Slawomir Wesolkowski

DMEA: a direction-based multiobjective evolutionary algorithm

A novel direction-based multi-objective evolutionary algorithm (DMEA) is proposed, in which a population evolves over time along some directions of improvement. We distinguish two types of direction: (1) the convergence direction between a non-dominated solution (stored in an archive) and a dominated solution from the current population; and, (2) the spread direction between two non-dominated solutions in the archive. At each generation, these directions are used to perturb the current parental population from which offspring are produced. The combined population of offspring and archived solutions forms the basis for the creation of both the next-generation archive and parental pools. The rule governing the formation of the next-generation parental pool is as follows: the first half is populated by non-dominated solutions whose spread is aided by a niching criterion applied in the decision space. The second half is filled with both non-dominated and dominated solutions from the sorted remainder of the combined population. The selection of non-dominated solutions for the next-generation archive is also assisted by a mechanism, in which neighborhoods of rays in objective space serve as niches. These rays originate from the current estimate of the Pareto optimal front’s (POF’s) ideal point and emit randomly into the hyperquadrant that contains the current POF estimate. Experiments on two well-known benchmark sets, namely ZDT and DTLZ have been carried out to investigate the performance and the behavior of the DMEA. We validated its performance by comparing it with four well-known existing algorithms. With respect to convergence and spread performance, DMEA turns out to be very competitive.

A Review of the Use of Computational Intelligence in the Design of Military Surveillance Networks

This chapter is a review of how computational intelligence methods have been used to help design various types of sensor networks. We examine wireless sensor networks, fixed sensor networks, mobile ad hoc networks and cellular networks. The goal of this review is to describe the state of the art in using computational intelligence methods for sensor network design, to identify current research challenges and suggest possible future research directions.

A dominance-based stability measure for multi-objective evolutionary algorithms

Over the years, we have been applying multi-objective evolutionary algorithms (MOEAs) to a number of real-world problems. solving multi-objective optimization problems (MOPs) in the real world faces a number of challenges including when to terminate the algorithm. This paper addresses this challenge by introducing what we call a “stability measure”. We use this measure to estimate when to stop the multi-objective evolutionary search.

Multi-objective evolutionary optimization of a military air transportation fleet mix with the flexibility objective

The Non-dominated Sorting Genetic Algorithm-II is applied to a multi-objective air transportation fleet-mix problem for finding flexible fleet mixes. The Stochastic Fleet Estimation model, which is Monte Carlo-based, is used to determine average annual requirements that a fleet must meet. We search for Pareto-optimal combinations of platform-to-task assignments that can be used to complete stochastically generated scenarios. Solutions are evaluated using three objectives, with a goal of maximizing flexibility in accomplishing each task within its closure time, and minimizing fleet cost and total task duration. Optimization over all three objectives found very flexible low cost fleets, which were not discovered using previous two-objective and three-objective optimizations.

Evaluating the Flexibility of Military Air Mobility Fleets

The ability of an organization to perform some critical military tasks in a timely manner may depend on the availability of a sufficient number of appropriate vehicles. Therefore, the decision of which is the best military fleet-mix for a given set of requirements should take into consideration, in addition to cost, the ability of the fleet to perform tasks when some of its vehicles are unavailable. In this paper, a measure of the flexibility of military air mobility fleets is presented that evaluates their ability to perform tasks in a timely manner taking into account the possibility that some aircraft in the fleet may be unavailable at any given time. This measure computes the number of aircraft that must be unavailable in order to render a fleet incapable of performing each task in a timely manner. The utility of the flexibility measure is demonstrated by using it as an objective in a multiobjective optimization framework to compute nondominated fleets with respect to cost and flexibility. An artificial data set that is representative of real military air mobility data is used to illustrate how the new flexibility measure may be used to aid decision makers with their fleet mix problems.

TraDE: Training device selection via multi-objective optimization

Training planning is a recurring military problem. Since training programs can utilize multiple training devices with varying costs and training capabilities, selecting the types of devices required is a complex trade-off problem. Furthermore, the placement of these devices is critical due to the time and costs involved in travelling to and from the location of a training device. In this paper, we introduce a device bin-packing-and-location-based model, Training Device Estimation (TraDE), to study the computation of heterogeneous device mixes including the location of each device with respect to numerous objectives including various costs and training time. We apply the multi-objective Non-dominating Sorting Genetic Algorithm II to the TraDE model on a population represented by two-dimensional chromosomes. Finally, we also present a new mutation type to handle the nonlinearity inherent in a dual optimization problem which includes scheduling and location optimization. We clearly show that the new mutation operator produces superior results to the standard mutation operator.

The Tyche And Safe Models: Comparing Two Military Force Structure Analysis Simulations.

In the past, several force structure analyses have been conducted for the Canadian Armed Forces using moderate fidelity (e.g., Tyche) and low-fidelity (e.g. Stochastic Fleet Estimation or SaFE) simulation models within optimization frameworks. Monte Carlo discrete event simulations like Tyche are computationally expensive and can only be used in optimizations that require few force structure evaluations. The SaFE model acts as a simple surrogate model that can be utilized by more global optimization techniques. SaFE, originally developed to study air mobility fleets, was adapted to accommodate a larger set of capabilities and more scheduling heuristics so that the performance of many force structures can be quickly assessed while minimizing a set of objectives. The amount of time required to find the SaFE optimal force structures is significantly less than using Tyche. This indicates that SaFE could be an important tool for discovering paretooptimal force structures (within the space of all possible mixes) that would represent practical lower bounds on the force structure requirements for accomplishing expected future scenarios. The purpose of this paper is to compare and contrast the use of Tyche and SaFE through simulation optimizations on a given dataset.

Multi-objective optimization of the fleet mix problem using the SaFER model

One of the most important tasks for an organization which transports cargo and people is the determination of number and type of platforms which will be needed. Due to the presence of multiple conflicting objectives, such as cost and performance, this problem may be considered multi-objective. In order to estimate the fleet that can fulfill the scenario requirements, the Stochastic Fleet Estimation - Robust (SaFER) model was previously developed. It uses scheduling heuristics and optimization. However, using the SaFER model within a multi-objective optimization framework is not computationally feasible; therefore, a surrogate model is proposed in this paper to approximate SaFER for use in the fitness evaluations of schedule cost objectives. An artificial military air mobility dataset is used to demonstrate the increase in speed of the surrogate model over SaFER, and the accuracy of the surrogate model in estimating schedule costs versus SaFER.

SaFESST: Stochastic Fleet Estimation under Steady State Tasking via evolutionary fleet scheduling

Militaries involved in transportation of people and cargo need to be able to assess which tasks they can or cannot do given a specified fleet of heterogeneous platforms (such as vehicles or aircraft). We introduce the Stochastic Fleet Estimation under Steady State Tasking (SaFESST) model to determine which tasks will not be achievable. SaFESST is a bin-packing model which uses a fleet configuration (the assignment of specific platforms to each of the tasks) to fit each task from a scenario within the platform bins (the height of the bin represents the number of platforms). Each individual platform is represented by a strip of scenario length which is packed by sub-tasks it can carry out. SaFESST is run on a set of 10,000 scenarios for a single fleet configuration. Results are reported on various statistics of tasks that are unachievable.

Estimating force mix lower bounds using a multi-objective evolutionary algorithm

Nations will always experience conflicting pressures to reduce both (i) the funding of militaries and (ii) the probability that they will not be able to respond to scenarios that may arise. We develop a multiobjective evolutionary algorithm (MOEA) to generate force mix options that trade-off between lower bounds for objective (i) versus objective (ii). A set of military assets or force mix is evaluated against multiple instances of the future, each composed of a mix of stochastically generated realistic scenarios based on historically derived parameters. Scenario success is evaluated by matching each occurrence with a course of action (CoA) whose force element (FE) demands can be met. The lower bound on (i) comes from the assumption that a nation has complete flexibility to engage in scenarios at times that minimize simultaneous demand on FEs. The results are compared with the results from Tyche, a discrete event Simulator, which provides an more realistic, though pessimistic, point estimate of objective (ii). Results confirm the expected relative behavior of both models.