Particle algorithms for optimization on binary spaces

We discuss a unified approach to stochastic optimization of pseudo-Boolean objective functions based on particle methods, including the cross-entropy method and simulated annealing as special cases. We point out the need for auxiliary sampling distributions, that is parametric families on binary spaces, which are able to reproduce complex dependency structures, and illustrate their usefulness in our numerical experiments. We provide numerical evidence that particle-driven optimization algorithms based on parametric families yield superior results on strongly multi-modal optimization problems while local search heuristics outperform them on easier 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

A variable neighborhood search algorithm with reinforcement learning for a real-life periodic vehicle routing problem with time windows and open routes

Based on a real-life container transport problem, a model of Open Periodic Vehicle Routing Problem with Time Windows (OPVRPTW) is proposed in this paper. In a wide planning horizon, which is divided into a number of shifts, a fixed number of trucks are scheduled to complete container transportation tasks between terminals subject to time constraints. In this problem, the routes traveled by trucks are open, as returning to the starting depot is not required in every single shift but every two shifts.Our study shows that it is unrealistic to address this large scale and nonlinearly constrained problem with exact search methods. A Reinforcement Learning Based Variable Neighbourhood Search algorithm (VNSRLS) is developed for OPVRPTW. The initial solution is constructed with an urgency level-based insertion heuristic, while different insertion selection strategies are compared. In the local search phase of VNS-RLS, reinforcement learning is used to guide the search, adjusting the probabilities of operators being invoked adaptively according to the change of generated solutions’ feasibility and quality. In addition, the impact of sampling neighbourhood space in single solution-based algorithms is also investigated. Three indicators are designed in the proposed Sampling module to set the starting configuration of local search.Experiment results on different sizes of real and artificial benchmark instances show that, the proposed Sampling scheme and feasibility indicator decrease the infeasible rate during the search. However, Sampling’s contribution to solution quality improvement is not significant in this single solution-based algorithm. Comparing to the exact search and two state-of-the-art algorithms, VNS-RLS produces promising result

Solving the boolean satisfiability problem using multilevel techniques

There are many complex problems in computer science that occur in knowledge-representation (artificial thinking), artificial learning, Very Large Scale Integration (VLSI) design, security protocols and other areas. These complex problems may be deduced into satisfiability problems where the Boolean Satisfiability Problem (SAT) may be applied. This deduction is made in order to simplify complex problems into a specific propositional logic problem. The SAT problem is the most well-known nondeterministic polynomial time (NP) complete problem in computer science. It is a Boolean expression which is composed of a specific amount of variables (literals), clauses that contain disjunctions of the literals and conjunctions of the clauses. The literals have the logical values TRUE and FALSE, the task is to find a truth assignment that makes the entire expression TRUE. The main goal of the thesis is to solve the SAT problem using a clustering technique - Multilevel - combined first with Tabu Search and combined thereafter with finite Learning Automata. Tabu Search and finite Learning Automata are two very efficient approaches that have been used to solve SAT. Benchmark experiments are conducted in order to disclose whether combining Multilevel with existing solutions to solve SAT will provide better results - than the two mentioned approaches alone - mainly in terms of computational efficienc

A Discrete and Improved Bat Algorithm for solving a medical goods distribution problem with pharmacological waste collection

The work presented in this paper is focused on the resolution of a real-world drugs distribution problem with pharmacological waste collection. With the aim of properly meeting all the real-world restrictions that comprise this complex problem, we have modeled it as a multi-attribute or rich vehicle routing problem (RVRP). The problem has been modeled as a Clustered Vehicle Routing Problem with Pickups and Deliveries, Asymmetric Variable Costs, Forbidden Roads and Cost Constraints. To the best of authors knowledge, this is the first time that such a RVRP problem is tackled in the literature. For this reason, a benchmark composed of 24 datasets, from 60 to 1000 customers, has also been designed. For the developing of this benchmark, we have used real geographical positions located in Bizkaia, Spain. Furthermore, for the proper dealing of the proposed RVRP, we have developed a Discrete and Improved Bat Algorithm (DaIBA). The main feature of this adaptation is the use of the well-known Hamming Distance to calculate the differences between the bats. An effective improvement has been also contemplated for the proposed DaIBA, which consists on the existence of two different neighborhood structures, which are explored depending on the bat's distance regarding the best individual of the swarm. For the experimentation, we have compared the performance of our presented DaIBA with three additional approaches: an evolutionary algorithm, an evolutionary simulated annealing and a firefly algorithm. Additionally, with the intention of obtaining rigorous conclusions, two different statistical tests have been conducted: the Friedman's non-parametric test and the Holm's post-hoc test. Furthermore, an additional experimentation has been performed in terms of convergence. Finally, the obtained outcomes conclude that the proposed DaIBA is a promising technique for addressing the designed problem

Improving the efficiency of Bayesian Network Based EDAs and their application in Bioinformatics

Estimation of distribution algorithms (EDAs) is a relatively new trend of stochastic optimizers which have received a lot of attention during last decade. In each generation, EDAs build probabilistic models of promising solutions of an optimization problem to guide the search process. New sets of solutions are obtained by sampling the corresponding probability distributions. Using this approach, EDAs are able to provide the user a set of models that reveals the dependencies between variables of the optimization problems while solving them. In order to solve a complex problem, it is necessary to use a probabilistic model which is able to capture the dependencies. Bayesian networks are usually used for modeling multiple dependencies between variables. Learning Bayesian networks, especially for large problems with high degree of dependencies among their variables is highly computationally expensive which makes it the bottleneck of EDAs. Therefore introducing efficient Bayesian learning algorithms in EDAs seems necessary in order to use them for large problems. In this dissertation, after comparing several Bayesian network learning algorithms, we propose an algorithm, called CMSS-BOA, which uses a recently introduced heuristic called max-min parent children (MMPC) in order to constrain the model search space. This algorithm does not consider a fixed and small upper bound on the order of interaction between variables and is able solve problems with large numbers of variables efficiently. We compare the efficiency of CMSS-BOA with the standard Bayesian network based EDA for solving several benchmark problems and finally we use it to build a predictor for predicting the glycation sites in mammalian proteins

Combining an artificial intelligence algorithm and a novel vehicle for sustainable e-waste collection

Mobile collection of waste electrical and electronic equipment is a collection method that is convenient for residents and companies. New opportunities to use mobile apps and internet applications facilitate the ordering of waste pickups from households and preparation of a collection plan for a waste collection company. It improves the secondary raw materials collection in a circular economy approach after recycling waste equipment. This study presents a combined methodology for improving the efficiency of e-waste collection. An online ewaste collection supporting systemuses a Harmony Search algorithm for route optimization of waste collection vehicles. The results of the optimization are better compared to other artificial intelligence algorithms presented in the literature and the number of visited collection points is higher from1.2%–6.6% depending on the compared algorithm. To increase the efficiency ofwaste loading and packing, a novel collection vehicle body construction is presented. The design includes the convenient loading of waste from both sides of the vehicle and the rear side being equippedwith a hydraulic lift. The proposed vehiclemodel can be used for e-waste collection in placeswith limited parking spaces or where the parking time is limited, such as in densely populated city centers. The waste equipment packing efficiency increases and eliminates the necessity of including a container loading problem in the algorithm and allows increasing waste equipment number loaded in a collection vehicle

A Heuristic Approach to the Theater Distribution Problem

Analysts at USTRANSCOM are tasked with providing vehicle mixtures that will support the distribution of requirements as provided in the form of TPFDD. An integer programming model exists to search for optimal solutions to these problems, but it is fairly time consuming, and produces only one of potentially several good quality solutions. This research constructs a number of heuristic approaches to solving the TDP. Two distinct shipping methods are examined and applied through both constructive and probabilistic vehicle assignment processes. Multistart metaheuristic approaches are designed and used in conjunction with the constructive and probabilistic approaches. Random TPFDDs of size 20, 100 and 1000 are tested, and solutions are compared to those obtained by the integer programming approach. The heuristic models implemented in this research develop feasible solutions to the notional TPFDDs in less time than the integer program. They can very quickly identify a number of good quality solutions to the same problem

Search with evolutionary ruin and stochastic rebuild: a theoretic framework and a case study on exam timetabling

This paper presents a state transition based formal framework for a new search method, called Evolutionary Ruin and Stochastic Recreate, which tries to learn and adapt to the changing environments during the search process. It improves the performance of the original Ruin and Recreate principle by embedding an additional phase of Evolutionary Ruin to mimic the survival-of-the-fittest mechanism within single solutions. This method executes a cycle of Solution Decomposition, Evolutionary Ruin, Stochastic Recreate and Solution Acceptance until a certain stopping condition is met. The Solution Decomposition phase first uses some problem-specific knowledge to decompose a complete solution into its components and assigns a score to each component. The Evolutionary Ruin phase then employs two evolutionary operators (namely Selection and Mutation) to destroy a certain fraction of the solution, and the next Stochastic Recreate phase repairs the “broken” solution. Last, the Solution Acceptance phase selects a specific strategy to determine the probability of accepting the newly generated solution. Hence, optimisation is achieved by an iterative process of component evaluation, solution disruption and stochastic constructive repair. From the state transitions point of view, this paper presents a probabilistic model and implements a Markov chain analysis on some theoretical properties of the approach. Unlike the theoretical work on genetic algorithm and simulated annealing which are based on state transitions within the space of complete assignments, our model is based on state transitions within the space of partial assignments. The exam timetabling problems are used to test the performance in solving real-world hard problems