Discrete Particle Swarm Optimization for the minimum labelling Steiner tree problem

Particle Swarm Optimization is an evolutionary method inspired by the social behaviour of individuals inside swarms in nature. Solutions of the problem are modelled as members of the swarm which fly in the solution space. The evolution is obtained from the continuous movement of the particles that constitute the swarm submitted to the effect of the inertia and the attraction of the members who lead the swarm. This work focuses on a recent Discrete Particle Swarm Optimization for combinatorial optimization, called Jumping Particle Swarm Optimization. Its effectiveness is illustrated on the minimum labelling Steiner tree problem: given an undirected labelled connected graph, the aim is to find a spanning tree covering a given subset of nodes, whose edges have the smallest number of distinct labels

Adaptive primal-dual genetic algorithms in dynamic environments

This article is placed here with permission of IEEE - Copyright @ 2010 IEEERecently, there has been an increasing interest in applying genetic algorithms (GAs) in dynamic environments. Inspired by the complementary and dominance mechanisms in nature, a primal-dual GA (PDGA) has been proposed for dynamic optimization problems (DOPs). In this paper, an important operator in PDGA, i.e., the primal-dual mapping (PDM) scheme, is further investigated to improve the robustness and adaptability of PDGA in dynamic environments. In the improved scheme, two different probability-based PDM operators, where the mapping probability of each allele in the chromosome string is calculated through the statistical information of the distribution of alleles in the corresponding gene locus over the population, are effectively combined according to an adaptive Lamarckian learning mechanism. In addition, an adaptive dominant replacement scheme, which can probabilistically accept inferior chromosomes, is also introduced into the proposed algorithm to enhance the diversity level of the population. Experimental results on a series of dynamic problems generated from several stationary benchmark problems show that the proposed algorithm is a good optimizer for DOPs.This work was supported in part by the National Nature Science Foundation of China (NSFC) under Grant 70431003 and Grant 70671020, by the National Innovation Research Community Science Foundation of China under Grant 60521003, by the National Support Plan of China under Grant 2006BAH02A09, by the Engineering and Physical Sciences Research Council (EPSRC) of U.K. under Grant EP/E060722/1, and by the Hong Kong Polytechnic University Research Grants under Grant G-YH60

Mixed integer programming and adaptive problem solver learned by landscape analysis for clinical laboratory scheduling

This paper attempts to derive a mathematical formulation for real-practice clinical laboratory scheduling, and to present an adaptive problem solver by leveraging landscape structures. After formulating scheduling of medical tests as a distributed scheduling problem in heterogeneous, flexible job shop environment, we establish a mixed integer programming model to minimize mean test turnaround time. Preliminary landscape analysis sustains that these clinics-orientated scheduling instances are difficult to solve. The search difficulty motivates the design of an adaptive problem solver to reduce repetitive algorithm-tuning work, but with a guaranteed convergence. Yet, under a search strategy, relatedness from exploitation competence to landscape topology is not transparent. Under strategies that impose different-magnitude perturbations, we investigate changes in landscape structure and find that disturbance amplitude, local-global optima connectivity, landscape's ruggedness and plateau size fairly predict strategies' efficacy. Medium-size instances of 100 tasks are easier under smaller-perturbation strategies that lead to smoother landscapes with smaller plateaus. For large-size instances of 200-500 tasks, extant strategies at hand, having either larger or smaller perturbations, face more rugged landscapes with larger plateaus that impede search. Our hypothesis that medium perturbations may generate smoother landscapes with smaller plateaus drives our design of this new strategy and its verification by experiments. Composite neighborhoods managed by meta-Lamarckian learning show beyond average performance, implying reliability when prior knowledge of landscape is unknown

Optimal Microgrid Topology Design and Siting of Distributed Generation Sources Using a Multi-Objective Substrate Layer Coral Reefs Optimization Algorithm

n this work, a problem of optimal placement of renewable generation and topology design for a Microgrid (MG) is tackled. The problem consists of determining the MG nodes where renewable energy generators must be optimally located and also the optimization of the MG topology design, i.e., deciding which nodes should be connected and deciding the lines’ optimal cross-sectional areas (CSA). For this purpose, a multi-objective optimization with two conflicting objectives has been used, utilizing the cost of the lines, C, higher as the lines’ CSA increases, and the MG energy losses, E, lower as the lines’ CSA increases. To characterize generators and loads connected to the nodes, on-site monitored annual energy generation and consumption profiles have been considered. Optimization has been carried out by using a novel multi-objective algorithm, the Multi-objective Substrate Layers Coral Reefs Optimization algorithm (Mo-SL-CRO). The performance of the proposed approach has been tested in a realistic simulation of a MG with 12 nodes, considering photovoltaic generators and micro-wind turbines as renewable energy generators, as well as the consumption loads from different commercial and industrial sites. We show that the proposed Mo-SL-CRO is able to solve the problem providing good solutions, better than other well-known multi-objective optimization techniques, such as NSGA-II or multi-objective Harmony Search algorithm.This research was partially funded by Ministerio de Economía, Industria y Competitividad, project number TIN2017-85887-C2-1-P and TIN2017-85887-C2-2-P, and by the Comunidad Autónoma de Madrid, project number S2013ICE-2933_02

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 (“efficient”) 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 “quickly” (reasonable run-times), with “high” probability, provable “good” 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

No-regret Dynamics and Fictitious Play

Potential based no-regret dynamics are shown to be related to fictitious play. Roughly, these are epsilon-best reply dynamics where epsilon is the maximal regret, which vanishes with time. This allows for alternative and sometimes much shorter proofs of known results on convergence of no-regret dynamics to the set of Nash equilibria

A modular hybrid simulation framework for complex manufacturing system design

For complex manufacturing systems, the current hybrid Agent-Based Modelling and Discrete Event Simulation (ABM–DES) frameworks are limited to component and system levels of representation and present a degree of static complexity to study optimal resource planning. To address these limitations, a modular hybrid simulation framework for complex manufacturing system design is presented. A manufacturing system with highly regulated and manual handling processes, composed of multiple repeating modules, is considered. In this framework, the concept of modular hybrid ABM–DES technique is introduced to demonstrate a novel simulation method using a dynamic system of parallel multi-agent discrete events. In this context, to create a modular model, the stochastic finite dynamical system is extended to allow the description of discrete event states inside the agent for manufacturing repeating modules (meso level). Moreover, dynamic complexity regarding uncertain processing time and resources is considered. This framework guides the user step-by-step through the system design and modular hybrid model. A real case study in the cell and gene therapy industry is conducted to test the validity of the framework. The simulation results are compared against the data from the studied case; excellent agreement with 1.038% error margin is found in terms of the company performance. The optimal resource planning and the uncertainty of the processing time for manufacturing phases (exo level), in the presence of dynamic complexity is calculated