A guided search non-dominated sorting genetic algorithm for the multi-objective university course timetabling problem

Copyright @ Springer-Verlag Berlin Heidelberg 2011.The university course timetabling problem is a typical combinatorial optimization problem. This paper tackles the multi-objective university course timetabling problem (MOUCTP) and proposes a guided search non-dominated sorting genetic algorithm to solve the MOUCTP. The proposed algorithm integrates a guided search technique, which uses a memory to store useful information extracted from previous good solutions to guide the generation of new solutions, and two local search schemes to enhance its performance for the MOUCTP. The experimental results based on a set of test problems show that the proposed algorithm is efficient for solving the MOUCTP

A simplex-like search method for bi-objective optimization

We describe a new algorithm for bi-objective optimization, similar to the Nelder Mead simplex algorithm, widely used for single objective optimization. For diferentiable bi-objective functions on a continuous search space, internal Pareto optima occur where the two gradient vectors point in opposite directions. So such optima may be located by minimizing the cosine of the angle between these vectors. This requires a complex rather than a simplex, so we term the technique the \cosine seeking complex". An extra beneft of this approach is that a successful search identifes the direction of the effcient curve of Pareto points, expediting further searches. Results are presented for some standard test functions. The method presented is quite complicated and space considerations here preclude complete details. We hope to publish a fuller description in another place

A nature-inspired multi-objective optimisation strategy based on a new reduced space searching algorithm for the design of alloy steels

In this paper, a salient search and optimisation algorithm based on a new reduced space searching strategy, is presented. This algorithm originates from an idea which relates to a simple experience when humans search for an optimal solution to a ‘real-life’ problem, i.e. when humans search for a candidate solution given a certain objective, a large area tends to be scanned first; should one succeed in finding clues in relation to the predefined objective, then the search space is greatly reduced for a more detailed search. Furthermore, this new algorithm is extended to the multi-objective optimisation case. Simulation results of optimising some challenging benchmark problems suggest that both the proposed single objective and multi-objective optimisation algorithms outperform some of the other well-known Evolutionary Algorithms (EAs). The proposed algorithms are further applied successfully to the optimal design problem of alloy steels, which aims at determining the optimal heat treatment regime and the required weight percentages for chemical composites to obtain the desired mechanical properties of steel hence minimising production costs and achieving the overarching aim of ‘right-first-time production’ of metals

Visualising the Landscape of Multi-Objective Problems using Local Optima Networks

This is the author accepted manuscript. The final version is available from ACM via the DOI in this recordThe codebase for this paper is available at https://github.com/fieldsend/mo_lonsLocal optima networks (LONs) represent the landscape of optimisation problems. In a LON, graph vertices represent local optima in the search domain, their radii the basin sizes, and directed edges between vertices the ability to transit from one basin to another (with the edge width denoting how easy this is). Recently, a network construction approach inspired by LONs has been proposed for multi-objective problems which uses an undirected graph, representing mutually non-dominating solutions and neighbouring links, but not basin sizes. In contrast, here we introduce two formulations for multi/many-objective problems which are analogous to the traditional LON, using dominance-based hill-climbing to characterise the search domain. Each vertex represents a set of locally optimal solutions, with basins and ease of transition between them shown. These LONs vary depending on whether a point-based (dominance neutral optima) or set-based (Pareto local optima) representation is used to define mode construction. We illustrate these alternative formulations on some illustrative problems.We discuss some of the underlying computational issues in constructing LONs in a multiobjective as opposed to uni-objective problem domain, along with the inherent issue of neutrality — as each a vertex in these graphs almost invariably represents a set in our proposed constructs.Engineering and Physical Sciences Research Council (EPSRC

A hybrid model for multi-objective capacitated facility location network design problem

One of the primary concerns on many traditional capacitated facility location/network problems is to consider transportation and setup facilities in one single objective function. This simple assumption may lead to misleading solutions since the cost of transportation is normally considered for a short period time and, obviously, the higher cost of setting up the facilities may reduce the importance of the transportation cost/network. In this paper, we introduce capacitated facility location/network design problem (CFLNDP) with two separate objective functions in forms of multi-objective with limited capacity. The proposed model is solved using a new hybrid algorithm where there are two stages. In the first stage, locations of facilities and design of fundamental network are determined and in the second stage demands are allocated to the facilities. The resulted multi-objective problem is solved using Lexicography method for a well-known example from the literature with 21 node instances. We study the behaviour of the resulted problem under different scenarios in order to gain insight into the behaviour of the model in response to changes in key problem parameters

Optimal dynamic operations scheduling for small-scale satellites

A satellite's operations schedule is crafted based on each subsystem/payload operational needs, while taking into account the available resources on-board. A number of operating modes are carefully designed, each one with a different operations plan that can serve emergency cases, reduced functionality cases, the nominal case, the end of mission case and so on. During the mission span, should any operations planning amendments arise, a new schedule needs to be manually developed and uplinked to the satellite during a communications' window. The current operations planning techniques over a reduced number of solutions while approaching operations scheduling in a rigid manner. Given the complexity of a satellite as a system as well as the numerous restrictions and uncertainties imposed by both environmental and technical parameters, optimising the operations scheduling in an automated fashion can over a flexible approach while enhancing the mission robustness. In this paper we present Opt-OS (Optimised Operations Scheduler), a tool loosely based on the Ant Colony System algorithm, which can solve the Dynamic Operations Scheduling Problem (DOSP). The DOSP is treated as a single-objective multiple constraint discrete optimisation problem, where the objective is to maximise the useful operation time per subsystem on-board while respecting a set of constraints such as the feasible operation timeslot per payload or maintaining the power consumption below a specific threshold. Given basic mission inputs such as the Keplerian elements of the satellite's orbit, its launch date as well as the individual subsystems' power consumption and useful operation periods, Opt-OS outputs the optimal ON/OFF state per subsystem per orbital time step, keeping each subsystem's useful operation time to a maximum while ensuring that constraints such as the power availability threshold are never violated. Opt-OS can provide the flexibility needed for designing an optimal operations schedule on the spot throughout any mission phase as well as the ability to automatically schedule operations in case of emergency. Furthermore, Opt-OS can be used in conjunction with multi-objective optimisation tools for performing full system optimisation. Based on the optimal operations schedule, subsystem design parameters are being optimised in order to achieve the maximal usage of the satellite while keeping its mass minimal

Increasing the density of available pareto optimal solutions

The set of available multi-objective optimization algorithms continues to grow. This fact can be partially attributed to their widespread use and applicability. However this increase also suggests several issues remain to be addressed satisfactorily. One such issue is the diversity and the number of solutions available to the decision maker (DM). Even for algorithms very well suited for a particular problem, it is difficult - mainly due to the computational cost - to use a population large enough to ensure the likelihood of obtaining a solution close to the DMs preferences. In this paper we present a novel methodology that produces additional Pareto optimal solutions from a Pareto optimal set obtained at the end run of any multi-objective optimization algorithm. This method, which we refer to as Pareto estimation, is tested against a set of 2 and 3-objective test problems and a 3-objective portfolio optimization problem to illustrate its’ utility for a real-world problem

Representations of molecules and materials for interpolation of quantum-mechanical simulations via machine learning

Computational study of molecules and materials from first principles is a cornerstone of physics, chemistry and materials science, but limited by the cost of accurate and precise simulations. In settings involving many simulations, machine learning can reduce these costs, sometimes by orders of magnitude, by interpolating between reference simulations. This requires representations that describe any molecule or material and support interpolation. We review, discuss and benchmark state-of-the-art representations and relations between them, including smooth overlap of atomic positions, many-body tensor representation, and symmetry functions. For this, we use a unified mathematical framework based on many-body functions, group averaging and tensor products, and compare energy predictions for organic molecules, binary alloys and Al-Ga-In sesquioxides in numerical experiments controlled for data distribution, regression method and hyper-parameter optimization