Wiese, SODA'15]. We show that both variants are W[1]-hard. Furthermore, we present a PAS for 2DKR. For all considered problems, getting time f(k,epsilon)n^O(1), rather than f(k,epsilon)n^g(epsilon), would give FPT time f'(k)n^O(1) exact algorithms by setting epsilon=1/(k+1), contradicting W[1]-hardness. Instead, for each fixed epsilon>0, our PASs give (1+epsilon)-approximate solutions in FPT time. For both MISR and 2DKR our techniques also give rise to preprocessing algorithms that take n^g(epsilon) time and return a subset of at most k^g(epsilon) rectangles/items that contains a solution of size at least k/(1+epsilon) if a solution of size k exists. This is a special case of the recently introduced notion of a polynomial-size approximate kernelization scheme [Lokshtanov et al., STOC'17].

In this work, a method to control the parameters of Differential Evolution (DE) algorithm is proposed. Here the control parameters of DE are co-evolved by Particle Swarm Optimization (PSO) algorithm. The classical DE algorithm has two main control parameters: Scale Factor (F) and Cross-over Rate (CR). These are selected on trial-and-error basis for solving optimization problems. Several optimization problems lead to optimal or sub-optimal solution by proper selection of control parameters of the DE algorithm. In this proposed method, PSO algorithm is used to tune the scale factor and cross-over rate in DE algorithm. Basically PSO algorithm is used as a meta-optimizer for DE algorithm. The proposed method is termed as mPSO-DE in this paper. The mPSO-DE algorithm is applied on 12 benchmark unconstrained optimization problems. The obtained results are compared with that of classical DE algorithm. From the experimental studies, it has been found that the proposed mPSO-DE algorithm performed better than DE algorithm.

A differential evolution algorithm with intersect mutation operator

This parameters selection is an important issue in the research of ¿-support vector regression machine (¿-SVRM), whose nature is an optimization selection process. Motivated by the effectiveness of differential evolution (DE) algorithm on optimization problem, a new automatic searching method based on DE algorithm was proposed. Experimental results demonstrate that ¿-SVRM model optimization based on DE algorithm has better prediction capability compared with the methods based on genetic algorithm (GA), ant colony optimization (ACO) and particle swarm optimization (PSO).

Thiswork proposes a Differential Evolution (DE) algorithm based energy management system (EMS) to optimize the performance of a microgrid in the presence of renewable energy sources. Various types of distributed generators (DGs), namely Micro Turbine (MT), Phosphoric Acid Fuel Cell (PAFC), Wind Turbine (WT), Photo-voltaic (PV) and battery (batt) are present in the micro-grid. Out of these DGs, WT and PV have a randomized natural behavior. To optimize the micro-grid operation and cover the uncertainty in power generation from the renewable resources, the incentive based demand response programs are incorporated in the EMS. The performance of EMS is optimized by minimizing the operating cost of the micro-grid and by minimizing its pollutant emissions using DE algorithm. The results obtained using DE algorithm are compared with the Particle Swarm Optimization (PSO) based reported results. On comparison the proposed DE algorithm is found to be superior in terms of solution quality and convergence speed.

Shuffled frog leaping algorithm and its application to 0/1 knapsack problem

Community search on attributed networks has recently attracted great deal of research interest. However, most of existing works require query users to specify some community structure parameters. This may not be always practical as sometimes a user does not have the knowledge and experience to decide the suitable parameters. In this paper, we propose a novel parameter-free contextual community model for attributed community search. The proposed model only requires a query context, i.e., a set of keywords describing the desired matching community context, while the community returned is both structure and attribute cohesive w.r.t. the provided query context. We theoretically show that both our exact and approximate contextual community search algorithms can be executed in worst case polynomial time. The exact algorithm is based on an elegant parametric maximum flow technique and the approximation algorithm that significantly improves the search efficiency is analyzed to have an approximation factor of 1/3. In the experiment, we use six real networks with ground-truth communities to evaluate the effectiveness of our contextual community model. Experimental results demonstrate that the proposed model can find near ground-truth communities. We also test both our exact and approximate algorithms using eight large real networks to demonstrate the high efficiency of the proposed algorithms.

In swarm intelligence, Particle Swarm Optimization (PSO) and Differential Evolution (DE) have been successfully applied in many optimization tasks, and a large number of variants, where novel algorithm operators or components are implemented, has been introduced to boost the empirical performance. In this paper, we first propose to combine the variants of PSO or DE by modularizing each algorithm and incorporating the variants thereof as different options of the corresponding modules. Then, considering the similarity between the inner workings of PSO and DE, we hybridize the algorithms by creating two populations with variation operators of PSO and DE respectively, and selecting individuals from those two populations. The resulting novel hybridization, called PSODE, encompasses most up-to-date variants from both sides, and more importantly gives rise to an enormous number of unseen swarm algorithms via different instantiations of the modules therein. In detail, we consider 16 different variation operators originating from existing PSO- and DE algorithms, which, combined with 4 different selection operators, allow the hybridization framework to generate 800 novel algorithms. The resulting set of hybrid algorithms, along with the combined 30 PSO- and DE algorithms that can be generated with the considered operators, is tested on the 24 problems from the well-known COCO/BBOB benchmark suite, across multiple function groups and dimensionalities.

Network reconfiguration for loss reduction in a distribution system is a very important way to save the electrical energy. This article proposes a hybrid evolutionary algorithm to solve the distribution feeder reconfiguration problem. The algorithm combines a fuzzy adaptive particle swarm optimization with a differential evolution algorithm, called the fuzzy adaptive particle swarm optimization–differential evolution. The fuzzy adaptive particle swarm optimization includes two parts. The first part is fuzzy adaptive binary particle swarm optimization, which determines the status of tie switches (open or closed), and the second part is fuzzy adaptive discrete particle swarm optimization, which determines the sectionalizing switch number. In the proposed algorithm, due to the results of binary particle swarm optimization and discrete particle swarm optimization algorithms that highly depend on the values of their parameters (such as the inertia weight and learning factors), a fuzzy system is employed to adaptively adjust the parameters during the search process. The differential evolution algorithm is combined with the fuzzy adaptive particle swarm optimization algorithm to improve its performance. The proposed algorithm is tested on two distribution test feeders. The results of simulation show that the proposed method is very powerful and is guaranteed to obtain the global optimization.

Background: By observing the high prevalence of failures in the surgical treatment of myocardial revascularization (MR), with the use of the Left Internal Thoracic Artery (LITA) as a graft, evidenced by the international literature, it was sought to demonstrate the prevalence of lesions that would not allow the use of LITA as a graft in myocardial revascularization surgery, with possible alteration in the surgical management performed by the cardiac surgeon, and reduction of the morbimortality of these patients. Objectives: To evaluate the prevalence of atherosclerotic lesions of the LITA, through selective preoperative angiography, in patients submitted to coronary angiography and indicated for myocardial revascularization. We also analyzed other lesions that made the use of LITA unfeasible as a main graft in cases of myocardial revascularization surgery (MRS). Methods: This was a cross-sectional, prevalence study that evaluated, through selective angiography, the LITA of 39 patients with a median age of 63 years, submitted to coronary angiography, with indication of Coronary Artery Bypass Graft (CABG). Categorical variables were compared by chi-square test and Fisher's exact test. The single continuous variable, age, was tested for normality by the Kolmogorov-Smirnov test, described in median (P25; P75) and the groups compared with the Mann-Whitney test. The level of statistical significance adopted was p < 0.05. The analyzes were performed in SPSS® software version 20. Results: It was identified the presence of 7.7% of disorders in the LITA that made it unfeasible to be used. In all of the patients there was no specific symptomatology evidencing the lesion. No variable was shown as a predictor for the occurrence of the outcomes. Conclusion: The prevalence of the lesions found in the study was significant, indicating that a preoperative evaluation of LITA could bring future benefits to the patients submitted to CABG.

On the optimality of exact and approximation algorithms for scheduling problems

An improved mixed-integer particle swarm optimization (MI-PSO) algorithm is presented, which is called asynchronous updating particle swarm optimization (AU-PSO). The proposed algorithm speeds up convergence rate of PSO by handling discrete and continuous decision variables differently. The discrete variables have a possibility holding previous values, while the continuous variables are treated normally. This kind of treatment provides more chances to find a better solution. The proposed AU-PSO is then examined by test functions and successfully applied in a design of circular antenna array.

This paper presents the results of the nonlinear system modelling approach based on the use of fuzzy rules optimized by different population based optimization algorithms. Fuzzy rule based models with different number of the rules are used to describe the some nonlinear systems in the literature. Firstly, parameters of the fuzzy models are determined by the artificial bee colony (ABC) algorithm. To demonstrate the efficiency of the ABC algorithm, its modelling ability is compared with the other two powerful population based algorithms, particle swarm optimization (PSO) and differential evolution algorithm (DEA). Simulation results show that a successful model performance with good description ability in the modelling of nonlinear or complex systems can be obtained by using one of the population based algorithms in design of the fuzzy rule based models. DOI: http://dx.doi.org/10.5755/j01.eie.22.5.16336