Novel Baeyer–Villiger-type oxidation of 4,5-epoxymorphinan derivatives

Article abstract of DOI:10.1016/j.tetlet.2020.152714

A novel molecular oxygen-mediated Baeyer–Villiger-type oxidation specific to the morphinan skeleton has been discovered. The reaction of a ketone bearing a bicyclo[2.2.2]octenone skeleton with KOH (pellet) in refluxing tBuOH under an oxygen atmosphere (balloon) afforded unexpected cyclopropanecarboxylic acid and ketolactone derivatives. The reactive sites (carboxylic acid and ester) in those products are oriented over the C-ring in the morphinan skeleton, and thus such morphinan compounds would be useful intermediates to design ideal κ opioid receptor agonists.

Full text of DOI:10.1016/j.tetlet.2020.152714

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Procedia Engineering 186 (2017) 349 – 356
XVIII International Conference on Water Distribution Systems Analysis, WDSA2016
A System for Optimal Design of Pressure
Constrained Branched Piped Water Networks
a
b
N. Hooda , O. Damani *
a, b
Department of Computer Science and Engineering,
Indian Institute of Technology Bombay, Mumbai, India
Abstract
Rural water networks in the developing world are typically branched networks with a single water source. The main design decision
to be made for such networks is the choice of pipe diameters from a discrete set of commercially available pipe diameters. Larger
the pipe diameters, better the service (pressure), but higher is the capital cost. In general, each link (connection between two nodes)
in the network can consist of several pipe segments of differing diameters. For such networks, existing design tools solve the
constrained-optimization problem heuristically [1] [2]. In [3], an ILP formulation is proposed for the special case of one pipe
diameter per link. This means that currently one can either get an optimal solution for the special case of one piped segment per
link or get a non-optimal solution for the general case of multiple pipe segments per link. In this work, we come up with a model
that solves the general formulation while still maintaining optimality. Our model has an LP formulation. It not only manages to
optimally solve the general case, it also has a runtime performance that is better than both the heuristic approach to the general
problem as well as the optimal approach to the specific problem (one pipe per link). To aid the designers of piped water networks,
we have developed an optimization system called JalTantra that implements this model. It also has GIS functionality integrated for
ease of providing network details. It is publicly available at http://www.cse.iitb.ac.in/jaltantra/ .
©
©2 20 01 16 6T Th eh Ae uA t hu ot hr so .r Ps .u bP lui sbh l ei sd h be yd Eb lys e Ev li se er vL i ted r. LT ht di s. is an open access article under the CC BY-NC-ND license
(
Ph tet ep r: /- / rc er ve ai et iwv e uc on md emr or ne ss .po or gn /sl ii cb ei ln i st ye s o/ bf y t-hn ec - on rd g/ 4a n. 0i /z) i. ng committee of the XVIII International Conference on Water Distribution
PSe ye sr -t re emv ise .w under responsibility of the organizing committee of the XVIII International Conference on Water Distribution Systems
Keywords: Water distribution network; Network cost optimization; Linear program
*
Corresponding author. Tel.: +91-93230-03401.
E-mail address: damani@cse.iitb.ac.in
1877-7058 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of the organizing committee of the XVIII International Conference on Water Distribution Systems
doi:10.1016/j.proeng.2017.03.211

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N. Hooda and O. Damani / Procedia Engineering 186 (2017) 349 – 356
1
. Introduction
Piped water network cost optimization has been studied for more than 30 years now. Several constrained
optimization techniques from Linear Programming [4] to Genetic Algorithms [13] have been employed to solve
various variations of the cost optimization problem. In this work, we focus on the cost optimization of rural piped
water networks. These networks are typically gravity fed, since reliable electricity supply is not a given. Pumps are
deployed only at the water source and not in the rest of the distribution network. Acyclic (branched) networks are
common since the redundancy provided by cyclic (looped) networks is an unaffordable luxury.
One of the most important aspects in the design of these systems is the choice of pipe diameters from a discrete set
of commercially available pipe diameters. In general, each link (connection between two nodes) can consist of several
pipe segments of differing diameters. The larger the pipe diameters, the better the service (pressure), but the higher
is the capital cost. The branched piped water network cost optimization problem is the selection of pipe diameters that
minimize the system cost while providing the requisite service (pressure at demand points).
BRANCH [1] is an optimization tool by the World Bank that attempts to minimize pipe cost for branched pipe
networks with a single water source. Though it has limited capabilities in terms of number of pipes (at most 125), and
does not guarantee optimal solution, it is used ([11], [14], [15]) in the developing world as the only alternatives are
expensive commercial tools like WATERGEMS [2]. Even WATERGEMS does not guarantee optimal solution since
it uses a genetic algorithm.
In [3], an ILP formulation is proposed for the special case of one pipe diameter per link. This means that currently
one can either get an optimal solution for the special case of one piped segment per link [3] or get a non-optimal
solution for the general case of multiple pipe segments per link [1], [2]. In this work, our aim is to come up with a
formulation that solves the general formulation while still maintaining optimality.
For the general problem, in addition to the user provided pressure and flow related constraints, following additional
constraint is inferred from [5]: in the optimal solution, each link consists of at most two pipe segments of adjacent
diameters from the available diameter set. We take two approaches to the multiple pipes per link formulation. In the
first approach, we use the fact that the optimal solution will contain at most two pipe segments per link [5]. In the
other approach, we make no assumption on the number of pipe segments per link. Surprisingly, the latter formulation’s
runtime performance is much better than the former. But knowing the structure of the optimal solution and trying to
capture that as a constraint led to a much worse runtime performance! The second formulation solves the problem
optimally and efficiently. Its solution indeed only contains at most two pipe diameters for each link in the network.
The structure that we were trying to enforce for the first formulation has come out naturally in the second.
Using the general formulation we have implemented a water network design system called JalTantra. The system
also has GIS integration for ease of adding network details. The overall goal for JalTantra is wide reaching and will
attempt to solve several network design constraints like source selection, storage location/capacity, choice of pipe
diameters, water supply scheduling, cost allocation etc. The scope of the present study is restricted to determining the
pipe diameters in a single source acyclic (branched) network.
The rest of the paper is structured as follows. Section 2 describes the problem formulation. Section 3 is a brief
description of the environment used to build the JalTantra system. Section 4 describes the comparison results of the
different models on six different networks. Conclusions and future work directions are presented in Section 5.
Nomenclature
O(.)
NL
The total pipe cost which is a function of the pipe diameters chosen for each link
The number of links in the network
D
i
Pipe diameter for the link i
L
i
Length of link i
C
i
Cost per unit length of link i, a function of the pipe diameter D
i
NP
Number of commercially available pipe diameters
th
th
x
ij
boolean variable, 1 if the i link uses the j diameter, 0 otherwise
The minimum pressure that must be maintained at node n
The head supplied by the reference node R
Pn
H
R

N. Hooda and O. Damani / Procedia Engineering 186 (2017) 349 – 356
351
E
n
The elevation of node n
S
HLij
n
Set of pipes that connect node n to the reference node R
Headloss in link i due to diameter j
2
. Problem Formulation
.1. Problem Definition
The typical rural piped water network consists of a source MBR (mass balancing reservoir), demand nodes, and
2
pipes connecting them. If required, pumps are used to supply water from a water body to the MBR which then feeds
the remaining network by gravity. A gravity fed network has its MBR located at a higher elevation so that no pumping
is required for the downstream network. An example network is shown in Figure 1. It consists of 5 nodes and 4 links.
Node 1 is the source for the network, and nodes 2, 4 and 5 are the demand points. Node 3 is a zero demand node. Such
nodes are typically introduced at intermediate points of high elevation.
Fig. 1. Gen_5 network
Nodes in the network have water demands and minimum pressure requirements that must be maintained. The
design process involves selecting the diameters for the pipes that must be used to supply these nodes. Lower the
diameter, lower is the cost of the pipes. But lower diameters cause higher friction losses in the pipes which may lead
to insufficient pressures at the demand nodes. Therefore the optimization goal is to minimize pipe cost under the
constraint of minimum pressure requirements at the demand nodes. The choice of diameter is to be made from a
discrete set of commercial pipe diameters that are available.
Rural piped water networks are typically branched (acyclic) as compared to urban networks which are frequently
looped. In our present study we restrict ourselves to single source acyclic piped water networks. Since the network is
acyclic, flow in each link can be computed easily from the node demands. The pumping from source to MBR is not
considered. Instead we assume a source that is able to maintain the supply of water at the given head (head at a point
is the height to which water naturally rises. The pressure at a point is the difference between its head and elevation.).
Formally, we are solving the following optimization problem:
x Input: Source node<head>, Nodes<elevation, water demand, minimum pressure requirement>, Link<start/end
node, length>, Commercial pipe diameter<cost per unit length, roughness>
x Output: Length and diameter of pipe segments for each link
x Objective: Minimize total pipe cost
x Constraints:
○
○
○
Pressure at each node must exceed minimum pressure specified
Water demand must be met at each node
Pipe diameters can only take values from provided commercial pipe diameters
2
.2. One Pipe Per Link
[
3] has an Integer Linear Programming (ILP) formulation for the problem where only one pipe diameter is used
per link. It uses binary variables to represent the choice of commercial pipe to be made for each link. Henceforth we
use the term OnePipe model while referring to this formulation.

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N. Hooda and O. Damani / Procedia Engineering 186 (2017) 349 – 356
2
.2.1. The Objective Function:
The objective function to be minimized is the total cost of the pipes chosen for the links in the network. The
diameters D can only be chosen from the set of available commercial pipe diameters. This restriction is represented
i
via binary variables xij. The objective function is:
ே
௅ ே௉
ܱ
ሺǤ ሻ ൌꢀ෍ ෍ ܮ ܥ ሺܦ ሻݔ
௜ ௜௝ ௜௝ ௜௝
௜
ୀଵ ௝ୀଵ
2
.2.2. Pipe constraint:
For each link the objective function has terms for each of the available commercial pipe diameters. Since each link
is to be installed with only one diameter, it means that exactly one of the binary variables corresponding to each link
must be one. Therefore we get the following pipe constraint for each link i:
ே
௉
෍
ݔ௜௝ ൌ ͳ
௝
ୀଵ
2
.2.3. Node constraint:
At each node a minimum amount of pressure needs to be maintained. The pressure at any node is calculated from
the headloss in the pipes connecting the node to the reference node i.e. the source for the network. We use the Hazen-
Williams formula for headloss. Therefore the pressure constraint for each node n is:
ே
௉
ܲ
௡
൑ꢀܪെ ܧ െꢀ ෍ ෍ ܮܪ ݔ
ோ ௡ ௜௝ ௜௝
௜
אௌ೙ ௝ୀଵ
ଵǤ଼ହଶ
݂
݈ݓ݋௜
ͳͲǤ͸ͺ כ ܮ כ
௜
ݑ݋ݎ݄݃݊݁ݏݏ௝
ܪܮ௜௝
ൌ
ସǤ଼଻
݀
݅ܽ݉݁ݐ݁ݎ௝
2
.3. Two Pipes Per Link
The previous formulation assumes a single pipe diameter for each link in the network. But this might not be (and
usually isn’t) the optimal solution. In the most general case, we could have several pipes of varying diameters for a
single link in the network. In [5] it is shown that in the optimal solution each link will consist of at most two pipe
segments of adjacent diameters. The above will hold if the commercial pipe cost is a convex function of a power of
its diameter, which is the case in practice. To incorporate this knowledge about optimal solution structure we modify
the objective function, as given next.
2
.3.1. The Objective Function:
To generalize the formulation in order to account for multiple pipes per link we introduce two new continuous
variables for each link: li1 and li2. The previous boolean variable representing the choice of commercial pipe for each
link is now broken into two: xij1 and xij2. Here li1/ li2 represent the length of the two pipes for link i and xij1/ xij2 represent
the choice of diameters for the two pipes. The modified objective function is:
ே
௅ ே௉
ܱ
ሺǤ ሻ ൌꢀ෍ ෍ ܥ௜௝ଵ൫ܦ௜௝ଵ൯݈ ݔ ൅ ܥ௜௝ଶሺܦ௜௝ଶሻ݈ ݔ
௜ଵ ௜௝ଵ ௜ଶ ௜௝ଶ
௜
ୀଵ ௝ୀଵ

N. Hooda and O. Damani / Procedia Engineering 186 (2017) 349 – 356
353
This formulation is not linear since we have products like li1 * xij1 both of whose terms are variables. We linearize
this equation by introducing zij1
:
ݖ௜௝ଵ ൌ ݈ ݔ
௜ଵ ௜௝ଵ
This nonlinear equality is represented by the following set of linear inequalities:
ݖ௜௝ଵ ൑ ܮ௜ݔ௜௝ଵ ݖ௜௝ଵ ൑ ݈௜ଵ, ݖ௜௝ଵ ൒ ݈௜ଵ െ ꢀܮ ሺͳ െ ݔ௜௝ଵሻ
,
௜
A similar set of inequalities will be introduced for zij2 as well. This linearization is possible since z is a product of
a continuous variable and a boolean variable. Our new objective function:
ே
௅ ே௉
ܱ
ሺǤ ሻ ൌꢀ෍ ෍ ܥ௜௝ଵ൫ܦ௜௝ଵ൯ݖ௜௝ଵ ൅ ܥ௜௝ଶሺܦ௜௝ଶሻݖ௜௝ଶ
௜
ୀଵ ௝ୀଵ
2
.3.2. Pipe Constraint
As before, the choice of pipe diameter must be made from the available commercial pipe diameters.
ே
௉
෍
ݔ௜௝ଵ ൌ ͳ
௝
ୀଵ
Similar equalities hold for xij2. We also have following additional constraint for each link i.
݈௜ଵ ൅ꢀ݈௜ଶ ൌ ܮ௜
2
.3.3. Node Constraint
The node constraint for minimum pressure requirement now changes since length of each pipe segment is no longer
a constant. The node constraint in each link i now becomes: (possible since HLij is linear in the length of the pipe)
ே
௉
ܲ
௡
൑ꢀܪെ ܧ െꢀ ෍ ෍ ܮܪԢ ሺݖ ൅ ݖ௜௝ଶሻꢀ
ோ
௡
௜௝ ௜௝ଵ
௜
אௌ೙ ௝ୀଵ
ଵǤ଼ହଶ
݂
݈ݓ݋௜
ͳͲǤ͸ͺ כ
ݑ݋ݎ݄݃݊݁ݏݏ௝
ܪܮԢ௜௝
ൌ
ସǤ଼଻
݀
݅ܽ݉݁ݐ݁ݎ௝
2
.3.4. Performance
On testing the new formulation, the runtime performance is found to be very poor. Whereas for the OnePipe model
a 100 node network can be solved in 1.5 seconds, the new formulation cannot solve optimally even a 10 node network
before getting timed out at 100 seconds.
The reason for this is the large number of new constraints that are added to the system. Previously all constraints
were linear in the number of nodes. We had only one constraint for each link and one for each node (for an acyclic
network number of links is one less than the number of nodes). But now, in order to introduce zij1 and zij2, we have
introduced 6 new constraints for each (link, pipe diameter) combination.

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N. Hooda and O. Damani / Procedia Engineering 186 (2017) 349 – 356
2
.4. Proposed Model
In the previous formulation to introduce multiple pipes per link, we determine the lengths of the two pipes in the
link and independently assign a commercial pipe diameter to each. This causes a blowup in the number of constraints.
To overcome this, we ignore the two pipe segment structure and model each link as being made up of pipes for
each possible commercial pipe diameter. All that remains is to determine the length of each component. No explicit
choice is made as to which pipe diameter is chosen. The pipe component is chosen if it has non-zero length.
We introduce continuous variables lij and do away with the binary choice variables xij. Each link is made up of NP
components corresponding to the NP pipe diameters. lij then represents the length of each of these components.
2
2
2
.4.1. The Objective Function:
We replace the terms l *xij with lij in our objective cost:
i
ே
௅ ே௉
ܱ
ሺǤ ሻ ൌꢀ෍ ෍ ܥ ሺܦ ሻ݈
௜௝ ௜௝ ௜௝
௜
ୀଵ ௝ୀଵ
.4.2. Pipe constraint:
Now the pipe constraint simply reduces to:
ே
௉
෍ ݈௜ ൌ ܮ௜
௝
௝
ୀଵ
.4.3. Node constraint:
i
In the node constraint we replace xij * L with lij:
ே
௉
ܲ
௡
൑ꢀܪെ ܧ െꢀ ෍ ෍ ܮܪԢ ݈ ꢀ
ோ ௡ ௜௝ ௜௝
௜
אௌ೙ ௝ୀଵ
We now have a more general formulation for our pipe diameter optimization problem. If the necessary convexity
conditions [5] are met, our solution should naturally contain only two pipes per link with adjacent diameters.
As in the case of OnePipe the number of constraints is linear in the number of nodes and the performance turns out
to be much better. Table 1 shows the size of model in terms of variables and constraints for the two approaches.
Table 1: Model Size (m is the number of pipe diameters which is taken as 10)
Two Pipe Approach
General Approach
Node
N
Constraints
6n + 8nm
860
Variables
Constraints
Variables
2n + 4nm
420
2n
nm
1
1
0
20
200
2000
00
8600
4200
200
For a 100 node network we have around 200 inequalities for the general formulation. But for the two-pipe model,
a network with just 10 nodes the number of constraints is around 800! Also by eliminating binary variables and
replacing them with continuous variables we have converted what is an Integer Linear Program (ILP) to a Linear
Program (LP). While ILPs are NP hard [12], LPs can be solved in Polynomial time [6]. This is very significant since
we are able to solve the LP formulation of a 1000 node network in two seconds even though it contains 2000
constraints.

N. Hooda and O. Damani / Procedia Engineering 186 (2017) 349 – 356
355
3
. JalTantra System Description
The above model has been implemented in the JalTantra system. The implementation is done using Java 7 [9] and
GLPK 4.55 [8] Linear Program Solver. Java ILP 1.2a [10] is used as the Java interface to the GLPK library. It also
uses Google Maps API [7] for GIS functionality which allows the user to easily mark the network details as well as
extract information like node elevation and pipe lengths. A sample use case is shown in figure 2 below. The system
is freely available at http://www.cse.iitb.ac.in/jaltantra.
Fig. 2. GIS feature in JalTantra
4
. Results
We have tested the OnePipe, our proposed model as well as BRANCH over six different networks. Three of these
are real world examples from villages of Thane district in Maharashtra, India. The other three networks are artificially
generated to test the system performance over a range of network sizes. Both the OnePipe model and the proposed
model are tested using the GLPK LP solver library. A timeout of 100 seconds is used. If the timeout period elapses,
the solver outputs the best feasible result found so far rather than the global optimum.
Table 2 presents the performance in terms of objective cost as well as running time of the three methods over all 6
test networks. For the Gen_100 network, BRANCH terminated with a memory overflow message. Since the stated
maximum number of nodes is 125, the Gen_1000 network is not run on BRANCH.
The time taken by both the OnePipe model and our proposed model is less than half a second for the first four
networks. But the ILP vs. LP nature is borne out for the two larger networks. In fact, for the Gen_1000 the OnePipe
model also gets timed out.
Being optimal, our proposed model indeed outperforms both BRANCH and the OnePipe model for all six networks
in terms of objective cost. Both BRANCH and our proposed model use a more general formulation and hence better
cost results are to be expected. Our model performs better than BRANCH since we use a LP formulation that is solved
optimally whereas BRANCH uses a heuristic approach. In fact, for two of the first four networks even the OnePipe
model performs better than BRANCH.
Table 2: Comparison of Performance over all six networks

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N. Hooda and O. Damani / Procedia Engineering 186 (2017) 349 – 356
BRANCH
Cost
1000 Rs)
OnePipe Model
Cost
Proposed Model
Network
Number of
Nodes
Time
(msec)
119380
34878
4207
1105
-
Time
(msec)
429
Cost
Time
(msec)
387
(
(1000 Rs)
24,317
(1000 Rs)
24,181
28,895
21,184
1949
Mokhada
Shahpur
Khardi
37
24,652
29,082
21,281
1958
-
21
29,523
356
318
11
21,267
256
247
Gen_5
5
2020
243
228
Gen_100
Gen_1000
100
1000
93,718
1531
Timeout
90,512
5,62,564
628
-
-
5,80,578
2023
5
. Conclusions
For the cost optimization of piped water networks, we have presented a general formulation that is optimal as well
as faster than both the previous formulations for the specific problem of one pipe segment per link, and the heuristic
approach used in available software. In the process, we found that, quite counter-intuitively, modeling of inferred
constraints that capture the structure of the optimal solution worsens the runtime performance. We have implemented
our solution in a water network design system JalTantra. JalTantra also has GIS integration for ease of adding network
details to the optimization engine.
Reservoir costs are an important component of the capital cost of a piped water network. Reservoir locations and
elevations are currently inputs to the optimizer. But these can also be made variables and be part of the optimization
problem by adding the reservoir costs to the objective function and adding relevant constraints relating to allocation
of nodes to reservoirs.
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